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Spin-lattice relaxation : a probe for molecular geometry and motion in solution Wong, Kim Fah 1979

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SPIN-LATTICE RELAXATION: A PROBE FOR MOLECULAR GEOMETRY AND MOTION IN SOLUTION by KIM FAH(WONG B.Sc. (Hons.), Univers ity of Malaya, 1972 M.Sc , University of Malaya, 1975 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Chemistry) We accept th i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March, 1979 © Kim Fah Wong, 1979 In presenting th i s thesis in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers ity of B r i t i s h Columbia, I agree that the Library shal l make i t f ree ly avai lable for reference and study. I further agree that permission for extensive copying of th i s thesis for scholar ly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publ icat ion of th i s thesis for f inanc ia l gain shal l not be allowed without my written permission. n 4 . 4 . Chemistry Department of , i The Univers ity of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date Apr i l 10, 1979 ABSTRACT The relevant theory and experimental protocol whereby proton sp in-l a t t i c e relaxation rates (R-j-values) can be used to assign quant ita- t i v e l y the geometry of molecules in solut ion are described. It i s shown that proton R-j-values can provide an accurate measure of so lut ion geometry for r i g i d molecules which have well dispersed proton n.m.r. spectra, and for which the interproton distances do not span an excessive range. The method i s based on ident i f y ing the magnitudes of s p e c i f i c , d ipole-dipole interproton relaxat ion contributions (p-values) from measured i n i t i a l slope proton R-j-values. These p-values can be obtained from either (a) a combination of non-select ive, s ing le -se l ec t i ve , double-selective and t r i p l e - s e l e c t i v e pulse experiments, or (b) se lect ive deuteration. The interproton distances (r) can then be e x p l i c i t l y calculated v ia the dipole-dipole formalism (P « r " 6 ) . The interproton distances between the three bicycloheptene r ing protons of 1,2,3,4,7,7-hexachloro-6-0-exo-benzoyl-bicyc1o[2.2.1]hept-2-ene (J_), determined by method (a), were in excel lent agreement with those obtained from computer simulation and Dreiding molecular models. I n i t i a l s lope, non-selective Revalues for the protons of 1,2,3,4-tetra-O-trideuterioacetyl-B-rj-arabinopyranose (2_), i t s 5,5-dideuterio-(3) and both isomeric 5-deuterio-derivatives (;4,5_) were determined at 400 MHz. Simple intercomparisons between these data {method (b)} gave p-values, from which interproton distances were ca lcu lated; these values were in very close agreement with those obtained by neutron - i i i -d i f f r a c t i o n . Method (a) was also used to evaluate the p-values for 2; these data were es sent ia l l y the same as those obtained by (b). The qual i ty control experiments necessary for quant itat ive con-formational analysis are i l l u s t r a t e d . These includes (a) a p ract ica l de f i n i t i on of an i n i t i a l slope R-j-value, (b) an evaluation of the extent of d ipole-dipole relaxat ion contr ibut ions, and (c) the use of carbon-13 R-j-values to detect the presence or absence of anisotropic motion. It i s demonstrated that a combination of non-selective and s ing le - se lect i ve relaxat ion experiments provides quant itat ive informa-t ion concerning the v a l i d i t y of the i n i t i a l slope approximation and the extent to which each proton is relaxed v ia the dipole-dipole mechanism. A comprehensive evaluation of the a p p l i c a b i l i t y and l i m i t a -t ion of carbon-13 R-j-values along with deuterium Revalues as "probes" for molecular motion i s also presented. F i n a l l y , preliminary surveys of the appl icat ion of the method to systems having substantial anisotropic motion, systems having complex, second order spectra, and systems with conformational time-averaging are given to place the methodology into chemical contexts which were not a p r i o r i designed to be optimized for the approach described herein. - i v -TABLE OF CONTENTS CHAPTER 1 INTRODUCTION 1 CHAPTER 2 DIPOLAR SPIN-LATTICE RELAXATION IN COUPLED SPIN SYSTEM: THEORETICAL CONSIDERATION AND PRACTICAL FORMULATION 13 2.1 Introduction 13 2.2 General Formulation 20 2.3 Intramolecular Dipole-Dipole Interaction 25 2.4 Evaluation of Spectral Densities and Molecular Motions 31 2.5 Cross-correlat ion Effects 37 2.6 Evaluation of P-JJ and TJJ Terms 37 2.7 Contributions to p* Terms 39 2.8 Spin-Latt ice Relaxation: Effects of Non-Selective Pulses 40 2.9 Spin-Latt ice Relaxation: Effects of S ingle-Selective Pulses 42 2.10 Spin-Latt ice Relaxation: Effects of Double-Selective Pulses 46 2.11 Spin-Latt ice Relaxation: Effects of T r i p l e -Select ive Pulses 50 2.12 Determination of Internuclear Distances 51 2.13 Carbon-13 Spin-Latt ice Relaxation: A Probe fo r Molecular Rotational Motion 52 2.14 Tightly Scalar Coupled Spin Systems 56 CHAPTER 3 QUANTITATIVE DETERMINATION OF INTERPROTON DISTANCES FOR DIAMAGNETIC MOLECULES IN SOLUTION VIA THE MEASUREMENT OF SELECTIVE PROTON SPIN-LATTICE RELAXATION RATES 60 3.1 Introduction 60 3.2 Spin-Latt ice Relaxation Measurements 63 3.3 The I n i t i a l Slope Approximation 72 3.4 The Overall Extent of Dipole-Dipole Relaxation .. 78 3.5 Evaluation of Interproton Relaxation Contributions, p ^ - va lue s 79 3.6 Tumbling Motion of ]_ : Carbon-13 Spin-Latt ice Relaxation 82 3.7 Evaluation of Interproton Distances 87 3.8 Dynamic Range of the Method 91 3.9 Transient Nuclear Overhauser Enhancement 93 3.9.1 S ingle-Select ive Pulse 93 3.9.2 Double-Selective Pulse 95 3.10 Conclusion 101 - V -CHAPTER 4 PROTON SPIN-LATTICE RELAXATION RATES MEASURED AT 400 MHz: A QUANTITATIVE DETERMINATION OF THE GEOMETRY OF DIAMAGNETIC MOLECULES IN SOLUTION 102 4.1 Introduction 102 4.2 Evaluation of P-jj-values from Deuteration Experiment 109 4.3 Proof of Isotropic Motion 114 4.4 Evaluation of Interproton Distances 117 4.5 S ingle-Select ive Pulse and Proof of Dipole-Dipole Mechanism 120 4.6 Evaluation of p-jj-values v ia Double-Selective Pulse Measurements 122 4.7 Evaluation of p-jj-values v ia T r ip le -Se lect i ve Pulse Measurements 126 4.8 Dynamic Range Limitat ion 130 4.9 Deuterium-induced Proton Chemical Shi fts 130 4.10 Conclusion 133 CHAPTER 5 STUDIES OF MOLECULAR ROTATIONAL DIFFUSION OF CARBOHYDRATES IN SOLUTION 135 5.1 Introduction 135 5.2 General Theory I: Carbon-13 Spin-Latt ice Relaxation and Molecular Reorientation 137 5.3 Results and Discussion I: Carbon-13 Spin-Latt ice Relaxation 146 5.4 General Theory II: Deuterium Spin-Latt ice Relaxation and Molecular Motion 194 5.5 Results and Discussion II: Deuterium Spin-Latt ice Relaxation 195 5.6 Conclusion 202 CHAPTER 6 APPLICATIONS OF SELECTIVE AND NON-SELECTIVE PROTON SPIN-LATTICE RELAXATION RATES 204 6.1 Introduction 204 6.2 Phenyl Derivatives 204 6.3 Glucopyranose Derivatives 221 6.4 A Sucrose Derivative 235 CHAPTER 7 A PRELIMINARY EVALUATION OF THE DETERMINATION OF THE AGLYCON-SUGAR, PROTON RELAXATION CONTRI-BUTIONS OF GLYCOSIDES, INCLUDING DISACCHARIDES, BY SPECIFIC DEUTERATION 245 7.1 Introduction 245 7.2 Results and Discussion 246 7.3 Conclusion 257 - v i -CHAPTER 8 SUMMARY 258 CHAPTER 9 EXPERIMENTAL 261 9.1 N.M.R. Measurements 261 9.2 Error Analysis 270 9.3 N.M.R. Sample Preparations 271 9.4 Sources of Materials 272 REFERENCES 281 APPENDIX I TWO-PULSE INVERSION-RECOVERY SEQUENCE FOR DETERMINATION OF REVALUES 287 APPENDIX II PROGRAM "NEWCART" 288 - v i i -LIST OF TABLES CHAPTER 2 2.1 Eigenstate Bases for the AMX Spin System 20 CHAPTER 3 3.1 Spin-Latt ice Relaxation Rates of 1_ in Deuterio-benzene Solution 70 3.2 Averaged Values of the Spin-Latt ice Relaxation Rates for 1 74 3.3 Interproton Relaxation Contributions 80 3.4 Calculated Values for the Fractional Inter-proton Relaxation Contributions for 1_ 81 3.5 Carbon-13 Relaxation Rates and Nuclear Overhauser Enhancement Factors for Those Carbons of 1_ Which Bear Hydrogen Substituents 83 3.6 Ratios of the Interproton Distances for H- l , H-2 and H-3 of 1_ from Various Sources 88 3.7 Interproton Distances Between H- l , H,2 and H-3 of 1 90 CHAPTER 4 4.1 Chemical Sh i f ts and Coupling Constants Data for the Protons of Compound 2 Measured at 400 MHz ... 108 4.2 Non-Selective Spin-Latt ice Relaxation Rates for Compounds 2 to 5 Measured at 400 MHz 109 4.3 The P^ -va lue s where i = 1 to 5a or 5e and j = 5a and 5e for Compound 2_ 112 4.4 Pij - v a l u e s for { i,j} = {1 to 4} Calculated from Compound 3_ 114 4.5 Carbon-13 n.m.r. Parameters for 115 4.6 The C-H Bond Lengths for Compound 2_ from Neutron D i f f rac t ion Measurement 116 4.7 The Ratio of Interproton Distances for Compound 2 118 - vi i i -4.8 4.9 4.10 4.11 4.12 4.13 4.14 CHAPTER 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Comparison of Interproton Distances for Compound 2_ as Obtained from Proton R]-values and from Neutron D i f f rac t i on Measurements 119 Double-Selective Revalues for Some of the Protons of 2 122 The p-jj-values Calculated from the Double-Selective Pulse Experiment for Compound 2_ 124 The Tr ip le -Se lect i ve Spin-Latt ice Relaxation Rates for H-2, H-3 and H-4 of Compound 2 127 The Pi --values for H-2, H-3 and H-4 of Compound 2 Calculated from eqs. [4.10] 129 Deuterium Isotope-Induced Proton Chemical Shi fts for Compound 3_, 4 and 5_ Measured at 400 MHz 132 Comparison of Deuterium Isotope-Induced Chemical Shifts of Proton-i and the Internuclear Separations Between Proton-i and the Deuteron ... 134 Carbon-13 Chemical Sh i f t s , Spin-Latt ice Relaxa-t ion Rates and ^3C-{TH> Nuclear Overhauser Enhancement Factors for Monosaccharides 150 Carbon-13 Chemical Sh i f t s , Spin-Latt ice Relaxation Rates and 1 3 C-{ H> Nuclear Overhauser Enhancement Factors fo r 1,4-Linked and 1,1-Linked Disaccharides 152 Carbon-13 Chemical Sh i f t s , Spin-Latt ice Relaxation Rates and ' 3 C-{ lH) Nuclear Overhauser Enhancement Factors for 1,6-Linked Disaccharides 154 Carbon-13 Chemical Sh i f t s , Spin-Latt ice Relaxation Rates and 13c- {"IH } Nuclear Overhauser Enhancement Factors for Lac t i t o l and Ma l t i t o l 156 Average Carbon-13 R-|-values for Monosaccharides . 163 Average Carbon-13 Ri-values for 1,4-Linked Disaccharides 164 Average Carbon-13 Revalues for 1,6-Linked Disaccharides 165 - i x -5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 5.18 5.19 CHAPTER 6 6.1 6.2 Average Carbon-13 Revalues for Lac t i to l and Ma l t i t o l ! 166 The Deviations from the Mean R-|-values for the Ring Carbons of Some Monosaccharides 168 Comparison of C-H Bond Lengths from Neutron D i f f rac t i on Data 170 Calculated Rotational Diffus ion Constants and the Corresponding Correlat ion Times for Some Carbohydrate Derivatives 180 Comparison of a/b Values Derived from Carbon-13 R]-values and Those Obtained by Simple Geometrical Calculations 181 Carbon-13 Chemical Shifts and Spin-Latt ice Relaxation Rates for Mono- and Di-Saccharides in DMS0-d6 186 Rotational Diffus ion Constants and the Corresponding Correlat ion Times 188 Ratios of (Ri-values in DMS0)/(Ri-values in D20) for Compounds 7, 10. and 1l_ 190 Deuterium Chemical Shi fts and Spin-Latt ice Relaxation Rates for Compounds 23_ and 24 199 Carbon-13 Spin-Latt ice Relaxation Rates for Compounds 25^  and 26_ 201 Deuterium Quadrupolar Coupling Constants for Compounds 23 and 24 202 Calculated Rotational Correlat ion Times and the Corresponding Rotational Diffus ion Constants for Compounds 23 and 24^  203 Proton Relaxation Rates for Compounds 27_ and 28_ . 205 Carbon-13 Chemical Shi fts and Relaxation Rates, and 13C-{1H) n.O.e. Factors fo r the Carbons Bearing Hydrogen Substituents in Compound 27_ 208 6.3 The Observed Change in the Chemical Shi fts of the Protons of 27_ as a Function of Its Concentration in Deuteriobenzene 210 - x -6.4 Calculated P-j.-values for Compounds 27 and 28 ... 211 6.5 Measured and Calculated i^g/^g Values f ° r Compounds 27 and 28 213 6.6 The Calculated Intramolecular Interproton Dis-tances for H-5 and H-6 of Compounds 27_ and 28 ... 216 6.7 Proton R-j-values of Compounds 30 and 3J_ 224 6.8 Calculated P-J ^ -values for H-l and H-5 of Compounds 30 and 3J_ 229 6.9 Calculated Interproton Relaxation Contribu-tions for Compounds 30 and 31_ 231 6.10 Interproton Distances for 30 and 3J_ 232 6.11 The Carbon-13 Spin-Latt ice Relaxation Rates and Chemical Shi fts for Compound 32_ 240 CHAPTER 7 7.1 Spin-Latt ice Relaxation Rates for the Anomeric Protons of Methyl D-glucopyranosides 249 7.2 Calculated Values for the Relaxation Contr i -butions to the Anomeric Proton from the Methyl Protons 249 7.3 Non-Selective Spin-Latt ice Relaxation Rates for the Protons of Methyl Tetra-0-trideuterioacetyl-D-glucopyranosides 251 7.4 Non-Selective Spin-Latt ice Relaxation Rates for the Anomeric Protons of Disaccharides 255 APPENDIX II II.1 Parameter L i s t i ng for Program NEWCART 289 - x i -LIST OF FIGURES CHAPTER 1 1.1 Values of proton s p i n - l a t t i c e relaxation rates for alkenes 7 1.2 Sp in - l a t t i ce relaxat ion rates for the anomeric protons of some pyranose sugars 8 CHAPTER 2 2.1 Diagrammatic representation of a three-spin system to i l l u s t r a t e the difference between cross-relaxation and cross -corre lat ion between the spins 19 2.2 Interlevel t rans i t i on rates between the eigen-states of the longitudinal component of the spin operators for the AMX spin system 21 2.3 Comparison between the e f fect of a 10% error in an experimentally determined P j j / P - j k value versus the resultant error in the calculated r i k / r i j v a 1 u e 5 3 2.4 Plot of the ra t i o of interproton distances as a function of the inverse ra t i o of interproton dipolar relaxation contributions for a molecule which i s tumbling i s o t r op i ca l l y 54 2.5 Plot of R A(ns)/R A(A) versus J/5 fo r a two-spin system to demonstrate the e f fect of t ight coupling on determination of R-j -values 57 2.6 Plot of RJ(ns)/RJ(?) as a function of W - J T - J . fo r the d ipolar in teract ion of two sp in-1/2 nuclei i and j 58 CHAPTER 3 3.1 Proton n.m.r. spectrum (100 MHz) of ]_ 61 3.2 Pa r t i a l 100 MHz proton n.m.r. spectra of 1_, showing a two-pulse non-selective invers ion-recovery determination of the s p i n - l a t t i c e relaxation rates of H- l , H-2 and H-3 65 - xi i -3.3 Pa r t i a l 100 MHz proton n.m.r. spectra of 1_, showing the s ing le - se lect i ve determination of the s p i n - l a t t i c e relaxation rate of H-2 using a two-pulse inversion-recovery sequence ... 67 3.4 Par t i a l proton n.m.r. spectra of 1_, showing the se lect ive determination of the se lec-t i ve relaxat ion rates of the H-l and H-3 resonances 68 3.5 Semi logarithmic plots of [M-j (°°)-M1 ( t ) ] versus " l i t t l e t " for the H-l resonance Of 1 75 3.6 Semi logarithmic plots of [M- (°=)-Mi (t)]/M-j («>) versus t/T-|(ns) for the most rapidly and the most slowly relaxing protons of 1_ 76 3.7 Carbon-13 n.m.r. (20 MHz) spectrum of 1 84 3.8 The symmetric e l l i p s o i d a l representation of the tumbling motion of 1_ 86 3.9 Diagrammatic representation of the inverse s i x th power dependence of d ipolar interproton interact ion on interproton distances 92 3.10 Changes in i n tens i t i e s of H-l and H-3 of compound 1_ as a resu l t of a se lect ive 180° pulse applied to H-2 94 3.11 The same curves as i n F ig . 3.10 with t extended to larger values 95 3.12 The changes in the i n tens i t i e s of H-2 and H-3 of compound 1_ as a resu l t of a se lect ive 180° pulse applied to H-l 96 3.13 The changes in the i n tens i t i e s of H-l and H-2 as a resu l t of a se lect ive 180° pulse applied to H-3 97 3.14 The change in in tens i ty of H-2 as a resu l t of a se lect ive 180° pulse applied simultaneously to H-l and H-3 98 3.15 The change in intens i ty of H-3 as a resu l t of a se lect ive 180° pulse applied simultane-ously to H-l and H-2 99 3.16 The change in intens i ty of H-l as a result of a se lect ive 180° pulse applied simultaneously to H-2 and H-3 100 - xi i i -CHAPTER 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 CHAPTER 5 5.1 5.2 5.3 100 MHz proton n.m.r spectrum of 2_ 104 400 MHz n.m.r. spectra of (a) 2, (b) 3, and (c) 4 and 5 105 400 MHz " 'H n.m.r. spectrum of 2_ with resolut ion enhancement to show the long-range sp in-spin couplings 106 400 MHz ^H n.m.r. spectra of 3^ , 4 and 5_ to show long-range spin-spin couplings and deuterium-induced i sotopic sh i f t s 107 P a r t i a l l y relaxed ^H n.m.r. spectra (400 MHz) of 2 depicting the inversion-recovery sequence of measuring non-selective Revalues ... 110 The non-selective Revalues of 3_ 113 The v i c i na l 1 H- 1 H couplings of 2 120 Proton n.m.r. spectrum (400 MHz) of 2_ showing the se lect ive inversion of the H-l t rans i t ions .. 121 These spectra show the double-selective inversion of (a) H- l , H-2; (b) H- l , H-3; and (c) H-5a, H-5e of compound 2 at 400 MHz 123 Proton n.m.r. spectrum (400 MHz) of 2 showing the se lect ive inversion of the H-2, H-3 and H-4 t rans i t ions 128 P lot of some representative rat ios of i n t e r -proton distances versus the inverse rat ios of interproton relaxat ion contributions for compound 2 showing the "dynamic range" of d ipolar interact ion 131 Calculated carbon-13 R-| rat ios as a function of the tumbling or spinning 141 Plot of D||/Dj_ versus e(C-He) for methyl B-D-lactoside 143 Plot of the r a t i o D||/Dj_ versus b/a for a r i g i d e l l i p s o i d a l body rotat ing in a viscous medium 145 - x iv -5.4 Proton-decoupled 20 MHz carbon-13 n.m.r. spectra of methyl B-D-lactoside with and without 1 3C-{" 1H) n.OT-e 147 5.5 1 3 C-{ 1 H} O.e. measurement for C-l and C-T of Compound 1_3 148 5.6 P a r t i a l l y relaxed 20 MHz carbon-13 n.m.r. spectra of methyl B-JJ-lactoside showing use of the two-pulse inversion-recovery sequence for measurement of s p i n - l a t t i c e relaxat ion rates 149 5.7 Proton-decoupled 20 MHz carbon-13 n.m.r. spectra of (a) D-glucopyranose, (b) D_-ga1 actopyranose, (c) metfiyl a-D-galactopyranoside, and (d) methyl B-D-galactopyFanoside 157 5.8 Proton-decoupled 20 MHz carbon-13 n.m.r. spectra of a series of 1,4-linked disaccharides and a 1,1-linked disaccharide 158 5.9 Proton-decoupled 20 MHz carbon-13 n.m.r. spectra of a series of 1,6-1 inked disaccharides 160 5.10 Proton-decoupled 20 MHz carbon-13 n.m.r. spectra of (a) 6-0_-(B-D-glucopyranosyl-D-galactopyranose and (b) 6-0_- (B^p_-glucopyranosyl7-£-galacto-pyranose-6,6-d2 _ ~ 161 5.11 Proton-decoupled 20 MHz carbon-13 n.m.r. spectra (a) l a c t i t o l and (b) ma l t i t o l 162 5.12 P lot of percent enhancement in carbon-13 R-j-values as a function of percent shortening i n a C-H bond 169 5.13 A diagrammatic representation of the posit ions of the molecule-fixed pr inc ipa l axes of methyl 0-D-lactoside 172 5.14 The two types of rotamer about the C- l ' -0-4-C-4 b lycos id ic centre of a disaccharide 175 5.15 Plots of D||/Dj_ versus e(C-He) for a - lactose and methyl B-D-lactoside 179 5.16 Diagrammatic representation of intramolecular hydrogen-bonds for methyl B -D-cel lobios ide 184 5.17 Carbon-13 n.m.r. spectra of (a) a-D-galacto-pyranose, (b) lactose, and (c) celTobiose in DMS0-dc 187 - XV -5.18 Carbon-13 R-j-values of methyl 3-0- . trideuterioacetyl-4,6-0_-benzyl idene-2-deoxy-a-D-ribo-hexopyranoside 191 5.19 Proton-decoupled carbon-13 n.m.r. spectrum (20 MHz) of methyl 3 -0-t r ideuter ioacety l -4,6-0-benzylidene-2-deoxy-a-D-ribo-hexopyranoside ... 192 5.20 P a r t i a l l y relaxed deuterium n.m.r. spectra (61.42 MHz) of compound 24, depicting the two-pulse inversion-recovery sequence fo r measure-ment s p i n - l a t t i c e relaxation rates 196 5.21 Deuterium n.m.r. spectra (61.42 MHz) of 23 in acetone and benzene 198 CHAPTER 6 6.1 Proton n.m.r. spectrum (100 MHz) of compound 27 . 206 6.2 The calculated interproton distances for 2_7 209 6.3 The calculated distance from the centroid of the methyl protons to H-6 218 6.4 The 100 MHz proton n.m.r. spectra of 29 and 30 .. 222 6.5 The proton n.m.r. spectra (100 MHz) of 30_ and 31_ in deuterioacetone and deuteriobenzene 223 6.6 The conformation of the methyl group of 30 233 6.7 The conformation of the methyl group of 3_]_ 234 6.8 The non-selective Revalues for the protons of 32_ measured at 360 MHz 237 6.9 360 MHz proton n.m.r. spectrum of 32 237 6.10 Values for the v i c i na l proton-proton coupling constants for compound 32_ 243 CHAPTER 7 7.1 The reducing and nonreducing rings of a disaccharide 245 7.2 100 MHz 1 H n.m.r. spectra of methyl B-D-glucopyranoside, showing a two-pulse non-se lect ive inversion-recovery determination of the s p i n - l a t t i c e relaxation rates 247 - xvi -100 MHz H n.m.r. spectra of methyl B-D-glucopyranoside, showing the s ingle-seTective determination of the s p i n - l a t t i c e relaxat ion rate of H-l using a two-pulse invers ion-recovery sequency The 100 MHz proton n.m.r. spectrum of 39 Comparison of spectra obtained v ia the audiomodulation and ta i l o red exc i tat ion methods A diagrammatic representation of the rotat ing reference frame model of a s p i n - l a t t i c e relaxation measurement using a two-pulse inversion-recovery sequence - x v i i -LIST OF FLOW SHEETS CHAPTER 9 1 Synthesis of 6-0- (3-D-glucopyranosyl )-D-galactopyranose-6,6'~d2 T 279 2. Synthesis of 1:2, 3:4-di-0-isopropy1idene-a-D-gal actopyranose-6 ,6 1 -d2 280 - xvi i i -ACKNOWLEDGEMENT I am very grateful to Dr. L.D. Hall fo r his guidance and constant encouragement which have made the work described herein enjoyable and rewarding. While i t i s impossible to thank the many indiv iduals who have helped in the completion of th i s thes i s , I am pa r t i cu l a r l y indebted to the fo l lowing: Dr. H.D.W. H i l l fo r helpful discussions and for pro-viding the prototype apparatus used for the ta i l o red exc i tat ion exper i -ments; Drs. K. Bock, W.E. Hull and W. Schittenhelm who provided various h i gh - f i e l d n.m.r. spectra at a time when su i tab le f a c i l i t i e s were not avai lable at the University of B r i t i s h Columbia; Roland Burton for assistance in computer programming; Dr. J.M. Berry for his help with several syntheses; Dr. J.D. Stevens for providing several s p e c i f i c a l l y deuterated sugars; and to others who kindly provided various samples and whose names are mentioned in the text . F i n a l l y , I g ra te fu l l y acknowledge the award of a Canadian Common-wealth Scholarship for the duration of th i s study. - 1 -CHAPTER 1 INTRODUCTION The aim of th i s thesis i s to document a complete experimental pro-tocol whereby proton s p i n - l a t t i c e relaxat ion rates (Reva lues ) * can be used for determining quant i tat i ve ly the solution geometry of complex organic molecules. The importance of such studies can be appreciated i f one rea l i zes that in p r inc ip le there are only three properties of matter that can be used to measure quant i tat ive ly the geometry of a molecule; these, along with the names of the corresponding techniques in parenthesis, are: 1. D i f f rac t ion (X-ray, neutron, e lect ron) ; 2. Dipolar coupling (magnetic resonance); 3. Moment of i ne r t i a (microwave spectroscopy). Of these, method 2 i s more e f fec t i ve and simpler than e i ther methods 1 and 3 for assigning the geometry of molecules in so lut ion; indeed, for solute molecules dissolved in a f l u i d medium i t i s the only pract ica l approach. D i f f r ac t i on techniques, though the most powerful fo r s o l i d state studies, have an important fundamental l im i t a t i on when applied to studies of l i q u i d s ; Phys ica l ly the process of s p i n - l a t t i c e relaxat ion can be characterized by e i ther a f i r s t order rate constant, R] (in units of s e c " ' ) , or a f i r s t order time constant, T] (in units of sec). Ri = 1/T]. In older l i t e r a t u r e on s p i n - l a t t i c e relaxat ion studies T]-va1ues are frequently reported. In th i s thesis for reasons that w i l l become apparent Revalues w i l l be used and s p i n - l a t t i c e relaxat ion rates, where appropriate, w i l l be hereafter referred to as R-|-values. - 2 -d i f f r a c t i on data represent a one-dimensional quantity, the average of para-meters which, in general, vary with the three dimensions of the system, re l a t i ve or ientat ions within the system, and time. Furthermore, d i f f r a c t i on techniques can only be applied to simple f l u i d systems, and for molecules possessing high i n t r i n s i c symmetry. The determination of molecular structure by microwave spectroscopy i s l imited to molecules that can ex i s t in the vapour phase, and high molecular symmetry i s also a pre-requ i s i te . Dipolar interact ions are manifested in a number of ways.* The one which concerns the present study is the magnetic d ipole-dipole interact ion between protons on the same molecule. Although the importance of magnetic d ipole-dipole interact ion had been recognized in the la te 1940's, i t was the studies of the nuclear Overhauser enhancement (n.O.e) by Anet and Bourn^ in 1965 which f i r s t demonstrated for chemists the considerable diagnostic potential of the intramolecular d ipole-d ipole relaxat ion mechanism of protons for evaluating conformational properties of organic molecules in so lut ion. It was shown that the intramolecular n.O.e. of protons occurring v ia the intramolecular d ipole-d ipole relaxat ion mechanism depends on the inverse s ix th power of the internuclear distances, and hence can be read i ly related to the conformation of a molecule. Since those f i r s t pioneering experiments many other studies, reviewed in deta i l by Noggle and 2 Schirmer , have amply confirmed the chemical u t i l i t y of n.O.e. experiments. * For example, nuclear s p i n - l a t t i c e re laxat ion , nuclear spin-spin re laxat ion, nuclear d ipolar coupling in molecules p a r t i a l l y oriented in a l i q u i d c r y s t a l , electron d ipole-d ipole interact ions , and electron-nuclear i n t e r -action of paramagnetic species. - 3 -Indeed recent developments in pulse Fourier transform (F.t. ) nuclear magnetic resonance (n.m.r.) spectrometers have made such experiments com-p lete ly routine for the chemist. It remains however that many proton-proton ('H-{'H}) n.O.e. exper i -ments lead to results which cannot be eas i l y interpreted. For example, the observation of low enhancement may be due to e i ther one or a combina-t ion of several factors: 1. Large internuclear distances; 2. Fa i lure of the dipole-dipole relaxat ion mechanism; 3. The "three-spin e f f e c t " . 3 ' 4 * C lear ly ambiguities a r i s ing in th i s way could be resolved i f qua l i ty control experiments were avai lable for quant i tat ive ly ident i fy ing spec i f i c i n t e r -proton d ipole-d ipole contr ibut ions; however, these are not eas i l y developed. Since the phenomenon of n.O.e. occurs as a resu l t of nuclear s p i n - l a t t i c e re laxat ion, i t i s obvious that i f i t were possible to measure the R-j-value of indiv idual protons one might be in a more powerful pos it ion to ident i f y spec i f i c interproton d ipole-d ipole relaxat ion contributions and thereby obtain a deeper understanding of n.O.e. experiments; furthermore, relaxat ion measurements might of themselves provide a powerful a l ternat ive to the n.O.e. experiment. The "three-spin e f f ec t " may be regarded as a three-body problem where the presence of a t h i r d spin interferes with the measurement of the n.O.e. between the other two spins such that the apparent n.O.e. i s less than the true value. The three-spin e f fect i s commonly present in mu l t i -spin system and i s a nuisance in 'H-{'H} n.O.e. determination in most organic molecules. - 4 -A consideration of the s impl i f ied version of the d ipole-d ipole mechanism shown in eq. [1 .1]* for two mutually relaxing protons w i l l reveal 2 2.2 i j why the measurement of proton Revalues i s a powerful technique in the determination of spec i f i c interproton dipolar relaxat ion contr ibutions. If proton i receives relaxat ion contributions from several other protons j on the same molecule then eq. [1.1] can be written as Rj °^P.. [1.2a] 1 i i J ? ? ? where Y i Y j P i j = ~J> T i J [1.2b] i j Thus, i d en t i f i c a t i o n of a l l the pairwise interproton relaxat ion contr ibut ion terms, p . . (in units of s e c - 1 ) , for a molecule by fac to r i za t ion from the experimentally measured R^-values could provide a unique method for assigning the molecule's geometry. The determination of p. .-values and the subsequent ca lcu lat ion of interproton distances, and hence solution geometry i s the RJ = R-j-value for spin i Y-j = gyromagnetic r a t i o of spin i (in units of rad sec '^G" 1 ) fi = Planck 's constant divided by 2ir o r^. = internuclear distance between spins i and j (in units of A) T-. = rotat ional cor re lat ion time of the internuclear vector jo in ing spins i and j (in units of sec rad " l ) - 5 -pr inc ipa l objective of the work described here. The theory for d ipole-dipole s p i n - l a t t i c e relaxat ion of Bloembergen, 5 Pu r ce l l , and Pound, often referred to in the l i t e r a t u r e as the BPP theory, was already developed by 1948 and the e x p l i c i t formulation of th i s theory by Solomon^ was given in 1955. Since the publ icat ion of the BPP theory many more elaborate theories on nuclear magnetic relaxation have been developed, re la t ing . re laxat ion rates more e x p l i c i t l y to molecular parameters by various mathematical and physical techniques, examples i n -7-12 13 14 eludes the density matrix formalism, the method of Kubo, ' the 15 16 Fokker-Planck equation, * projection operators, the L i o u v i l l e represen-t a t i o n , ^ ' ^ and the concept of i r r eve r s i b l e thermodynamics J 9 , 2 0 ^ Q mention a few. However, the Bloembergen-Solomon theory i s conceptually rather sa t i s f y ing and considerably more useful to the pract i s ing chemists at large, and i t s appl icat ion in a multipspin system w i l l be discussed in Chapter 2 of th i s thes i s . Unfortunately l i t t l e of the potential of the Bloembergen-Solomon theory was recognized (the exception being the " i n d i r e c t " experiments of Anet and Bourn^) by chemists. Although by the ear ly 1970's experimental methods for measuring Revalues using non- se lect ive pulse techniques were widely ava i lab le i t i s unfortunate that the experimental pulse procedures (pr ior to 1968) lacked the s e l e c t i v i t y which would be required to study molecules with several d i f fe rent sets of magnetic nuc le i . Thus at the experimental level reasons existed for the neglect of proton s p i n - l a t t i c e relaxat ion by the chemist. The two experimental breakthroughs upon which the work of th i s thesis 21 rests came in 1968 with the report by Void et a l . of the non-selective 22 pulse F.t. method, and by Freeman and Wittekoek of the audiomodulation 21 pulse technique. B r i e f l y , the method of Void involves the appl icat ion of - 6 -an intense, non-selective 180° radiofrequency ( r f ) pulse which t ips (nutates)* the magnetization vectors of a l l the d i f fe rent sets of nuclear spins in the system to the -z d i rect ion in the rotat ing frame and the subsequent monitoring of the i r recovery to the +z d i rect ion by a non-se lect ive 90° pulse. The se lect ive pulse technique of Freeman and Witte-22 koek is as fol lows. The magnetization vector of a chosen t rans i t i on ( l ine) is i n i t i a l l y inverted by a weak 180° pulse in the rotat ing frame without perturbing any neighbouring t rans i t ions . At some l a te r time, t , the residual magnetization i s forced into or through the observation (xy) plane by a second 360° pulse. Thus, by 1968 the necessary theory and experimental methodology were both ava i lab le . Even so, the opportunity of combining these to study organic molecules was not widely recognized by chemists for several reasons. For example, i t was not obvious from the theory whether or not i t was possible to define an Revalue for a proton which was scalar coupled as part of a complex spin system. Furthermore, a complete understanding of proton R-j-values would have to take into account the c ros s - re laxat ion * * between d i f fe rent nuclear magnetizations and the c ros s -cor re la t ion * * of or ientat ion of d i f fe rent sp in-pa i r s ; and i t was not c lear that th i s was possible. The nutation ( f l i p ) angle, a , i s defined as a = YB-,T d, where y i s the gyromagnetic ra t i o of the spin and B] and x p are respect ively the strength and duration of the r f pulse. Typ i ca l l y , x p i s in the order of ysec for a non-selective pulse and msec for a se lect ive pulse. ** The meanings of these two terms w i l l be become c lear in Chapter 2; they are not related to each other. - 7 -Nevertheless in 1969, in th i s laboratory, R. Burton and C.W.M. Grant, 22 using a home-built version of the Freeman-Wittekoek audiomodulation spectro-meter measured the proton Revalues of c i s - and trans-alkenes. The results of these measurements, summarized in F ig. 1.1, c l ea r l y demonstrated an Br Br / = C \ H H 17.1 Br >"< H Br 10.5 H 17.1 10.5 Cl CI >=< H H 12.8 12.8 8.7 H CI \ / C = C ^ Cl 8.7 34.7 37.2 11.6 EtO.C CO.Et EtO.C H H H c=c c=c^ / C = C \ H H H CO.Et H OCOMe 80.0 80.0 34.7 27.9 F ig. 1.1 Values of proton s p i n - l a t t i c e relaxation rates in units of 10 sec" l fo r alkenes. The data for 1,2-dibromo- and 1,2-dichloro-ethylenes, and maleic and fumaric acid diethyl esters were determined with a se lec t i ve , audio-pulse spectrometer^ 3 using ^0.5M solut ions. The v iny l acetate data24 w e r e obtained by con-ventional F.t. method on a M3.1M so lut ion. interest ing geometrical dependence of proton Revalues. It i s read i ly seen that in every instance the protons of a c i s isomer relax more rapid ly than those of the trans isomer. A pa r t i c u l a r l y interest ing feature of the proton Revalues of v iny l acetate i s that the sum of the R^-values of the trans and methine protons i s almost-equal to that of the c i s proton, suggesting that the dominant relaxation mechanism involved intramolecular proton i n te r -25 actions. Although measurements were made for a sugar and an a l k a l o i d , further extensions were hindered by the l im i ted frequency s e l e c t i v i t y of the method. - 8 -26 27 In pursuing the potential of proton R e v a l u e s , CM. Preston ' in 1972, using a Varian XL-100 (15) spectrometer and the non-selective pulse 21 28 F.t. technique of Void et a l . and of Freeman and H i l l extended the measurement of proton R e v a l u e s to a number of complex sugar molecules. 27 Her data for a series of pyranose sugars in aqueous solutions are summarized in F ig. 1.2. CH,OH OH 435 OH D-glucopyranose CH,OH OH —o OH D-galactopyranose D-mannopyranose -3 -1 Fig. 1.2 Sp i n - l a t t i c e re laxat ion rates (10 sec ) for the anomeric protons of some pyranose sugars in 0.1M aqueous solutions at 42°C. Note that for each sugar the ax ia l anomeric proton, H- l , of the B anomer relaxes more rap id ly then i t s equatorial counterpart in the a anomer. The data for D-glucopyranose and D-galactopyranose immediately show that H-4 has l i t t l e or no influence on the relaxat ion of the anomeric proton. The difference between the data for D-glucopyranose and D-mannopyranose shows - 9 -that H-2 makes some contr ibtuion to the relaxat ion of H - l , but forces one to conclude that the dominant sources of R-j-dif ferent ia l between the ax ia l and equatorial anomeric protons must be H-3 and H-5, the impl icat ion here * being that H-l i s nearer to H-3 a and H-5 a than i s H-l . Towards the end of her studies CM. Preston with H.D.W. H i l l and R. Jones performed preliminary se lect ive pulse experiments using the " t a i l o red 29 exc i ta t i on " technique of Tomlinson and H i l l in an attempt to quant i tat ive ly ident i f y proton-proton dipolar re laxat ion contr ibutions. Although the study was not pursued to completion, the resu lts indicated a promising area for further invest igat ion. However, i t was also c lear that there were a number of fundamental problems which required solut ion before the approach could be regarded as a quant itat ive method for assigning the geometry of diamagnetic molecules in so lut ion; and th i s provided the main stimulus for the present work. It proved to involve a number of separate challenges. F i r s t , i t was necessary to place on an acceptable theoret ica l basis the de f i n i t i on of an e f fec t i ve Reva lue for a proton which was scalar coupled to a complex spin system - - in th i s regard i t proved possible to re ly on the " i n i t i a l slope * * 30 approximation" previously formulated by Freeman et a l . - - with pa r t i cu la r emphasis on " f i r s t order homonuclear spectra". Second, i t was necessary to evaluate at the experimental leve l the use of se lect ive pulse methods for determining relaxation contributions associated with the d ipole-d ipole * Subscript ' a ' refers to the proton at the axia l posit ion of the pyranose sugar r ing while that of ' e ' refers to the proton at the equatorial pos i t ion. A more detai led discussion on the concept of the " i n i t i a l slope approxi-mation" w i l l be given in Chapter 2. The c r i t e r i on used in th i s thesis for the de f i n i t i on of a " f i r s t order homonuclear spectrum" w i l l be given in Chapter 2, section 2.14. - 10 -mechanism and also the theory of such experiments. Following from th i s i t was of interest to determine with what accuracy R-j-values could give so lu-t ion geometry of molecules. Several other re lated, challenging opportunities also existed. For example, a proper evaluation of the use of se lect ive 31-33 deuteration as a method for measuring interproton relaxat ion contr ibu-tions was in order; th i s w i l l be discussed in Chapter 4. Chapter 2 of th i s thesis w i l l summarize the relevant theory for a l l 5 these experiments. The approach used i s based on the or ig ina l work of BPP and an attempt i s made to give the theory in a form which relates d i r e c t l y to the se lect ive pulse experiments {which are described l a t e r in t h i s thes is (Chapter 3)} and in language which i s d i rected, as far as poss ible, to the pract i s ing chemist rather than the n.m.r. spectroscopist or theoret ic ian. In th i s regard several important r e s t r i c t i on s were f e l t to be acceptable. The theory i s only taken as fa r as the three-spin (1=1/2) f i r s t order homo-nuclear level of the AMX type for several reasons. In the f i r s t place, because the se lect ive pulse experiments can in fact only be applied to f i r s t order spectra. Secondly, because most organic studies tend to involve f i r s t order spectra. F i n a l l y , the three-spin case can be extended r a t i ona l l y to other l inear f i r s t order spectra i f that be necessary. Nevertheless a b r i e f mention of t i g h t l y coupled (nonf irst order) spectra w i l l be given at the end of Chapter 2. Chapter 3 w i l l present a detai led discussion of jus t one molecule; the purpose being to i l l u s t r a t e in a simple three-spin system the operation of the experimental and theoret ica l treatments developed in Chapter 2. In th i s regard two methods for performing se lect ive pulse s p i n - l a t t i c e relaxation measurements and the potential of proton R^-values for assigning molecular geometry, w i l l be i l l u s t r a t e d . - n -Chapter 4 describes a quant i tat ive determination of the solut ion geo-metry of a carbohydrate der ivat ive using non-selective relaxation rates in 31 -33 conjunction with spec i f i c deuteration to i dent i f y the magnitudes of spec i f i c interproton relaxat ion contr ibut ions; the calculated interproton distances are there compared with those obtained for the s o l i d state, using neutron d i f f r a c t i o n . Also, a comparison of the two methods of evaluating p. . -va lues, the se lect ive pulse experiments and the spec i f i c deuteration experiments, w i l l be made in the same chapter. I t w i l l be reca l led from eq. [1.1] that the d ipole-d ipole relaxat ion mechanism includes the motional tumbling* time of the molecule and in Chapter 5 two methods for evaluating th i s important parameter w i l l be described. As w i l l be seen these two methods depend on the measurement of carbon-13 and deuterium Revalues. Although the theory concerning molecular reor ientat ion w i l l be given in Chapter 2, the more pract ica l formulae w i l l be given in Chapter 5. The appl icat ion of the above approach i s further i l l u s t r a t e d in Chapters 6 and 7. Thus Chapter 6 discusses the appl icat ion of non-selective and se lect ive pulse experiments, and the se lect ive deuteration method to organic systems in which anisotropic motion, intermolecular relaxat ion and conforma-t iona l mobi l i ty are present, and demonstrates how p^-values and molecular geometries can be obtained for these systems. Chapter 7 provides another example of the use of the se lect ive deuteration method. F i na l l y Chapter 8 * The term motional cor re lat ion time i s used by the n.m.r. spectroscopist to characterize molecular motion because molecular reor ientat ion i s incor-porated in the re laxat ion rate expressions through cor re lat ion functions which describe the random reor ientat ion of the molecule. However to the chemist molecular motion is better described by the term motional tumbling time because motion is phys ica l ly implied by the word tumbling. wherever i s appropriate, in th i s thes i s , the term tumbling w i l l be used in place of the term cor re la t ion . These two terms w i l l be regarded as equivalent. - 12 -presents an overview of the methodology as now practised in th i s laboratory, and serves as a Summary to th i s thes i s . I t w i l l be noted that most of the molecules studied herein are carbo-hydrates. The interest in sugars i s not accidental - - simply, the wide dispersion of the proton spectra of sugars coupled with the i r defined con-f igurat ions makes them ideal models fo r n.m.r. studies. Furthermore, the importance of these substances in the i r own r i gh t , and as b io log ica l sub-s t rates , ensures that data on t he i r so lut ion geometries f ind wide in teres t . - 13 -CHAPTER 2 DIPOLAR SPIN-LATTICE RELAXATION IN COUPLED SPIN SYSTEMS: THEORETICAL CON-SIDERATION AND PRACTICAL FORMULATION 2.1 Introduction The Hamiltonian for a nuclear spin system in a constant magnetic f i e l d BQ and time-dependent magnetic f i e l d s B n can be written as H(t) = HQ + H^t ) + H y ( t ) [2.1] where HQ represents the usual time-independent spin Hamiltonian including chemical sh i f t s and scalar couplings; H-j(t) represents the time-dependent interact ions with coherent external magnetic f i e l d s ; H^(t) allows for a random perturbation (ar is ing from random molecular motion) which causes 34 35 relaxat ion ' and u spec i f ies the relaxat ion mechanism. 35 Employing the assumption of weak coupling between the spin system and i t s surroundings, the master equation for the density matrix of the spin 8 35 system can be written in the Redfield notation ' as - i D y H ^ t U t t ) ] - r (o ( t ) -a (») ) [2.2] where the re laxat ion term r ( a ( t ) - a ( ° ° ) ) i s given by r ( c a b ( t ) - a a b H ) = - ^ a b c d ( o c d ( t ) - a c d ( - ) ) [2.3] on a nondegenerate eigenstate basis |a>, |b>, etc. , diagonal in H Q; c r ^ t ) i s an element of the density matrix a ( t ) , and o a | 3 ( 0 0 ) i s the Boltzmann equi-l ib r ium value; R a 5 c d i s a re laxat ion element which "couples" the motion of - 14 -o a| 3(t) to that of every other density matrix element. However, the analysis of s p i n - l a t t i c e relaxat ion in scalar coupled spin systems requires a detai led knowledge only of the time evolution of the spin populations, which are given by the diagonal elements of the density matrix operator shown in eq. [2.2]. When the r f perturbation B-| i s applied in the form of a pulse, the Hamiltonian H-j(t) can be omitted in eq. [2.2] and, since H (t)<<HQ ( va l id at f i e l d i n ten s i t i e s normally employed in mag-netic resonance experiments), the diagonal elements of eq. [2.2], in between 34 35 r f pulses, become ' (°aa( t »-°aa(-» kl w ab " J H a b < " ' b b < t ) - 0 b b ( " » ^ where dt a a a a b/a a u bfa W ab = R aabb = f W ^ " ^ [2.5] and Gabab = <a|Hu(t)|b><b|Hy(t+T)|a>* [2.6] Wab = Wba [2.7] k^b i s the in te r leve l t rans i t i on rate between the eigenstates |a> and |b>; G a b a b ^ 1 S t ' i e c o r r e l a t 1 o n function which re lates w"^ to the Hamiltonian causing re laxat ion at frequency u> during the corre lat ion period T ; u> i s defined as oi={E -£^)/i\ where E g represents the energy of the a^*1 level associated with |a>. The bar in eq. [2.6] indicates an ensemble average, which i s the process by which microscopic t rans i t i on p robab i l i t i e s are con-verted to macroscopic t rans i t i on rates. - 15 -Equation [2.4] i s the f ami l i a r master equation for populations N a ( t ) ( = a a a ( t ) ) , j Le . , dN,(t) ' ~?T = (N a ( t ) -N a ( - ) ) l Wab - E W a b (N b ( t ) -N b ( - ) ) [2.8] dt bfa bpa where the a leve l population i s denoted by N,(t) and i t s Boltzmann e q u i l i -a brium value by N («>). The general solut ion to eq. [2.8] for the spin-a l a t t i c e relaxat ion of a t rans i t i on ( l ine) in a n.m.r. spectrum i s given by^ 6 N a ( t ) - N b ( t ) = i {A k (a ) -A k (b ) }e " X k t [2.9] k 1 a = 2 n - l fo r intramolecular interact ion of n spin-1/2 nuc le i , otherwise a has a larger value. The A^'s are determined by the i n i t i a l conditions of the experiment and the X k ' s by the W a b ' s . Thus, i t follows from eq. [2.9] that the general k inet i c equation for the evolution of the longitudinal magneti-zation i s mult iexponential, and the evaluation of the ^ ' s i s numerically very d i f f i c u l t . Although recent progress has been made in reducing the com-putational complexity involved in evaluating eq. [2.9] for weakly coupled 37 38 "simple" heteronuclear spin systems by "normal modes" analys i s , ' s im i la r s imp l i f i c a t i on does not appear to be feas ib le for most proton (homonuclear) spin systems, which at best are only pseudofirst order. Fortunately, Freeman 30 et a l . showed that the i n i t i a l section of the magnetization recovery curve immediately a f te r the perturbing pulse can be approximated by a s ingle rate constant ( i . e . s ingle exponential) in the time interval o to t seconds pro-viding that the condition <Wab " W a / t 2 ~ 1 £2.10] - 16 -holds for a l l b, c f a. This i n i t i a l slope approximation is pa r t i cu l a r l y useful when extended to proton spin systems; at the i n i t i a l slope, an e f fect i ve R-|-value can be defined for a proton that i s scalar coupled as part of a complex spin system. This i n i t i a l rate value i s most conveniently obtained by monitoring the recovery of the tota l longitudinal spectral mag-net izat ion of the proton at the appropriate i n i t i a l slope. As w i l l be seen, the i n i t i a l slope interproton R-j-value so obtained can by i t s e l f provide quant itat ive information concerning the geometry of the molecule under study. An important feature associated with the i n i t i a l slope approximation is that multispin corre lat ion (cross-correlat ion) i s absent in the R e v a l u e which characterizes the i n i t i a l k i ne t i c evolution of the magnetization* of the nuclear spin. The importance of the absence of multispin corre lat ion at the i n i t i a l slope w i l l become apparent further on in the discussion. Of the many s p i n - l a t t i c e relaxat ion mechanisms possible in n.m.r. the most well studied and understood, both theo re t i ca l l y and experimentally, i s the d ipole-d ipole mechanism for spin-1/2 nuc le i . The wide in teres t in d ipole-d ipole interact ions in magnetic relaxat ion studies i s not acc identa l ; i t r e f l ec t s the fact that the s p i n - l a t t i c e relaxation of the two most im-portant and widely occurring magnetic nuclei (protons and carbon-13) generally occurs almost exc lus ive ly v ia th i s mechanism. A unique property of d ipolar relaxat ion i s the inc lus ion of large terms * For convenience the term "magnetization" or "nuclear magnetization" w i l l hereafter be used to mean the " t o t a l longitudinal spectral magnetization" of a nuclear spin as measured by i t s tota l signal i n ten s i t i e s (e.g. see eqs. [2.13] in the next sect ion), unless otherwise stated. - 17 -involving the simultaneous f l i p of two nuclear spins (m=0, ±2 t rans i t i ons * ) and on th i s basis i t can be dist inguished from other re laxat ion mechanisms such as chemical s h i f t anisotropy, sp in-rotat ional and scalar-coupl ing interact ions. This cross-relaxat ion e f fect was f i r s t quant i tat ive ly d i s -6 39 cussed by Solomon ' when he investigated the relaxat ion mechanisms of hydrofluoric ac id . Since th i s c l a s s i c work the occurrence of cross-re laxa-40 41 t ion effects has been well documented by Abragam , Shimizu and Fujiwara , * 42 43 - 44 Mackor and Maclean , Noggle, Hoffman and Forsen, Freeman, Wittekoek 30 45 and Ernst, and Campbell and Freeman, to name but a few. The phenomenon 2 of cross-relaxat ion is c lose ly related to that of n.O.e. and a d i rect quan-t i t a t i v e determination of cross-re laxat ion effects in mult ispin system pro-vides not only an important method of ident i f y ing relaxat ion mechanisms but also information concerning molecular structures and dynamics. A l l these studies on d ipolar cross-relaxations have conveniently been confined to two-spin systems because of t heo re t i ca l , conceptual and technical d i f f i c u l t i e s present in the three or more spin systems; the exception being the ind i rect studies of cross-relaxat ion effects in mult ispin systems v ia n.O.e. measure-ments. Because certa in useful features occur in systems with three or more coupled spins, which are not found in two-spin systems, considerable theo-r e t i c a l and experimental progress has been made recently in the analysis of s p i n - l a t t i c e relaxat ion in complex, mult ispin systems. In par t i cu la r i t i s * The symbol m denotes the net change in spin quantum number involved in a t r an s i t i on . For spin-1/2 nuc le i , m=0,±l,±2 t rans i t ions are commonly ca l led zero-, s ing le- and double-quantum t rans i t i on s , respect ive ly. A s ing le-quantum t rans i t i on involves one spin only whereas the zero- and double-quantum trans i t ions involve two spins at the same time. The m=0,±2 t rans i t ions give r i s e to cross-relaxat ion pathways which provide an e f f i c i e n t mechanism for d ipole-d ipole re laxat ion. - 18 -now possible to analyze in complete deta i l pulse experiments on AX 2 , AX^, AMX, AXY, AB 2 , ABC and AA'BB' spin systems.* One important feature associated with the dipolar relaxat ion of three or more coupled spins which has become apparent as a resu l t of the above studies i s the occurrence of cross -corre lat ion interference terms between d i f fe rent pairwise, intramole-cular dipolar in teract ions ; th i s produces d i f f e r e n t i a l relaxat ion behaviour within the components of a coupled mu l t ip le t . The fac to r i za t i on of cross-cor re lat ion terms from s p i n - l a t t i c e re laxat ion experiments of proton spin systems of most organic molecules i s generally very d i f f i c u l t and, since the pr inc ipa l objective of the work described in th i s thesis i s an experimental study of interproton dipolar cross-relaxat ion effects as geometrical probes, cross-correlat ions w i l l not be considered in any further deta i l here; never-theless where appropriate the existence of cross-corre lat ions w i l l be pointed out. Suff ice i t to say now that the study of cross-correlat ions in homo-nuclear mult ispin systems may well provide an important and rewarding area for future n.m.r. studies. op AC A~7 As described elsewhere ' ' ' and reviewed in deta i l in th i s chapter relaxat ion expressions can be formulated such that c ross -corre lat ion interference effects can be e f f e c t i v e l y compensated for and, with proper experimental design, one can invest igate cross-relaxat ion mechanisms in coupled mult ispin systems d i r e c t l y and quant i tat i ve ly . With regard to the determination of molecular geometries the difference between cross-re laxat ion and cross -corre lat ion terms needs to be pointed out at th i s juncture; th i s i s best i l l u s t r a t e d by a simple example. Consider three spin-1/2 nuclei i , j , k in a r i g i d molecular frame and separated by * For an excel lent discussion on these spin systems see ref. 34. - 19 -F ig. 2.1 Diagramatic representation of a three-spin system used in the text to i l l u s t r a t e the difference between cross-relaxat ion and cross-cor re lat ion between the spins. actions i t depends on the inverse s ix th power of the internuclear distance between the two spins; thus, the d ipolar cross-relaxat ion between spins i and j depends on —-U- . In contrast, cross -corre lat ion occurs between two internuclear re laxat ion vectors; e.g., the cross -corre lat ion ef fect between r t . and rt . in the case of d ipolar interact ion depends on —777- • —-U- and r i j r i k J some function of the angle enclosed by r t j and r t ^ . In the next section of th i s chapter a deta i led derivat ion of the equa-t i on of motion for the nuclear magnetization of the AMX spin system w i l l be given in terms of i n te r l eve l t r an s i t i on rates between the eigenstates so that the effects of cross-re laxat ion in mult ispin systems can be eas i l y con-ceptual ized. Such a descr ipt ion also provides ins ight into the pr inc ipa l features governing mult ispin re laxat ion behaviour as studied by non-selective and se lect ive pulse experiments to be described in deta i l in Chapter 3. These discussions w i l l be confined to pseudofirst order homonuclear spin systems. Towards the end of th i s chapter (in Section 2.14) the effects of - 20 -t i ght scalar coupling on s p i n - l a t t i c e relaxat ion measurements and the c r i t e r i on for pseudofirst order spectra w i l l be given. 2.2 General Formulation The coupled AMX three-spin system* may be discussed in terms of the eignstate bases given in Table 2.1 and the in ter leve l t rans i t i on rates, Table 2.1 Eigenstate Bases fo r the AMX Spin System |a> 1 a > M> | aaa> |5> | 33a> |2> | 6aa> |6> | 3«3> |3> | a(Ba> |7> |aB6> |4> | aa3> |8> I ees> a and 3 are defined as fol lows. For spin-1/2 nuc le i , in units of h, I z |a> = l/2|a>, I z|3> = -1/2|6> , <a|a> <B|3> = 1 and <a|g> = 0. I z i s the longitudinal component of the spin operator taken along the d i rect ion of the Zeeman f i e l d . W ab ' d e f i n e d i n F l 9 - 2 - 2 - E x p l i c i t expressions for the W's w i l l be given in Section 2.3. A comprehensive discussion of the s p i n - l a t t i c e relaxation of coupled f i r s t order heteronuclear three-spin systems of the AIS type O^C, ^ ^F, 'H) i s given by Fagerness et a l . in ref. 47; the treatment given here i s based es sent ia l l y on th i s reference. - 21 -w,x Fig. 2.2 Inter!evel t rans i t i on rates between the eigenstates (given in Table 2.1) of the longitudinal component of the spin operators for the AMX spin system. The in te r leve l t rans i t i on rates, W ' s , are label led with subscripts to indicate both the net change in spin quantum number and the spin, or pair of spins, involved. Thus W J 1 ^ = WJA ; the t rans i t i on rate between levels 1 and 2 involves spirt A only with a net change in spin quantum number by one. Only three faces of the cube are labe l led as the opposite faces have the same t rans i t i on rates. Transit ions (diagonals of the cube) involving a net change in spin quantum number by three are neg l i g ib le and therefore not shown. From the de f i n i t i on of W's i t i s possible to express the time dependent evolution of the population N (t) of level a (a=l,2,...8) in terms of the a fol lowing coupled d i f f e r e n t i a l equations (cf. eq. [2.8]). An appropriate l i nea r transformation of the populations would cast eq. [2.11a] into a form in which the variables may be i den t i f i ed with the fami l i a r experimental - 2 2 -d_ dt i y t ) W l l W 1 A W W 1 X W 2 A M W 2 A X W 2 M X o • N 1 ( t ) - N ] (-) N 2(t) W 1 A w22 W O A M W O A X w i x 0 W 2 M X N 2(t ) - N 2 [-) N 3 ( t ) W 1 M W O A M W w33 W O M X W 1 A 0 w i x W W 2 A X N 3 ( t ) -N 3 [») N4(t) W 1 X W O A X W O M X W 4 4 0 W 1 A W 2 A M N 4 ( t ) -N 4 :-) N 5(t) W 2 A M W 1 M W , A 0 W 5 5 W O M X W O A X W 1 X N 5 ( t ) - N 5 :-) N 6(t) W 2 A X w i x 0 W I A W O M X W W66 W O A M W 1 M N 6(t ) - N 6 N 7(t) W 2 M X 0 w i x w 1 M W O A X W O A M W 7 7 W 1 A N 7 (t ) -N 7 ( -) N 8 ( t ) 0 W 2 M X W 2 A X W 2 A M W 1 X W 1 A W88 N 8(t ) -N 8 ( co) [2.11a] where -W = i W , . aa ^ ab-Wab = Wba [2.11b] [2.11c] quantit ies of magnetizations of the spins. The transformation i s N 1 ( t ) -N 2 ( t )+N 3 ( t ) -N 5 ( t )+N 4 ( t ) -N 6 ( t )+N 7 ( t ) -N 8 ( t ) = (2/y Ah)M A(t) [2.12a] N 1 ( t ) -N 3 ( t )+N 2 ( t ) -N 5 ( t )+N 4 ( t ) -N 7 ( t )+N 6 ( t ) -N 8 ( t ) = (2/v Mh)M M(t) [2.12b] N 1 ( t ) -N 4 ( t )+N 2 ( t ) -N 6 ( t )+N 3 ( t ) -N 7 ( t )+N 5 ( t ) -N 8 ( t ) = (2/y xh)M x(t) [2.12c] where M^, and M^ are the nuclear magnetizations of spins A , M and X, respect ive ly. Experimentally these magnetizations are given by. the tota l signal i n ten s i t i e s sampled by the monitoring pulse according to M A (t) = K A(A 1 + A 2 + A 3 + A 4 ) M M(t) = KM(M 1 + M 2 + M 3 + M4) [2.13a] [2.13b] *See next page. - 23 -M x (t) - K X(X 1 + X 2 + X 3 + X 4 ) [2.13c] where A , M n and X n (n=l...4) are the t rans i t i on l i n e i n ten s i t i e s at time t , and K's are proport iona l i ty constants for the spectrometer response to each of the A, M and X nuclear spin magnetizations. The time dependent evolution of these magnetizations can be eas i l y obtained by combining eqs [2.11] and [2.12]**: where M A(t) PA °AM °AX d dt M M(t) = °AM PM °MX M x (t) _ °AX °MX P X P A : s W2AM + W0AM + W2AX + W0AX °AM = W2AM " W0AM M A ( t ) -M A (») M M (t)-M M (-) M x ( t ) -M x (» ) [2.14] [2.15a] [2.15b] The other four parameters ( p M > p x , a A X » o M X ) can be obtained by appropriate permutation of the subscript spin labels in eqs. [2.15]. Equation [2.14] i s simply the equation of motion for the magnetizations of the A, M, X spins. It i s assumed in eq. [2.14] that cross -corre lat ion * Following Ernst and c o - w o r k e r s , 4 8 ' 4 9 eqs. [2.13] assume that ju s t before the monitoring pulse a l l off-diagonal density matrix elements are neg l i -g ib ly small. This i s probably va l id as long as the monitoring pulse i s applied only after the residual signal fol lowing an imperfect per-turbing pulse has decayed to zero. **continued on next page. - 24 -effects have been compensated for in the terms. The v a l i d i t y of th i s condition w i l l be discussed in Section 2 . 3 . The relaxat ion "matrix" of eq. [ 2 . 1 4 ] i s symmetric and contains two classes of "elements" - - the ** For a t r u l y f i r s t order AMX spin system (e.g. see ref. 47) detai led analysis gives _d dt P A °AM CTAX 6 A " _ M A " M A ( o o ) _ M M CTAM P M °MX 6 M M M - M M H M x °AX CTMX P X 6 X Mx-Mx(.) MAMX _ 6 A 6 M 6 X PA — where 6 A = W 1 A " W 1 A ' pA = W 1 A + W 1M + W i M + W 1 X + W i x MAMX = KA ( A r A 2 - A 3 + A 4 ) = V M i -V M 3 + V = K x ( X r X 2 - X 3 + X 4 ) M A M X ( ^ ) = 0 For a pseudofirst order proton AMX spin system the c ros s -cor re la t ion terms,6 e t c . , do not appear to be simply related to the " v i r t ua l magnetization" M/\MX A S 9 l v e n above. The simple product basis set given in Table 2.1 may have to be redefined to include the small second order e f fec t ar i s ing from the small J/6 (^0.1) value i f one i s to study the cross -corre lat ion e f fec t s . Nevertheless, fo r the present purpose eq. [ 2 . 1 4 ] , which only describes the k inet i c evolutions of the three " rea l magnetizations" MA, MM and Mx of the AMX system, provides an adequate basis for an experimental study of d ipolar cross-re laxat ion mechanisms in a pseudofirst order mult ispin system.50 - 25 -diagonal elements (p. ' s ) which represent the se l f - re l axa t i on terms and the off-diagonal elements ( a ^ ' s ) which are the cross-relaxat ion terms between the appropriate spins. Because the p^ ' s contain m = ±1 t rans i t i on s , they are a measure of nondipolar as well as d ipolar re laxat ion contr ibutions. However the a ^ j ' s are composed only of d ipolar contr ibut ions; hence the determination of o.-'s provides a quant i tat ive measure of those d ipolar terms. The pract ica l impl icat ion of eq. [2.14] i s that the p^ ' s and o.^'s can be separated and evaluated i f one follows the rate of recovery of n.m.r. signals after the spin populations have been prepared in some suitable nonequilibrium d i s t r i bu t i on . Thus the main aims of the rest of th i s chapter are: 1. To derive detai led expressions re la t ing the p^ ' s and C j j ' s to molecular parameters; and 2. To describe the techniques necessary to evaluate the p . ' s and o.. ' s defined in eqs. [2.14] and [2.15]. 2.3 Intramolecular Dipole-Dipole Interaction The d ipolar re laxat ion Hamiltonian H d ( t ) (=H (t) in eq. [2.1]), for an i so lated AMX spin system may be wr itten as the sum of a l l pairwise i n t e r -34 47 actions according to ' H d (t) \ H )m A m ( i , J ) F _ m ( i , J | t ) [2.16a] i , j m=-2 with H ) m A _ m ( i , J ) = A m ( i , j ) [2.16b] and (-1)"F ( i , j | t ) = F_(1,j|t). [2.16c] - 26 -The indices i and j include a l l the nuclear spins in the set {A,M,X} and .E 1 indicates a re s t r i c ted double sum such that each d i s t i n c t pair of spins in the set {A,M,X} i s taken only once. Relaxation pathways span from m=-2 to +2. The A^'s are the spin operators and are related to the f ami l i a r ra i s ing and lowering operators* by A ± 2 ( i , j ) = - I ± ( i ) l ± ( j ) [2.17a] A ± 1 ( i , j ) = ± [ I ± ( 1 ) I z ( j ) + I z ( i ) I ± ( j ) ] [2.17b] A o ( i ' j ) = " , ^ 4 I 2 ( 1 ) I z ( j ) - I + ( i ) I . ( j ) - I _ ( i ) I + ( j ) ] [2.17c] The F 's are the time-dependent l a t t i c e variables defined as ' F m ( i , J | t ) = ( p - ) \ . y . r - 3 . Y 2 > m [ 9 i j ( t ) , * . (t ) ] [2.18] where 9 ^ ( t ) and <^-j(t) are the polar and azimuthal angles which specify the time dependent or ientat ion of the internuclear relaxat ion vector* * r.. " i j * For spin-1/2 nuc le i , I+|a> = I_|3> = 0, I+|e> = |a> and I_ |a> = |3>. a , 3 and I z are defined i n Table 2.1. ** The term " re laxat ion vector" i s commonly used in n.m.r. re laxat ion terminology. Depending on the type of re laxat ion mechanism i t may define the internuclear vector, the pr inc ipa l axis of the e l e c t r i c f i e l d gradient, the pr inc ipa l axis of the chemical s h i f t tensor, or the pr inc ipa l axis of the sp in-rotat ion tensor. Relaxation is induced by the reor ientat ion of th i s vector. A l l molecular motions which leave the relaxat ion vector unaffected do not contribute to the relaxat ion rate. - 27 -between spins i and j re l a t i ve to the laboratory reference frame, and Y~ c., n is a normalized spherical harmonic of rank two. Using eqs. [2.6] and [2.16] the corre lat ion funct ion, G A B A B ( T ) > can be calculated: G a b a b ( x ) = <a|Hd(t)|b><b|Hd(t+x)|a> E' Z z"<aIA (i,j)Ib><b iA _(k,£)|a> i , j k,£ m X F m ( i , j ) F _ m ( k , £ | x ) [2.19] In l iqu ids the variables e^.^(t) and ^ j U ) contained in F m ( i , j | t ) are time dependent due to random molecular reor ientat ion and th i s introduces a random time behaviour into H d ( t ) . It i s generally true that t>>x** such that i t i s safe to assume <a|Hd(t)|b><b|Hd(t+x)|a> i s independent of t but depends only on x , the cor re lat ion period. This i s formalized by dropping t in the expression fo r Fm in eq. [2.19], The normalized spherical harmonics of rank two are defined as: Y 2 > 0 [ e i j ( t ) , ^ . . ( t ) ] = (5/16 1r) J s{3cos 2e...(t)-l} Y 2 , ± l [ 0 i J ( t M i j ( t ) ] = ? ( 1 5 / ^ ) % s i n 6 i j . ( t ) c o s e . j ( t ) e ± i ^ ' J ( t ) Y 2 j ± 2 [ e i j ( t ) , ^ i j ( t ) ] = ( 1 5 / 3 2 T r ) s i n 2 0 i : J ( t ) e ± 2 i ^ i J ( t ) ** t i s the experimental time scale. For example, in the conventional i n -version-recovery pulse experiment,21 180°-t-90°, t i s in the order of sec. However x i s in the order of 10""'"' sec in the case of l i q u i d . Thus, t>>x i s a v a l i d assumption. - 28 -The dipolar relaxat ion rates can be calculated by subst i tut ing eq. [2.19] into eq. [2.5]: = 2 6 k = > i V 1 - J ) i b > < b i ^ 1 ' J ) i a > J i j ! k £ M t 2 - 2 ° ] where J j j ^ (") i s defined as J 1 j ! k * M = 1 / 2 / H ) \ ( 1 . J ) F _ m ( k , £ | T ) e " i w T d T . [2.21] _ oo J J j k i, (co) i s the spectral density* at frequency to a r i s ing from the random reor ientat ion of the internuclear vectors r.. . and r ^ . Thus random mole-cular motion i s incorporated into the relaxat ion rate expressions through the corre lat ion functions which describe the reor ientat ion of the i n te r -nuclear vectors and r^ £. When ij=k£, one obtains the auto-correlat ion spectral density, j i " ^ . . ( to ) . However i f i j ^ k , J - ^ i , 0 ( w ) becomes the cross-cor re la t ion spectral density. Thus, cross -corre lat ion i s expected to be present in system containing more than two interact ing spins. Fortunately, as w i l l be shown, the time evolution of nuclear magnetization i s independent of c ross -corre lat ion e f fec t s . Since the depend e x p l i c i t l y upon i n t e r -nuclear distances and angles, molecular structure and motional behaviour become important factors in the expressions for spectral dens it ies to be given in the next section (Section 2.4). Spectral dens i t ies , J , have been defined in the l i t e r a t u r e in a number of ways using d i f fe rent l im i t s on the time integral and d i f fe rent sign con-ventions. The de f i n i t i on used here i s the same as that employed by workers using the Hubbard-Redfield formulation. Confusion should not ar i se pro-viding consistency of de f i n i t i on i s maintained. - 2 9 -The in te r leve l d ipolar t rans i t i on rates, W ^  appropriate to the AMX system may now be calculated using eq. [ 2 . 2 0 ] . Evaluating the spin matrix elements according to eqs. [ 2 . 1 7 ] , the fol lowing expressions for the i n te r -level t rans i t i on rates (shown on the top face of the cube in Fig. 2 . 2 ) can be obtained: W l 0 , 2 ~= W 1 A = " 2£ JAJW UA> + J A X ! A X ^ A > + 2 J ( A M , A X ^ K A ^ 2 2 a J HI ~= W 1 A = y^rnlrn^. + J A X 1 A X ^ A > " 2 J A M ! A X K > K A ^ 2 2 B J " i f s E W 2 A M = 2 J A M ! A M (*>A+UM> t 2 ' 2 2 ^ 4°}=- W 2 A M = 3°AM!AM ( UA-«M) t 2 - 2 2 d ^ * where to., i s the Larmor precessional frequency of spin i , and includes other random f luctuat ing f i e l d processes (of rank one) that do not corre late with the d ipo lar process. Further comments on these other contributions * to w i l l be given in Section 2 . 7 . Relaxation processes that do corre late with the dipolar one are assumed to be neg l i g ib le in eqs. [ 2 . 2 2 ] . The eight other i n te r leve l t rans i t i on rates shown on the other two faces of the cube in F ig. 2.2 can be expressed by permuting the spin labels in eqs. [ 2 . 2 2 ] . Observe that and contain the cross-corre lat ion spectral density, ^ ^ x ^ A ^ ' b u t W l t ' 1 ° P P o s l t e signs. Since in th i s study and are summed i t i s c lear then that cross -corre lat ion effects are compensated fo r in the p. terms defined in eq. [ 2 . 1 4 ] . - 30 -The relaxat ion rate parameters in eq. [2.14] can now be expressed in terms of the spectral densit ies by using eqs. [2.15] and [2.22]. PA a AM = ^ A M V V 0 ^ + J A M ! A M ( W A } + ^ A M I A M ^ A - V + 2 J A X ! A X ^ X ) - J A X ! A X K ) + 1 / 3 J A S ! A X ( W A - W X > + 2 W 1A t 2 - 2 3 ^ 2 J A M V W A V - 1 / 3 J A S ! A M ( W A ~ ^ L 2 - 2 3 ^ Defining P A M = Z ^ ] m ( ^ ) + JAM1AM<V + ^ A M " V V W M > and p* = 2W* A j [2.25] we have P A = P A M + P A X + P a [2.26] The other expressions for P M , P X , P A X , P M X , a^, am, p^ and p x can be readi ly obtained by permuting the indices. The de f i n i t i on for p ^ given in eq. [2.24] i s ident ica l in form with 6 35 the se l f - re l axa t i on term of the two-spin system. ' Equation [2.26] implies that the se l f - re laxa t ion rate of spin A i s the sum of the pairwise c on t r i -butions from spins M and X. This i s only true when tota l nuclear magneti-zations are considered and when the n.m.r. spectra of the spin system are f i r s t order. The expression for given in eq. [2.23b] i s also ident ica l in form with the cross-relaxat ion term of the two-spin system.^ This correspondence and s i m i l a r i t y between the f i r s t order two- and three-spin systems provides some useful conceptual, as well as p r a c t i c a l , re lat ionships - 31 -between the two systems. For example, the cross-relaxat ion term in the "double-select ive pulse" experiment to be described in Section 2.10 i s i n -dependent of the t h i r d spin - - th i s allows one experimentally to overcome the problem of three-spin e f fect which complicates equivalent n.O.e. studies. Also the unique property of the cross-relaxat ion terms, a..'s, allows one to d ist inguish the dipolar re laxat ion process from the other relaxation mechanisms, a l l of which are included in the p* term. Although a simple expression cannot be written for the p* term, the possible contributions to th i s can be l i s t e d and these are given in Section 2.7. 2.4. Evaluation of Spectral Densities and Molecular Motions The spectral densit ies given by eq. [2.18] can be evaluated according to the relaxat ion model used. Complete expressions for intramolecular d ipolar spectral densit ies for the three cases of spher ica l , symmetric and 38 asymmetric top molecule have been evaluated by Werbelow and Grant. In th i s section the auto-corre lat ion* spectral densit ies in the "extreme narrowing reg ion " * * w i l l be given as these pertain to the studies described 34 38 in th i s thes is . Performing the necessary transformations ' from the laboratory axes to the molecular pr inc ipa l axes in the ensemble averaging of * Expressions for cross -corre lat ion spectral densit ies are given in ref . 38. * * In the "extreme narrowing region or l i m i t " the spectral densit ies are i n - dependent of the Larmor frequency i . e . the frequency of the n.m.r. spectro-meter. - 32 -(-1) F ( i , j ) F_ ( i , j |T) one obtains: i j , i j [2.27] The symbols m and u are now dropped from the de f i n i t i on of J to indicate that i t i s evaluated in the extreme narrowing region. The auto-correlat ion spectral density, J . . .., i s seen to depend on the inverse s ix th power of the internuclear distance (KJ?) and the motional tumbling time ( x . . ) of th i s vector. In order to evaluate eq. [2.27] a physical model to describe the manner by which a molecule tumbles i s required. The simplest and most often used is the rotat ional d i f fus ion model. According to th i s model the molecule tumbles by means of a small-step Brownian d i f fus ion process with many steps required to reor ient by one radian. Since rotat iona l motions occur about some suitable axes in_ the molecule x . . i s expected to depend on i t s symmetry (or shape-factor*). A molecule with cubic symmetry tumbles with equal p robab i l i t y about any molecular pr inc ipa l axis. Such i sot rop ic motion i s characterized by a s ingle rotat ional d i f fus ion constant, D (in units of rad sec - ^) . The i so t rop ic tumbling time is then related to the rotat iona l d i f fus ion constant by To a good approximation, the rotat ional motion of an e l l i p s o i d a l molecule suspended in a f l u i d medium of v i s cos i t y n at temperature T can be (continued on next page) X . 6D [2.28] * - 33 -In molecules of less than cubic symmetry a s ingle d i f fus ion constant i s not s u f f i c i en t to characterize the rotat ional d i f f u s i on . In the general case 53 a rotat ional d i f fus ion tensor (rank two) i s required. Since a rotat ional d i f fu s ion tensor has nine components i t i s common pract ice to describe molecular reor ientat ion in a pr inc ipa l coordinate system such that these nine components are reduced to three independent pr inc ipa l components. This pr inc ipa l coordinate system of the rotat ional d i f fu s ion tensor i s often taken to coincide with that of the moment of i n e r t i a tensor of the molecule. For molecules with s u f f i c i en t symmetry th i s i s true. However, for molecules of low symmetry th i s i s probably not the case because the pr inc ipa l ro ta -t iona l d i f fus ion axes may be ro ta t i ona l l y sh i f ted from the pr inc ipa l i n e r t i a axes by intermolecular interact ions. In th i s thesis the pr inc ipa l axes of the rotat ional d i f fus ion tensor are assumed to coincide with those of the moment of i ne r t i a tensor of the molecule. Thus the tumbling motion of r i g i d molecules of less than ax ia l symmetry (asymmetric tops) can be described in terms of the reor ientat ion of the molecules about the x, y, z pr inc ipa l axes f ixed in the molecular frame. * b I described by the Debye-Stokes-Einstein-Perrin equation in which C-j T. = C.. n/T (i = x, y, z pr inc ipa l axes) depends only on the molecular volume and the shape of the molecule. This simple descr ipt ion of the hydrodynamic behaviour of a molecule in solut ion w i l l be used in th i s thes i s . It i s of interest to note that recent studies (e.g. see ref. 52 and references c i ted therein) include a correct ion T1 = ^Oi + C i ^ term at n = 0 to allow for ef fects such as i ne r t i a and intermolecular cooperative motions. - 34 -The reor ientat ion time about the i pr inc ipa l axis i s related to the corresponding component of the d i f fus ion tensor by x. = l/6D i (i = x, y, z) [2.29] where U^, and D z are the rotat ional d i f fu s ion constants about the x, y, z pr inc ipa l axes of the molecule. In th i s general case the motional corre-54 l a t i on (tumbling) time is given by • J , [ 2 - 3 0 ] where ' = 4D + D + D [2.31a] 1 x y z ' = D + 4D + D [2.31b] 2 x y z X „ = D + D.. + 4D, [2.31c] x y z \ - 6DS + 6(D 2 - L ) 1 / 2 C2.31d] A 5 = 6D S - 6(D 2 - L ) 1 / 2 [2.31e] Dc = (D v + D + D j / 3 [2.32a] S X j £-L = (D xD y + D xD z + D yD z)/3 [2.32b] - 35 -c 1 = 3m 2n 2 [2.33a]* c 2 = 3 l V [2.33b] c 3 = 3£ 2m 2 [2.33c] c 4 = d-e [2.33d] c_ = d+e [2.33e] b d = l/4[3(£ 4 + m4 + n 4 ) - l ] [2.34] e = 1/12[6 ( 3 A 6 m 2 n 2 - l ) + 6 (3m 4+6a 2n 2-l) x y + 6 z ( 3 n 4 +6£ 2 m 2 - l ) ] [2.35] 6 . = ( D r D s ) / ( D 2 - L 2 ) 1 / 2 9 i=x,y,z. [2.36] i , m, n are the d i rect ion cosines of the internuclear vector, r.,, with respect to the x, y, z pr inc ipa l axes of the molecule. Most molecules have rather i r regu lar shapes and would be expected to tumble an i so t rop ica l l y according to eqs. [2.30] to [2.36]; as a resu l t i t i s very d i f f i c u l t to extract molecular parameters from such a general anisotropic tumbling model. The question arises then whether or not a simpler approximation can be developed, which reduces the number of motional parameters in an asymmetric The c s given here d i f f e r from those given in Woessner's o r ig ina l formula-t ion (ref. 54) by a factor of one half because the def in i t ions of spectral densit ies given here d i f f e r by the same factor from those of Woessner's. - 36 -rotator and at the same time retains information concerning the anisotropic tumbling motion of the molecules. This brings us to the r i g i d el 1ipsoidal 54 (symmetric top) model of Woessner. As the name impl ies, two of the pr inc ipa l rotat ional d i f fus ion constants of the r i g i d e l l i p s o i d are defined * as being equal, such that Dx = f D z; th i s means that the reor ientat ion of the molecule can be described by i t s rotat ion about a s ingle pr inc ipal molecular axis. To emphasize t h i s , i t is a common pract ice to denote Dz by D|| and Dx = Dy by D^ , where D| | i s the rotat ional d i f fu s ion constant about the pr inc ipal axis and is the value about the perpendicular to the pr inc ipa l axis. Setting D x = D y in eqs. [2.28] to [2.33], one obtains: -1 T • • = D ( 3 c o s V r l ) 2 / 2 4 + 3 s i n 2 e i i co s 2 e i j / (5+D | | /D 1 ) + | s i n 4 e . ./(2+4D||/D i) [2.37]1 where e.. i s the angle between the internuclear vector, r.., and the p r i n c i -pal ax is. Many molecules that tumble an i so t rop i ca l l y , espec ia l l y those considered in th i s thes i s , can be adequately described by the r i g i d e l l i -psoidal model and th i s w i l l be discussed in deta i l in Chapter 5. Of course when D x = D y = Dz (spherical top) the molecule tumbles i s o t r op i c a l l y according to eq. [2.28]. *From symmetry consideration i t is immaterial which of the two pr inc ipal components are set equal. ** The reor ientat ion time about the pr inc ipa l axis can be defined as in eq. [2.29] i . e . x11 = 1/6DM and T J _ = l/6Dj_ Phys ica l ly i t i s more descr ipt ive to use reor ientat ion times and where appropriate th i s w i l l be used. - 37 -The auto-correlat ion spectral dens i t ies , J . . given in eq. [2.27] • J > i J can now be read i ly calculated when the appropriate are subst ituted. 2.5 Cross-correlat ion Effects It i s i n s t ruct i ve to consider b r i e f l y the contributions of cross-cor re lat ion spectral dens i t ies . For s imp l i c i t y , consider the case of i sot rop ic motion; the cross -corre lat ion spectral densit ies are related to 2 37 the auto-correlat ion spectral densit ies by a simple l/2(3cos fi-1) factor (cf. eq. [2.27]) f i 2 J i j , k , = 3/10 Y i p Y 3 k ^ T i j k £ { V 2 ( 3 c o s 2 0 i J k £ - 1 ) [2-39] r i j r k £ where ^ - j ^ i s the angle between the r^. and r^ £ vectors, and T ^ . ^ i s the cross -corre lat ion time. For the general case of anisotropic tumbling motion of molecules the re la t ions between cross -corre lat ion spectral densit ies and auto-correlat ion spectral densit ies are very complex. These expressions are given in ref . 38. Thus, the magnitude of cross -corre lat ion ef fects could be comparable to auto-correlat ion terms (where fi1-j|<£ % 0) or small* (when 90°), and the potential of cross -corre lat ion effects in proton n.m.r. studies merits further invest igat ion. 2.6 Evaluation of p.. and a . . Terms To s impl i fy th i s discussion we shal l consider a molecule tumbling i so -t r o p i c a l l y in the extreme narrowing region. Using eqs. [2.23], [2.24] and [2.27] one obtains: *Cross-corre lat ion effects w i l l vanish at = 54° 44' 8" (magic angle). - 38 -2 2^2 p..=IlIi_T.. [2.40] i j a.- = 1/2 P.. [2.41] Anisotropic reorientations can be eas i l y incorporated into these expressions by replacing t . • with the appropriate expressions given in eqs. [2.30] to [2.37]. Thus for a completely d ipolar process, the r a t i o a- V p ^ i s 50% for homonuclear spins tumbling in the extreme narrowing reg ion.* This also accounts for the fact that the maximum observable n.O.e. in proton spin systems i s only 50%; i t i s this rather narrow dynamic range that puts such a heavy demand on experimental accuracy in proton s p i n - l a t t i c e relaxat ion studies and n.O.e. studies. 40 Abragam , almost exc lus ive ly using operator techniques, obtained the above equations for two-spin systems in the fol lowing forms: 2 2.2 i j 2 2^2 i j where I. and I. are the nuclear spin quantum numbers of spins i and j , respect ive ly. Expression for p.. and a . , in the forms of eqs. [2.42] and * I f the extreme narrowing condition i s not va l id the r a t i o O ^ / P - J J W I 1 1 D E less than 50% even i f the interact ion i s completely d ipolar. - 39 -[2.43] become pa r t i cu l a r l y useful when the method of spec i f i c deuteration" 3 1 i s used to evaluate interproton cross-relaxat ion effects in mult ispin systems. Further discussion on the deuteration method of ident i fy ing spec i f i c i n te r -proton dipolar contributions w i l l be given in Chapters 4, 6 and 7. 2.7 Contributions to p. Terms It i s appropriate to comment on the various posssible contributions to the p.j term (eqs. [2.25] and [2.26]) at th is point. These relaxation con-tr ibut ions come from other processes which involve random f luctuat ing mag-netic f i e l d s and these include: 1. Dipole-dipole interact ions with nonresonant nuclear spins ( i n t r a - * and intermolecular, e.g., a deuteron in the solvent or lock sample); 2. Paramagnetic relaxation with paramagnetic species such as d i s -solved oxygen; 3. Spin-rotation re laxat ion; 4. Relaxation by chemical s h i f t anisotropy; or 5. Other appropriate mechanisms. A l l the above "externa l " re laxat ion contr ibut ions, with the exception of intermolecular d ipolar in teract ions , can be separated from the intramole-cular d ipolar terms (p.--values) with the appl icat ion of a combination of non-selective and se lect ive pulse experiments to be described in the next four sections in th i s chapter. Homonuclear or " l i k e " spins not included. - 40 -2.8 Spin-Latt ice Relaxation: Effects of Non-Selective Pulses In general terms a s p i n - l a t t i c e relaxation experiments consists of exc i t ing the spin system to a nonequi1ibrium state and then monitoring the level populations of the spin system as they return to the equi l ibr ium s ta te . * A homonuclear spin system may be excited with r f pulses that are so intense compared with the frequency width of the spectrum that a l l the resonances are es sent ia l l y uniformly excited to the nonequilibrium state. This i s a non-selective pulse experiment. For the AMX homonuclear three-spin system the k inet i c evolutions of the nuclear magnetizations of the spins immediately fol lowing a perturbing pulse are described by the three coupled d i f f e r e n t i a l equations given in eq. [2.14] which is reproduced below: M A (t) P A d dt = aAM M x (t) °AX A  M UMX MV P V M A ( t ) - M A H M M ( t ) - r y - ) M x(t)-M x(») [2.14] In general the solut ion to eq. [2.14] i s nonexponential. However, under the i n i t i a l slope condition given in eq. [2.10], a simple and pract ica l solut ion can be written for eq. [2.13] according to: -R,t M^t ) = M . H + {M.(0) - M.(»)} e " * l [2.44] For the reader who is not f ami l i a r with s p i n - l a t t i c e relaxat ion measurements a descr ipt ion of the standard 180°-t-90° pulse sequence for measuring R e -values is given in Appendix I. - 41 -where, for each spin i (i=A, M, X), M^ t ) speci f ies the magnetization close to the i n i t i a l slope, M.(0) spec i f ies the i n i t i a l condition of the exper i -ment and M. (°°) i s the Boltzmann equi l ibr ium value. A semilogarithmic plot of In {M^ (~)-M^ (t)} versus t i s l i nea r and the slope of th i s l i ne defines the relaxat ion rate appropriate to the i n i t i a l constraints imposed by the per-turbing pulse. Thus, fo l lowing a non-selective 180° perturbing pulse the i n i t i a l conditions of the experiment are Mn.(0) = - M.(») [2.45] for i = A, M and X. The non-selective relaxat ion rate, R^(ns), so derived for spin i = A, M, or X has a simple re lat ionsh ip with the more fundamental rate values of p.. and a.- according to R|(ns).- ^ ( P ^ j l + P* (2-46] for { i , j } = {A,M,X} and summing for each i over a l l j / i . The extreme narrowing l i m i t values of p . . and a.- are given by eqs. [2.40] and [2.41]. Essent ia l ly then, there are three unknown p . j 1 s in the AMX system ( P A M > P AX ' PMX^ a n c ' s ^ n c e t n e r e a r e non-selective relaxat ion rate values (Ri(ns)) these p — 's can be obtained e x p l i c i t l y according to 1 1 0 p AM R A(ns) 1 0 1 PAX 2 " 3 R^(ns) [2.47] 0 1 1 _ PMX _ Rf(ns) - 42 -and related to the geometry of the system. Thus the determination of p..-values from a s ingle non-selective ex-periment for a three-spin system of the AMX type is e x p l i c i t . For the general system containing n spin-1/2 nuclei (n>3) such analysis cannot be applied unambiguously because there are n(n-l)/2 p . . - va lues to be deter-mined from n measured RJ(ns)-values. However, depending on the r e l a t i ve dispos it ions of the spins, some p..-values can be disregarded, permitting one to obtain good estimates of the relevant p^-values v ia a simple analysis of the RJ(ns)-values and hence information concerning the geometry of the molecule. This method of evaluating p^-values in complex mult ispin systems that are approximately pseudofirst order w i l l be demonstrated in Chapters 4 and 6. The ef fect of a non-selective pulse may be regarded as "switching on" a l l the cross-relaxat ion paths of the spin states thereby increasing the observed relaxat ion rates by terms (a . . ' s ) that contain only d ipolar con-t r ibut ions . 2.9. Spin-Latt ice Relaxation: Effects of S ingle-Select ive Pulses In a n.m.r. spectrum where the chemical s h i f t differences between indiv idual resonances are s u f f i c i e n t l y large, as in the AMX spin system, the magnetization of a nuclear spin can often be excited with a se lect ive r f pulse without perturbing the other nuclear spins. For example, each of the four components of the resonance of spin A in the AMX system can be excited equally with a s ingle se lect ive 180° pulse without perturbing any of the t rans i t ions in the M and X resonances. For such a se lect ive pulse, the boundary conditions for the motions of the spins described by eq. [2.14] are - 43 -M f l(0) = - M f l H [2.48a] MM(0) = + W [2.48b] M (0) = + M x(») [2.48c] The resu l t ing s ing le - se lect i ve relaxat ion rate for spin A, R-j(A), obtainable from the i n i t i a l slope plot of ln {M A (» ) -M A ( t ) } versus t , i s given by where the t i l d e (-) i s introduced to designate that only the nuclear mag-net izat ion of spin A has been perturbed. In general, the s ing le - se lect i ve relaxat ion rate of spin i which i s part of a pseudofirst order mult ispin system may be defined by RJ(i) = £ P , , + P * [2.50] This leads to an extremely important conclusion and provides the fundamental qua l i ty control f o r the d ipole-dipole mechanism. If i t i s correct to assume that there is 100% dipolar i n te rac t ion , i . e . , = 0, then a combination of eqs. [2.41], [2.46] and [2.50] results in the fol lowing R A(A) = p A M + P A X + P A [2.49] r a t i o .55,56 for a pseudofirst order spin system. If p^  has a nonvanishing R-j(ns) = 1.5 [2.51] RJ(i) - 44 -value, the extent of intramolecular d ipole-d ipole interact ion for spin i , 56 is given by 2[RJ(ns) - R](1)] f n ( n s ) = 1 [2.52] [ ^ ( i ) ] where f n ( n s ) i s the f ract ion of re laxat ion of spin i a r i s i ng from the i n t r a -i * molecular d ipole-dipole mechanism. Clear ly f (ns) = 1 when p. = 0. Equation [2.51] then, embodies the c r i t e r i o n used to define the extent to which a par t i cu la r proton relaxes via the dipole-dipole mechanism. It i s th i s qua l i ty control experiment which confers a major advantage to the re laxat ion method over the n.O.e. method. The equivalent qua l i ty control for the l a t t e r would require a l l but the receptor resonance to be saturated, and th i s i s not ea s i l y performed in pract ice. It w i l l be reca l led that eq. [2.49] was obtained under conditions expressed in eqs. [2.48]. S imi lar conditions can occur in a non-selective pulse experiment when PAM = PAX K < PMX [ 2 - 5 3 ] According to eq. [2.53], at a time t ' seconds a f ter the non-selective excita-t ion pulse such that conditions expressed in eqs. [2.49] s t i l l approximately hold, i . e . , M A ( f ) = - M A(») [2.54a] M M ( t ' ) ~ + M M(») [2.54b] M x ( f ) = + M x(«) [2.54c] - 45 -then the plot of ln{MA(°°) - M A(t>t ')} versus t (for t>t ' ) provides a re laxa-t ion rate that would be es sent ia l l y equivalent to that of a s ing le - se lect i ve pulse experiment (cf. eq. [2.49]): RA (ns,A) = P a m + p A X + p* [2.55] where R A(ns,A) indicates a "non-select ive" relaxat ion rate of spin A obtained at the region of the magnetization recovery curve where a l l other spins have returned to the equi l ibr ium state. The conditions described by eqs. [2.53] to [2.55] w i l l be experimentally demonstrated in Chapter 3. Qua l i ta t i ve ly , one may imagine that the s ing le - se lect i ve pulse prepares the spin populations in a way that "switches o f f " the cross-relaxat ion paths of the perturbed spin by not allowing i t to "sample" the magnetizations of the other unperturbed spins. However, the unperturbed spins w i l l sample the magnetization of the perturbed spin because the motions of the unperturbed spins are "coupled" via the cross-relaxat ion paths to the that of the per-turbed spin. Thus, the i n i t i a l motion of the perturbed spin is independent of cross-relaxations while the i n i t i a l motion of any unperturbed spin depends only on i t s cross-relaxat ion with the perturbed spin. Consider, for example, the s ing le - se lect i ve inversion of spin A in the AMX system. The i n i t i a l motion of spin A i s given by p ^ + p A X +p A , whereas the i n i t i a l motion of spin M depends only on and that of spin X depends only on o^. In p r inc ip le then, the analysis of the i n i t i a l motions of the unper-turbed spins in a s ing le - se lect i ve pulse experiment provides a method of evaluating the a., terms. In pract ice, however, the method is l imi ted by the dynamic range of the motions of the unperturbed spins. In a mult ispin system th i s dynamic range i s given by - 46 -Y i °ik 2 y k z a i i K J7i 1 J where the y ' s and o's denote gyromagnetic rat ios and cross-relaxations respect ive ly, i designates the perturbed spin while k is the observed unper-turbed spin and j represents a l l unperturbed spins including k in the system. Thus, the evaluation of d ipolar cross-re laxat ion terms v ia the i n i t i a l motions of the unperturbed spins in a s ing le - se lect i ve pulse experiment becomes im-pract ica l for homonuclear (y^ = y^) spin systems; the dynamic range of the magnetization enhancement curve for spin k i s at most 25% ( in most instances i t i s much less than 25%) of the magnetization recovery curve of spin i when i i s se lec t i ve l y inverted by a 180° pulse. For heteronuclear spin systems where y^ > y^, the i n i t i a l enhancement rate of the magnetization of spin k when spin i i s inverted gives a d i rect measure of the term. The trans ient n.O.e. experiment discussed by Solomon^ and the dynamic n.O.e. 47 experiments described by Fagerness et a l . are examples of enhancements in the magnetization of the unperturbed spins a r i s ing from dipolar cross-relaxat ion interact ions with the magnetization of the perturbed spin. Since the occurrence of cross-relaxat ion necessitates the use of the i n i t i a l slope approximation, the non-selective and s ing le - se lect i ve pulse experiments together can provide quant itat ive information concerning the v a l i d i t y of the i n i t i a l slope approximation as w i l l be shown in Chapter 3. 2.10 Spin-Latt ice Relaxation: Effects of Double-Selective Pulses An obvious extension of the s ing le - se lect i ve pulse experiment i s the appl icat ion of two such se lect ive pulses simultaneously on two separate resonances. In a mult ispin system, any such double-selective pulse experiment = 47 -es sent ia l l y imposes the boundary conditions of a pseudotwo spin system on the equation of motion of the system. For example, suppose that a double-se lect ive pulse is used to perturb the nuclear magnetizations of spins A and M in the AMX system. Then the i n i t i a l constraints are: MA(0) = - M A H [2.56a] MM(0) = - M M(») [2.56b] Mx(0) = + M X H [2.56c] and at the i n i t i a l s lope, plots of InjM^. («.) - M^(t)} versus t for spins A and M resu l t in the double-selective relaxat ion rates for spins A and M given respect ively by <(A, M) = p A M + p M + a A M + P * [2.57] R 1 ( A ' M> - PAM + PMX + aAM + pM [2.58] - 48 -The notation R-j (A, M) is introduced to indicate the double-selective relaxa-tion rate of spin A when the resonances of spins A and M are simultaneously perturbed. According to eqs. [2.57] and [2.58], the effect of selectively perturbing the spin states of A and M is to isolate the cross-relaxation paths common to these two spins so that each can sample the other's magneti-zation and incorporate this enhanced effect into the observed relaxation rates. Although the double-selective pulse experiment identifies the cross-relaxation term between spins A and M, its magnitude cannot be deter-mined from this experiment alone; an additional experiment such as that of a single-selective pulse is required. Thus, the cross-relaxation between spins A and M is readily obtainable from eqs. [2.49] and [2.58]: a AM = RA (A, M) - RA(A) [2.59a] or a MA = R?(A, M) - R > ) [2.59b] Since i t is only reasonable to expect that a AM - a. MA [2.60] a more r e a l i s t i c experimental measure of the cross-relaxation between A and M would be - 4 9 -o m = 1/2{[R^(A,M) - R^(A)] + [R'^A.M) - R^M)]} [ 2 . 6 1 ] The pairwise interproton relaxat ion contr ibution between A and M can be obtained y_ia_ eq. [ 2 . 4 1 ] for the case ( W A + 0 J M ^ T A M < < 1 J 1 ' E ' ' PAM = 2 °AM [ 2- 6 2^ In instances where only non- and double-selective experiments can be performed, a re lat ionsh ip equivalent to eq. [ 2 . 6 1 ] can s t i l l be derived: am = 1/6{RA(A,M) - 2[R A(ns) - RA(A,M)]} + l/GJR^Ai) - 2[RfJ'(ns) - R^(A,M)]} [ 2 . 6 3 ] The p^-value can then be evaluated according to eq. [ 2 . 6 2 ] . The re l a t i ve e f f i c iency for the interact ion of A and M in the system can be defined by f A(M) = - ^ r - [ 2 . 6 4 ] R A(A) where f (M) i s the f rac t ion of re laxat ion that spin A receives from spin M via the dipole-d ipole mechanism. Note that in general f A(M) f f^(A). Equations [ 2 . 5 9 ] - [ 2 . 6 4 ] can be generalized for any two interact ing spins in a pseudofirst order homonuclear spin system. For complete dipolar re laxat ion £ f ^ j ) = ^ '(ns) = 1 [ 2 . 6 5 ] - 50 -Although only the spin states of A and M are excited by the double-se lect ive pulse, t he i r motions are in r e a l i t y not independent of that of spin X because the l a t t e r i s coupled to those of the former v ia the cross-relaxat ion terms, and a ^ . In fact the i n i t i a l magnetization enhancement rate of spin X i s given by a ^ x + o ^ . E s sent ia l l y spin X samples the mag-net izat ions of both spins A and M at the same time. As in the s ing le - se lect i ve pulse experiment the determination of + from the motion of spin X a r i s i ng from an exc i tat ion of the spin states of A and M i s not pract icable for homonuclear spin systems because of the narrow i n i t i a l slope range ava i lab le on the magnetization enhancement curve of spin X. However, for heteronuclear spin systems the v a l i d i t y of the i n i t i a l slope may span a larger section on the magnetization enhancement curve of an unperturbed spin so that the cross-relaxat ion terms such as + can be obtained. Note that the number of cross-relaxat ion terms af fect ing the i n i t i a l motion of an unperturbed spin depends on the set of inequivalent spins being se lec t i ve l y perturbed; only in the se lect ive exc i ta t ion of one spin in a mult ispin sytem does the i n i t i a l motion of an unperturbed spin depend uniquely on one cross-re laxat ion term. 2.11 Spin-Latt ice Relaxation: Effects of T r ip le -Se lect i ve Pulses Recall that in Section 2.8 i t was shown that for three i so la ted, mutually relaxing spins, the three p..-values can be e x p l i c i t l y calculated from a s ingle set of non-selective R e v a l u e s as shown in eq. [2.47]. Equation [2.47] can be extended to mult ispin systems provided that a t r i p l e -se lect i ve pulse experiment can be performed, i . e . , the se lect ive inversion of the resonances of three selected spins. Thus, for an A, M, X, ... mu l t i -spin system, - 51 -1 1 0 1 0 1 0 1 1 PAM PAX CNJIOO II R" PMX where = R ] ( A , M , X ) - 2[R](ns) - R ] ( A , M , X ) ] for i = A.M.X. [2.66b] Note the s i m i l a r i t y between eqs. [2.47] and [2.66]; the values for p.. can be readi ly solved. This i s important for systems in which the chemical s h i f t s of three protons are s u f f i c i e n t l y d i f fe rent from those of the others that the i r relaxat ion behaviour can be independently studied. This w i l l be demonstrated in Chapter 4. 2.12 Determination of Internuclear Distances Given the spec i f i c internuclear d ipole-dipole contr ibution terms, p.., determined from a combination of non-selective and se lect ive pulse exper i -ments, internuclear distances ( r . . ) can be calculated according to eq. [2.40] (and for s imp l i c i t y , assuming i sot rop ic motion in the extreme narrowing region) i f the x . . ' s are known. The values for T . • can be eas i l y estimated from carbon-13 or deuterium s p i n - l a t t i c e relaxat ion rates. For most organic molecules in solut ion carbon-13 Revalues are the most convenient probe for providing motional information and hence the type of re laxat ion model to be used to describe molecular reor ientat ions. When a molecule tumbles i s o t r op i c a l l y one may compare internuclear distances according to: r i k p i i 1 / 6 - J i = [2.67] r i j p i k - 52 -Equation [2.67] i s a very useful expression for solving stereochemical pro-blems since i f one r..-value is know, a l l other r. .-values can be calculated. Equation [2.67] has another important feature: i t demonstrates that the propagation of experimental errors in the relaxat ion rates through the inverse s ix th root ca lcu lat ion works in favour of the experimentalist. Thus a 10% error in a p ^ - va l ue reduces to a 1.7% uncertainty in the calculated internuclear distance. This i s graphical ly i l l u s t r a t e d in Fig. 2.3. Also, even i f a molecule tumbles somewhat an i so t rop i ca l l y , eq. [2.67] s t i l l pro-vides a reasonable measure of internuclear distances because a small aniso-t rop ic e f fect would be e f f ec t i ve l y reduced to a neg l ig ib le l e v e l ; as depicted in Fig. 2.3, a 10% error in the ra t i o P - . / P - K resu l t ing from aniso-1 J 1 K t rop ic e f fect alone would also be reduced to a 1.7% uncertainty in the ra t i o r . ./ r . . . In general, however, i t i s important to perform addit ional qua l i ty 1 J 1 J control experiments to show that anisotropic effects are neg l ig ib le or small before applying eq. [2.67] to stereochemical problems. On the debit s ide, however, eq. [2.67] reveals an important "dynamic range" l i m i t a t i o n ; thus for p ^ << p ^ . , the accuracy with which r ^ can be determined re l a t i ve to r.^ i s diminished considerably as depicted in F ig. 2.4. Further discussion on th i s dynamic range problem w i l l given when the experimental data are considered in l a te r chapters. 2.13 Carbon-13 Spin-Latt ice Relaxation: A probe for Molecular Rotational  Motion Although a comprehensive evaluation of the use of carbon-13 R-j-values, to probe the motion of organic molecules in solution is reserved unt i l Chapter 5, i t i s appropriate to b r i e f l y summarize at th i s juncture the formalism describing the geometrical dependence of carbon-13 Reva lues, - 53 -Fig. 2.3 Comparison between the e f fect of a 10% error in an experimentally determined P-jj/pjk value versus the resultant error in the calculated r-j^/ value ( i t i s approximately a 6:1 r a t i o ) . - 54 -l i k A i Fig. 2.4 P lot of the ra t io of interproton distances, r-j^/r-jj, as a function of the inverse ra t io of interproton dipolar relaxation contr ibut ions, P ^ / P - , , , for a molecule which i s tumbling i so-t r op i c a l l y . 1 J 1 K - 55 -because these values are used throughout th i s thesis as qua l i ty control parameters in attempts to detecttiie presence of anisotropic motion of the molecules being studied. The s p i n - l a t t i c e relaxat ion of a carbon-13 nucleus with d i r e c t l y bonded proton(s) in most organic molecules occurs exc lus ive ly v ia d ipole-dipole interactions with the proton(s); th i s can be t r i v i a l l y proved by measuring 13 1 C-{ H} n.O.e. factors. Under conditions of proton noise decoupling* in the extreme narrowing l i m i t and assuming complete dipolar in teract ions , the carbon-13 R-j-values are given by n, 2 2* 2 H Y C Y H T 1 R , ( 1 3 C) = ? ~ 6 TCH-i [ 2 ' 6 8 ] 1 1 r CH- i where i s the number of d i r e c t l y bonded protons. The expressions for for the d i f fe rent motional models are given in eq. [2.28] and eqs. [2.30]-[2.38]. Since r ^ is usually known and generally constant, the angular 13 dependence of T „ u and hence R,( C) becomes readi ly apparent. It i s to be expected that the re l a t i ve dispos it ions of the various C-H vectors w i l l in general be an important factor i s using carbon-13 R e v a l u e s as motional probes. Thus, i f a l l the C-H vectors in a molecule are e s sent ia l l y equi-v a l e n t ^ , oriented with respect to the molecular pr inc ipal coordinate system, the carbon-13 R-j-values w i l l be ident ica l within experimental error even i f the pr inc ipa l axes of the molecule are substant ia l ly d i f f e ren t , i . e . , the molecule tumbles an i so t rop ica l l y . An experimental example of th i s s i tuat ion The condition of decoupling is analogous to the e f fect of a s ing le - se lect i ve pulse. Under the influence of a continuous decoupling f i e l d , the "back-ground" populations of the proton spins are kept constant thereby preventing any cross-re laxat ion interact ion between the carbon-13 and proton spins. - 56 -w i l l be demonstrated in Chapter 5. 2.14 Tightly Scalar Coupled Spin Systems In p r inc ip le the treatment of s p i n - l a t t i c e relaxation in t i g h t l y coupled spin systems may proceed according to eq. [2.8] provided that i r reduc ib le eigenstate representations are used, espec ia l ly when degenerate spin states are i n -volved. However, i f simple spin product functions are used i t i s necessary 7 8 to use the Redfield-Bloch ' density matrix formulation. Since an excel lent 34 detai led discussion on t i g h t l y coupled spin systems can be found elsewhere, these systems w i l l not here be reviewed further. However i t is of interest to b r i e f l y consider the e f fect of t i gh t coupling on the ra t io of R A(ns)/R A(A) (eq. [2.52]) for an AB two spin-1/2 system. Following Noggle and Sch i rmer^ and assuming that the relaxat ion between the two spins is only d ipo lar , one obtains R?(ns) ? ? -~ = 1 + 1/2(1-0.4S*)/(l-0.IS*) [2.69a] R-| (A) where s 2 = ( J / 6 ) 2 [ 2 > 6 9 b ] (J/6T + 1 J and 6 are respect ively the coupling constant and chemical s h i f t difference between the two spins. Figure 2.5 shows a p lot of R A(ns)/R A(A) versus A A/~ J/6. For J/6 > 0.1 the ra t i o R^(ns)/R-|(A) decreases rapidly from the value of 1.50 with increasing J/5, eventually reaching the asymtoptic value of 1.33. Hence the l i m i t J/6 = 0.1 may be regarded as a reasonable c r i t e r i on for defining pseudofirst order spectra in n.m.r. s p i n - l a t t i c e relaxation - 57 -F ig. 2.5 P lot of R,(ns)/R,(A) versus J/6 for a two-spin system to demon-strate the e f fect of t i ght coupling on determination of Re-values. The meaning of the notation is defined in the text. experiments on homonuclear coupled spin systems. In pract ice, within experi -mental errors (^5%) a ra t i o of J/6 ^ 0 . 2 may s a t i s f a c t o r i l y define a pseudo-f i r s t order homonuclear spin system; and th i s de f i n i t i on w i l l be used through-out th i s thes is . 2.15 Effect of Extreme Narrowing Condition* Throughout this chapter i t has been assumed that molecules tumble in 2 2 the extreme narrowing region ((u).j+a>j) T^J<<1) in which case the measurement of s p i n - l a t t i c e relaxat ion parameters i s independent of the observing f r e -quency of the spectrometer. Under th i s condition i t was shown that for com-plete d ipolar interact ions in homonuclear spin systems RJ(ns)/R^(i) =1.5 (eq. [2.51]). This i s no longer true i f the extreme narrowing condition i s not s a t i s f i e d . Figure 2.6 shows a plot of R^(ns)/RJ(i) as a function of the product of the Larmor frequency of spin i and the motional tumbling time of the molecule. For s imp l i c i t y , F ig. 2.6 is obtained for a homonuclear _ The f i r s t experimental v e r i f i c a t i o n of the extreme narrowing condition was provided by Grant and co-workers, ref. 58. - 58 -Fig. 2.6 n i i 11 0 0 5 0. 0 2 " i — i — | i i i 11 0 5 1.0 i 1 — i — i i i i 11 2.0 3 0 4.0 10 2 0 3 0 C J i T i i Plot of R,1 (ns)/pJ ( i ) as a function of c o . x . - for the dipolar inter-action of two spin-1/2 nuclei i and j ; y • = y. and w. % w . . R i ( n s ) _ p i j + ° i j - . , x R]( i ) 6/O+4U>2T2..)-I 6/(1+4 w 2T 2 .)+3/(1+O.2T2.)+1 It i s assumed that p. = 0. pseudofirst order scalar coupled two-spin system with i so t rop ic motion. I t is further assumed that the relaxat ion mechanism is en t i re l y intramolecular d ipo lar . Thus for a proton spin system the ra t io R^(ns)/R^j(i) i s also a measure of the effectiveness of interproton d ipolar i n te ract ion . For any observing proton n.m.r. frequency, the e f f i c i ency of dipolar interact ion and hence the ra t i o R^J (ns)/RJ ( i ) are reduced for s u f f i c i e n t l y slow molecular 2 9 motions. When molecular motions become very slow such that (UJ.+M. ) T..>>1, RJ(ns)/R^(i) tends to zero which means that tends to -p^.^! Of course, for any given molecular motion, the extreme narrowing condition may no longer be s a t i s f i e d when the observing frequency is increased considerably. The above discussion on the e f fect of the extreme narrowing condit ion on the ra t i o RJ(ns)/RJ(i) for two spins shown in F ig. 2.6. is a general one and can be extended to s im i la r mult ispin systems. - 59 -As w i l l be seen the motional cor re lat ion times of the molecules studied in th i s thesis f a l l in the range 1 0 " 1 0 to 10~ 1 2 sec. rad ^ which permits the use of observing frequencies of several hundred megahertz without v i o l a -2 2 t ion of the extreme narrowing condit ion, (co.+u)-) T..<<1. - 60 -CHAPTER 3 QUANTITATIVE DETERMINATION OF INTERPROTON DISTANCES FOR DIAMAGNETIC MOLE-CULES IN SOLUTION VIA THE MEASUREMENT OF SELECTIVE PROTON SPIN-LATTICE RELAXATION RATES. 3.1 Introduction The v a l i d i t y and experimental appl icat ion of the general theory for quant i tat ive ly determining the mechanism and source of the various c on t r i -butions to the overal l relaxat ion of indiv idual nuclear spins in an AMX homonuclear spin system, given in the preceding chapter, w i l l be demonstrated in deta i l in th i s chapter. Several se lect ive pulse F.t. methods which can be used to quantitate relaxat ion contr ibution a r i s ing from the d ipole-d ipole mechanism w i l l be f u l l y documented here for the f i r s t time. And i t w i l l be shown that such measurements enable proton Revalues to be used to ca lcu late the solut ion geometry of the system under study. The bicycloheptenol de r i va t i ve * (1_) was chosen for th i s study because H H-2 i t has a well dispersed, simple proton n.m.r. spectrum of the AMX type (Fig. 3.1) and because the three bicycloheptenol r ing protons H- l , H-2 and H-3 have a f i x ed , e s sent ia l l y r i g i d spat ia l re lat ionsh ip. Because of the wide * The IUPAC name for th i s molecule i s 1,2,3,4,7,7-hexachloro-6-0-e JxiL-benzoyl-bicyclq[2.2.1] hept-2-ene. - 61 -Fig. 3.1 Proton n.m.r. spectrum (100 MHz) of 1_ in deuteriobenzene so lut ion (0.50M), with added tetramethyls i lane (TMS) (0.3%), at 35°C; th i s solut ion was not degassed. The chemical s h i f t differences (in Hz) between the indiv idual resonances of H - l , H-2 and H-3 are 6] 2 = 304 .7, 6 ^ 3 = 412.8, &2,3 = 108.1; and the corre-sponding magnitudes of the coupling constants ( in Hz), ignoring r e l a t i ve s igns, are J-|,2 = 7.6, J l , 3 = 2.5, J2,3 = 13.5. It can be seen that these three spins sa t i s f y the pseudofirst order (or approximately loosely coupled) 1 i m i t , - i . e . , J/6 4 0.1. The " s i gna l " marked by the aster isk (*) i s a " g l i t c h " in the spectrum; and unless otherwise mentioned, wherever .such a " s i gna l " (not marked by an aster i sk) may occur, i t should be regarded as an instrumental a r t i f a c t . - 62 -d i f f e r e n t i a l between the indiv idual interproton relaxat ion contributions the der ivat ive was also l i k e l y to provide a str ingent tes t for 1. Our understanding of the i n i t i a l slope approximation, and 2. The two-spin approximation often used in relaxat ion studies of mult ispin systems. The "motions" of the three protons H - l , H-2 and H-3 are readi ly described by _d dt M 2(t) ' M,(t) p l CT12 °13 °12 p 2 CT23 °13 °23 p 3 M 1(t)-M 1(oc) M 2 ( t ) - M 2 ( » ) M3(t)-M3(co) [3.1] where M^(t) i s the tota l longitudinal magnetization of proton i (i=l,2,3) at time t and M (^°°) i s the Boltzmann equi l ibr ium value for a s ingle proton. For intramolecular magnetic d ipole-d ipole interact ions in the extreme narrowing region: 1 J 7 i 1 J PA A + P,- . i=l»2,3 [3.2a] o. . - a • • IJ J1 [3.2b] 1 J P i j p j i = 2 a i j 2 2.2 Y i Y ^ T i j [3.2c] [3.2d] The p. term represents re laxat ion contributions from sources other than intramolecular d ipolar interact ions. The derivations of eqs. [3.1] and [3.2] - 63 -and the physical s ign i f icance of the relaxat ion parameters given in eqs. [3.2] have already been discussed at length in Chapter 2. According to eq. [3.1] i t is impossible to define a f i r s t order rate constant for the relaxat ion of the spins a f te r some i n i t i a l perturbation because the relaxat ion of each spin i s "coupled" to the relaxations of the other spins v ia the cross-relaxat ion terms (a. . ) . Fortunately, for the pract i s ing chemist i t i s frequently (almost invar iably) possible to obtain a " f i r s t order" Revalue simply by measuring the i n i t i a l slope of the mag-net izat ion recovery curve. I t w i l l be demonstrated that t h i s , seemingly naive, approach can provide R-j-values which, according to the best s tate-of -the-art c r i t e r i a , are quant i tat ive ly accurate; as shal l be shown the success of the approach i s c r i t i c a l l y dependent on the decision as to what const itutes an " i n i t i a l s lope". 3.2 Spin-Latt ice Relaxation Measurements The non-selective and se lect ive Revalues of H- l , H-2 and H-3 of com-21 * pound 1_ were determined with the standard two-pulse (180°-t-90°-AT-PD)^y oo or three-pulse (PD-180°-t-90°-AT-PD-90°-AT) N T sequence. Based on the extensive experience gained in th i s and other related studies, the two-pulse sequence i s recommended for measurements of R-|-values rather than the three-pulse sequence for the fol lowing reasons. F i r s t l y , the two-pulse t i s the " l i t t l e t " values used to monitor the recovery of the longitudinal magnetizations of the spins. AT is the acqu i s i t ion time, i . e . , the period during which the free induction decays ( f i d ' s ) are sampled. PD i s the pulse delay and is set such that a l l the perturbed nuclear magnetizations have returned to Boltzmann equi l ibr ium; often PD i s set so that PD+AT;>5T-| where T-j i s the relaxat ion time of the slowest relaxing spin in the system under study. The unit of t , AT and PD are usually the second. NT is the number of transients or acqu i s i t ions . - 64 -sequence allows the motions of the spins to be v i sua l l y followed through the p a r t i a l l y relaxed spectra and hence may often provide a rapid estimate of the Revalue of a pa r t i cu la r spin at the " n u l l " po in t . * Secondly, the two-pulse sequence retains a l l spectral information, e.g., when a spin system is se lec t i ve l y perturbed the motions of the unperturbed spins can be readi ly followed to provide information regarding trans ient Overhauser e f fec t s .^ Also, although the three-pulse sequence i s claimed to compensate for small changes in reso lut ion, in our hands i t did not appear to have better accuracy than the two-pulse sequence in relaxat ion measurements. Two methods were used to measure the non-selective and se lect ive R-j-values of H- l , H-2 and H-3 of 1_, namely, the "conventional" method and the 29 " t a i l o r ed exc i t a t i on " technique of Tomlinson and H i l l . Further deta i l s on the procedure used to measure the R e v a l u e s for H- l , H-2 and H-3 of 1_ are given in the Experimental section in Chapter 9. The set of spectra shown in Fig. 3.2 i l l u s t r a t e a t y p i c a l , non-selective relaxat ion experiment using a two-pulse sequence. The motion of the nuclear magnetization of each of the three protons can be progressively followed as one proceeds from spectrum A to G. The nul l point for H-l occurs at 5.5 sec, H-2 at 1.0 sec, and H-3 (not shown) at 1.2 sec. I t w i l l be of interest to compare the R e v a l u e s obtained from these nul l point times to those ca lcu-lated from the i n i t i a l slope, l a t e r in th i s discussion. The magnetization The " n u l l " point occurs at a time t n u n such that M-jUnull) = ° ' A t t h i s point on the magnetization recovery curve, R] = In 2/tnu l l - Although th i s i s a very useful p ract ica l re la t ionsh ip , i t should only be used qua l i t a -t i v e l y , because the Revalue so obtained may contain large systematic errors ; e.g., i t i s not an i n i t i a l slope value and therefore cross-relaxat ion and cross -corre lat ion are not accounted fo r , and i t i s very sens i t ive to any imperfection in the perturbing pulse. Fig. 3.2 - 66 -F ig . 3.2 Pa r t i a l 100 MHz proton n.m.r. spectra of 1_, showing a two-pulse non-selective inversion-recovery determination of the spin-l a t t i c e relaxat ion rates of H- l , H-2 and H-3 (see F ig. 3.1). A l l spectra were monitored on a degassed 0.50M solut ion in deuteriobenzene at 35°C as fo l lows: SW (Spectral Width) = 1000 Hz, AT = 4 sec, PI (180° pulse) = 136 usee; P2 (90° pulse) = 68 sec; PD = 50 sec; NT = 4, SE ( Sens i t i v i t y Enhancement) = 1.5 sec, and Al (Absolute Intensity) = 1. The time interva ls ( i . e . the " l i t t l e t " ) between the 180° and 90° pulses are indicated to the r ight of each spectrum. for H-2 in spectra E and F i s seen to be enhanced compared to the equi l ibr ium value in spectrum G by v i r tue of an increase in the tota l peak heights of the H-2 mul t ip let l ines in E and F re l a t i ve to G. This phenomenon can be attr ibuted to a transient Overhauser e f fect from the slowly relaxing spin, H- l . H-3 does not seem to experience such an e f fect from H-l ind icat ing that H-l receives most of i t s re laxat ion contributions from H-2; that th i s indeed i s the case w i l l be quant i tat ive ly shown l a te r . The spectra given in F ig. 3.3 are typ ica l of a s ing le - se lect i ve inver-sion-recovery experiment and those in F ig. 3.4 of a double-select ive invers ion-recovery experiment. As the motion of the se lec t i ve l y perturbed spin is followed through the p a r t i a l l y relaxed spectra, i t i s seen that the nul l point for the recovery of nuclear magnetization i s not well defined because each of the mult ip let l ines appears to nul l at s l i g h t l y d i f fe rent time, even though the tota l peak heights of the mul t ip let l ines tend to almost a zero value close to the nul l point. (Compare the i n tens i t i e s of H-2 in spectra C of Figs. 3.2 and 3.3.) Two effects may contribute to th i s " i n t en -s i t y anomaly": c ross -corre lat ion and/or imperfection in the perturbing pulse; in the present case the l a t t e r i s probably the pr inc ipa l cause since these spectra were obtained without the use of phase-alternation in the H- l 67 H - 2 H - 3 I 50.0 ii__3.0 _-UlL M 2.0 1.4 I f T 0.6 1L —0.1 sec 100 Hz i 1 Fig. 3.3 68 -H-1 H-2 H-3 n J 50.0 1 ML. _ M 10.0 6.0 3.0 1.4 Tr 0.8 100 Hz i i 0.4 0.1 sec - 69 -F ig. 3.3 Pa r t i a l 100 MHz proton n.m.r. spectra of 1_ showing the s ingle se lec t i ve determination of the s p i n - l a t t i c e re laxat ion rate of H-2 using a two-pulse inversion-recovery sequence. A l l spectra were monitored as fo r those in F i g . 3.2. The " l i t t l e t " values are given to the r i gh t of the respective spectra. The duration of the se l ec t i ve 180° pulse was 20 msec; the Gyrocode decoupler frequency was 58826 Hz with the attenuator set at 106 dB. F ig. 3.4 Pa r t i a l proton n.m.r. spectra of ]_ showing the se lect ive deter-mination of the se lect ive re laxat ion rates of the H-l and H-3 resonances fol lowing perturbation of both those resonances with a se lect ive 180°-pulse (duration, 20 msec) derived from the Gyrocode decoupler set at 58925 Hz and audio-moduated at 206 Hz (1/2 6-| 3 ) ; the attenuation was 109 dB. monitoring pulse. In the two sets of spectra shown in Figs. 3.2 and 3.3, the magnetization i n ten s i t i e s fo r the unperturbed protons are seen to vary with time; these values increase progressively to a maximum before gradually returning to t he i r equi l ibr ium values. This transient n.O.e. effects w i l l be quantita-t i v e l y discussed l a t e r (see Section 3.9). The numerical values for the various re laxat ion rates of H- l , H-2 and H-3 of 1_ are summarized in Table 3.1. Each value shown in Table 3.1 i s the average of four independent measurements conducted on the same sample. These values were found to be reproducible to within f i v e per cent. Table 3.1 Spin-Latt ice Relaxation Rates ( IO - 3 sec " 1 ) of 1 (0.50M) in Deuteriobenzene Solution (Degassed). Relaxation Rate Experiment 3 H-l H-2 H-3 AMC TEXd TEXd AMC TEXd 1. Non-Selective 153±5 105±4 e 151+5 105+4e 660+9 654±9 556+6 556+6 2. S ingle-Select ive 104±4 104±4 e 105±4 99± 4e 434±5 433±5 366±5 373+5 3. Ratio 1/2 1.47+0.06 1.48±0.07 f 1.52±0.03 1.5H0.03 1.52+0.03 1.49±0.03 Double-Selective 4. R](H-1, H-2) 144±5 1 51 ±5 476±5 485±5 - -5 R l (H - l , H-3) 116±4 115±4 - - 372±5 380±5 6. R^H-2, H-3) - - 643±9 629+9 535±9 559±9 Tr ip le -Se lec t i ve 7. R](H-1, H-2, H-3) 155±6 694±10 571+10 - 71 -Table 3.1 (continued) Measurements made at 35°C using a Varian XL-100 (15) spectrometer f i t t e d with a Varian 620L (16K) computer and a Line Tape unit (model C0600). bEach value i s the average of four independent determinations; two with the two-pulse 2I sequence and the other two with the three-pulse 2 8 sequence. A l l values are based on data co l lected for 0.1 < t < 1.5 sec unless other-wise stated. The errors are given as standard errors calculated from the standard deviations of the mean of the various independent measurements. Using the conventional audio-modulation technique. Using ta i l o red exc i ta t ion . eData co l lected for 8.0 < t < 12.0 sec. f A mean value of (102±4)10" 3sec" 1 for R ? _ 1 (H- l ) i s used. - 72 -3.3 The I n i t i a l Slope Approximation It i s evident from the previous discussion given in Section 2.1 of Chapter 2 on d ipolar re laxat ion in scalar coupled spin systems that there i s no unique de f i n i t i on of the s p i n - l a t t i c e relaxat ion for a proton or a group of protons which i s part of a scalar coupled complex mult ispin system. A unique de f i n i t i on of Revalues for protons cannot be made because of the occurrence of nonexponentiality in the magnetization recovery curve. There are two contr ibuting factor s ; these are cross-re laxat ion and cross-cor re la t ion . Cross-correlat ion gives r i se to d i f f e r e n t i a l re laxat ion rate within a scalar coupled mult ip let whereas cross-relaxat ion is caused by a " t rans fer " of magnetization from any neighbouring nonequilibrium spin. 30 Fortunately fol lowing the o r i g i na l suggestion of Freeman et a l . an adequate de f i n i t i on of an e f fec t i ve relaxat ion rate for a scalar coupled proton mult ip let can be based on a determination of the i n i t i a l slope of the mag-net izat ion recovery curve; and more importantly, the use of the i n i t i a l slope approximation based on the behaviour of the tota l magnetization i n -tens i ty of each proton substant ia l ly compensates for the ef fects of cross-relaxat ion and c r o s s - c o r r e l a t i o n . " 3 ^ ' ^ Although in p r i nc ip le th i s i n i t i a l slope approximation can be read i ly defined, i t has not previously been demonstrated in pract ice. It w i l l now be shown that the bicycloheptenol der i va t i ve , 1_, provides an excel lent demonstration of the v a l i d i t y of the i n i t i a l slope approxima-t ion and i l l u s t r a t e s in pract ica l terms how an adequate de f i n i t i on of the i n i t i a l slope of the magnetization recovery curve can be made. A l l evaluations of the non-selective Revalues of the two more rapidly relaxing protons (H-2, H-3) of 1_ using data obtained for t-values between 0.1 and 1.0 T^-periods gave es sent ia l l y the same slopes: th i s implies that - 73 -the relaxat ion was very close to exponential over that period. And i t was not surpr is ing that the s ing le - se lect i ve Revalues were also independent of the t-values chosen, since the relaxat ion behaviour of a se lec t i ve l y perturbed spin should be es sent ia l l y independent of c ros s - re laxat ion. * The s i tuat ion was somewhat more complicated for the more slowly relaxing (H-l) resonance. Again the s ing le - se lect i ve Revalue was found to be i n -dependent of the t-values used, but now the non-selective "R^-values" were very dependent. When data points were taken for 8.0 < t < 12.0 sec, a -3 -1 value of 105 x 10 sec was ca lculated. In contrast, calculat ions based on the t-values (0.1-1.5 sec) previously used for the H-2 and H-3 -3 -1 resonances gave an R-j-value (Table 3.2) of 152 x 10 sec . The reason for th i s s i gn i f i can t and expected difference is discussed more f u l l y in the next sect ion, and for the present, attention w i l l be directed to Figs. 3.5 and 3.6 where the plots for the experimental data points are given. Although the motion for the magnetization of H-3 is not shown, i t i s ident ica l to that shown for H-2 in Fig. 3.6. It should be noted that plots such as those given in Fig. 3.6 are pa r t i cu l a r l y useful. F i r s t l y , the intercepts of these plots have a value of two; th i s suggests that the pulses used in obtaining these data are very nearly i dea l . Secondly, because the non-selective R-j-values of H-2 and H-3 are independent of the choice of t-values for t <: t^(ns), i t can be inferred that a rapid estimate of these R-j-values from the " n u l l " point S t r i c t l y th i s i s not true as the motions of the magnetization of these are coupled; th i s e f fect i s manifested by the transient n.O.e. seen in the unperturbed spins (discussed in Section 3.9.). But because a se lect ive perturbing pulse does not es sent ia l l y drive the relaxat ion through the cross-relaxat ion paths the above statement i s probably v a l i d . \ - 74 -Table 3.2 Averaged Values of the Spin-Latt ice Relaxation Rates (10" sec ) for 1, Calculated from Table 3.1. Relaxation Rate Experiment H-l H-2 H-3 1. Non-Selective 152+4 657±6 556±4 2. S ingle-Select ive 103±2 c 434±4 370±4 3. Ratio 1/2 1.48±0.05 1.5U0.02 1.50±0.02 Double-Selective 4. RJ ( H - 1 , H-2) 148±4 480±4 5. RJ ( H - 1 , H-3) 116±3 - 376±4 6. R](H-2, H-3) - 636±6 547±6 Tr ip le -Se lec t i ve 7. RJ ( H - 1 , H^2, H^3) 155±6 684±10 571±10 Measurements made at 35°C using a Varian XL-100(15) spectrometer f i t t e d with a Varian 620L (1 OK) computer and a Line Tape unit (model C0600). bEach value is the average of eight independent determinations (unless otherwise mentioned); four with the two-pulse^ sequence and the other four with the three-pulse sequence. 2 Errors are given as standard errors calculated from the standard deviations of the mean of the various i n -dependent measurements. cAverage of 16 measurements. Average of 4 measurements. - 75 -2n o 0 °°OCD-H O o O o p H _ 1(H -1) = 1 0 3 ( x l 0 " 3 s e c ' 1 ' i n i t i a l s l ° P e ) 1 = 103 (x10" 3 sec - , t later stages) JL 2 8 2 i-—r~ 4 i 6 i 9 10 "il Usee) 13 14 o o o o o R , " ' ( n s ) ~l 1— 2 3 = 152 ( x l 0 " 3 s e c ~ , l initial slope) = 105 (x10 " 3 sec - \ later stages) —r-5 6 10 ii t(sec) 13 14 Fig. 3.5 Fig. 3.6 - 77 -F ig. 3.5 Semi logarithmic plots of [M-j (°°) - M-j(t)] versus " l i t t l e t " (sec) for the H-l resonance of 1_. The data points in the upper section were obtained from the i n i t i a l decay 0.1 < t i 1.5 sec, and from the terminal decay 8.0 < t < 12.0 sec of a s i ng le - se lec t i ve , inversion-recovery experiment. Note that both sets of points l i e on the same l i n e , corresponding to R^ - 1 (H- l ) = 104 x 10 " 3 sec " ' . The data points in the lower section were obtained for s imi la r time periods of a non-select ive, inversion-recovery experiment. Note that whereas the i n i t i a l (0.1 £ t £ 1.5 sec) Ri-value is 152 x I O - 3 s e c " ' , the value for the terminal data points (8.0 1 t £ 12.0 sec) is now 105 x 10 3 s e c " ' , which i s close to that of the se lect ive experiment. Fig. 3.6 Semilogarithmic plots of [M-j(°°) - M-j (t)]/M-j (°°) versus t/Ti (ns) for the most rapidly and the most slowly relaxing protons of 1_ (T-j(ns-) = 1/Ri(ns)). The data points in the upper section were obtained for H-2, the most rapidly relaxing proton, during the period 0.05 Ti(ns) <_ t _<1.0 T](ns) in a non-selective pulse experiment. Note that a l l the data points l i e on the b e s t - f i t s t ra ight l i n e . The data points in the lower section were obtained in the same experiment for H- l , the most slowly relaxing proton, but for the periods 0.01 Ti(ns) < t < 0.2 T](ns) and 1.2 Tj (ns) <_ t <_ 1.8 T] (ns). Note that the relaxat ion of H-2 is e s sent ia l l y exponential upto t-values of the order one T](ns) - value, while the relaxat ion of H-l i s strongly dependent on the choice of t-values. Observe that the non-selective R i -value fo r H-l fo r t << T](ns) i s ^1.5 time that for t ^ T-|(ns). would be very close to those calculated for the i n i t i a l slope (Table 3.2). This indeed was the case because the non-selective Revalues calculated for -3 -1 -3 -1 H-2 and H-3 from t ^ were respect ively 693 x 10 sec and 578 x 10 sec , and each of these values was only 5% higher than the corresponding values obtained from i n i t i a l slope ca lcu lat ions . However, the s i tuat ion for H-l would be considerably d i f fe rent because i t s non-selective Revalue is dependent on the choice of t-values. Thus, i t s non-selective Revalue obtained from t ^ was found to be 21% higher than that calculated from - 3 - 1 the i n i t i a l slope, i . e . , 126 x 10 sec . From the above i t can be inferred that although obtaining non-selective Revalues from nul l points - 78 -can be very usefu l , the approach i s at best qua l i t a t i ve . 3.4 The Overall Extent of Dipole-Dipole Relaxation It was shown in Chapter 2, Section 2.9, eq. [2.51], that the rat io R-j (ns)/R.| ( i ) should be 1.5 i f a l l of the relaxat ion of spin i arises v ia d ipole-d ipole interact ion with the other spins which are influenced by the non-selective pulse. The average R^-values from Table 3.2 for the H-2 and H-3 resonances which give rat ios of 1.51 ± 0.02 and 1.50 ± 0.02 respect ive ly, c l ea r l y show that both these resonances relax exc lus ive ly via d ipole-dipole interact ions - - and although this s t r i c t l y includes both i n te r - and intra-molecular contr ibut ions, i t seems reasonable to assume that, under the conditions which pertain here, intermolecular interact ions are neg l i g ib le . H-l For the H-l resonance, two values were avai lable for R-| (ns), one corresponding to the period (0.1 £ t < 1.5 sec) during which the other r ing protons were undergoing the major portion of the i r re laxat ion, and the second for much longer t-values (8.0 < t < 12.0 sec) during which time interval both H-2 and H-3 were almost completely relaxed. Clear ly the relaxat ion behaviour of H-l during th i s l a t t e r period i s e s sent ia l l y that which would fol low a se lect ive perturbation of H- l , an assertion which i s supported by the f inding that the R ^ ^ n s , H-l)-value (105 ± 6 (10~ 3 sec _ 1 ) ) H-1 ^ corresponding to th i s time interva l i s nearly ident ica l with the R-j (H-l) -3 -1 value (103 ± 6 (10 sec )). And the whole picture i s n ice ly rounded o f f H-1 by the f inding that the R-j" (ns) value obtained as an i n i t i a l slope gives a ra t io of 1.48 ± 0.05 with the se lect ive R e v a l u e . These points are c l ea r l y discernable from Fig. 3.5. We see here several important points. F i r s t , that a l l three r ing - 79 -protons are relaxing exclus ive ly v ia the dipole-dipole mechanism. Insofar that the R^-values obtained v ia the non-selective procedures are ident ica l with the values obtained from a se lec t i ve , t r i p l e inversion experiment involving the H- l , H-2 and H-3 resonances, i t follows that the relaxat ion only involves interact ions between those three protons; and s p e c i f i c a l l y i t may be asserted that the phenyl protons make no s i gn i f i can t contributions to the relaxat ion of the bicycloheptenol r ing protons. Although we have no independent evidence i t seems reasonable to assume that intermolecular interact ions are neg l ig ib ly small and hence that the relaxat ion of H- l , H-2 and H-3 occurs exc lus ive ly v ia the intramolecular d ipole-d ipole mechanism. 3.5 Evaluation of the Interproton Relaxation Contributions, p..-values The magnitudes of the indiv idual pairwise interproton relaxat ion con-t r ibut ions of 1_ were evaluated in four, independent ways* using the R-j-values given in Table 3.2. The p^-values l i s t e d in l i n e 1 of Table 3.3 were evaluated from a combination of the three sets of s ing le- and double-selective pulse experimental data; and the other three independent evaluations were made by an e x p l i c i t analysis e i ther of the s ingle set of non-selective R e -values, or the combined set of s ing le - se lect i ve R-j-values, or the combined non- and t r i p l e - s e l e c t i v e R^-values ( l ines 2 to 4 of Table 3.3). In sp i te of the rather high percentage error associated with the p ^ determinations, the internal consistency of these data (except that from the t r i p l e -se lect ive pulse) i s encouraging. And although the double- and t r i p l e -se lect ive pulse data appear to have larger systematic errors , as w i l l be The various relevant formulae are given in Chapter 2, Sections 2.8 to 2.11 - 80 -Table 3.3 Interproton Relaxation Contributions, p.. (10 sec ). Source of Data p l 2 p l 3 p 2 3 1. Double- and Single-Se lec t i ve 3 91 ±8 19±8 379±1.0 2. Non-Selective^ 84±3 17±3 354±3 3. S ingle-Selective* 5 84±3 19±3 350±3 4. T r i p l e - and Non-Se lec t i ve b 99±20 8±20 393±20 ' i j = [ R ] ( i J ) - RJ ( i ) ] + [ R J ( i , j ) - RJ( j ) ] Solving 1 0 1 p l 2 p l 3 p 2 3 = k H-l 'H-2 'H-3 where for non-selective pulse k=2/3, RJ = R J ( n s ) ; for s ing le - se lec t i ve pulse k=l, RJ = R^J(i); and for t r i p l e - and non-selective pulse k=2/3, RJ = RJ (H - l , H-2, H-3) - 2 [ R J ( n s ) - R](H-1, H-2, H-3)]. seen these se lect ive pulse experiments can provide an acceptably accurate method of measuring the solut ion geometry of diamagnetic molecules containing more than three interact ing proton spins. In view of the fact that a l l the non- and s ing le - se lect i ve R-j-values were already known to conform with a 1.5 r a t i o , the close agreement between these two sets of p^-values is hardly surpr i s ing. The indiv idual p^.-values given in Table 3.3 may be expressed as - 81 -f ract iona l re laxat ion contributions as shown in Table 3.4 according to (see also eq. [2.64] in Chapter 2) Table 3.4 Calculated Values for the Fractional Interproton Relaxation Contributions, f 1 (J)> for 1_. Experimental Source f 1 (J) Non- S ingle- Double- T r i p l e -Select ive Select ive Select ive Select ive f (2) 0.82±0.03 0.82±0.03 0.88±0.08 0.96±0.20 f 1 (3) 0.17±0.03 0.18+0.03 0.16±0.08 O.Q8±0.19 Total 0.99±0.04 1.00±0.04 1.06±0.11 1.04±0.28 f 2 ( l ) 0.19±0.01 0.18±0.01 0.2H0.02 0.23±0.05 f 2 ( 3 ) 0.82±0.01 0.8U0.01 0.87±0.02 0.9U0.05 Total 1.01±0.015 1.00±0.015 1.08±0.03 1.14±0.07 f 3 ( l ) 0.05±0.01 0.05±0.01 0.05+0.02 0.02±0.05 f 3 ( 2 ) 0.96±0.01 0.95+0.01 1.02±0.03 1.06±0.06 Total 1.01±0.015 1.00+0.015 1.07±0.04 1.08±0.08 A j ) = AL- [3.3] R]( i ) where f ^ j ) is the f ract iona l d ipolar re laxat ion spin i receives from j . The merit of casting the p..-values in the f ract iona l format i s that i t d i sp lays, in a very nice way, the r e l a t i ve accuracy of the various measure-ments. It is readi ly seen that the interproton dipolar interact ion between H-2 and H-3 can be determined with high accuracy followed by a sat i s factory evaluation of the H-l and H-2 in teract ion. However the dipolar interact ion - 82 -between H-l and H-3 can only be poorly estimated. I n tu i t i ve l y th i s i s to be expected because a very e f f i c i e n t re laxat ion pathway exists between H-2 and H-3 ( p ^ ^ 20p^)> a n d m u c n l e s s e f f i c i e n t relaxat ion mechanism between H-l and H-2 ( p 2 3 % 4 p 1 2 ) . If the relaxat ion of H-3 is considered i t i s seen that H-3 receives i t s relaxation contr ibut ion almost en t i re l y from H-2 (f (2) ^ 1) such that the neg l ig ib ly small re laxat ion contr ibution from H-l can hardly be evaluated with a reasonable ce r ta in ty , say <20% error. It can also be seen that values obtained from the double- and t r i p l e - s e l e c t i v e pulse experiment have large systematic er rors , although these errors do not appear to s i g n i f i c an t l y a f fect the distance measurement discussed l a te r in Section 3.7. The internal consistency of the experimental values i s provided by the fact that in a l l four cases the tota l f ract iona l re laxat ion contributions are e s sent ia l l y unity ( i . e . i ^ ( j ) = 1). 3.6 Tumbling Motion of 1: Carbon-13 Spin-Latt ice Relaxation Having obtained the various interproton pairwise re laxat ion contr ibu-t ions , p^ -va lues , i t is necessary to determine the reor ientat ion times T ^ of the interproton relaxat ion vectors, rT., by an independent experiment before the interproton distances, r.., can be extracted from the p..-values. Although the reor ientat ion times of the various interproton relaxat ion vectors in a molecule cannot be determined d i r e c t l y , an estimate of the presence of possible anisotropy in T . - can however be conveniently obtained via the s p i n - l a t t i c e relaxat ion of the appropriate carbon-13 nucleus with d i r e c t l y bonded proton(s). Since a detailed discussion on molecular motion w i l l be given in Chapter 5, only results and conclusions pertaining to the bicycloheptenol der ivat ive w i l l be given in th i s sect ion. - 83 -The R-j-values of a l l the protonated carbons of 1_ (Fig. 3.7) are summarized in Table 3.5. Table 3.5 Carbon-13 Relaxation Rates, R-. ( 1 0 _ 3 s e c _ 1 , ±5%), Nuclear Over-hanser Enhancement, n.O.e. (±0.15), Factors for Whose Carbon Atoms of l a Which Bear Hydrogen Substituents, at 35°C C-l C-2 C-ortho C-meta C-para R l 540 1050 600 596 800 n.O.e. 2.93 3.00 2.90 2.98 3.10 Measurements made on a 1.0M of j _ in deuteriobenzene, non-degassed in a 10 mm tube and using those parameters given in Fig. 3.7. b 58 Using gated decoupling and a l l other settings as in F ig. 3.7; n.O.e. here i s defined as the ra t io of the integrated intens i ty with n.O.e. to that of without n.O.e. That the observed C-{ H} n.O.e. factors for a l l the carbon atoms bearing hydrogen substituents are very nearly three "proves" that the sp in-l a t t i c e relaxation of those carbon-13 nuclei i s exclus ively d ipolar and the relaxat ion contributions are provided by the d i r e c t l y bonded proton(s)*. See page 85. - 84 -Fig. 3.7 Carbon-13 n.m.r. (20 MHz) spectrum of 1_ in deuterio-benzene (1.0 M) at 35°C, obtained with a Varian CFT-20 spectrometer using the fol lowing parameters: SW = 4000 Hz, AT = 1 sec, PW (Pulse Width) (90°).= 20 ysec, PD = 7 sec, SE = -0.4 sec, Al = 1. - 85 -That the relaxat ion rate of C-2 i s precisely twice that of C-l suggests the reor ientat ion motion of the three C-H internuclear re laxat ion vectors is e f f ec t i ve l y i d e n t i c a l , from which i t may be inferred that the motion of the corresponding interproton vectors is also i d e n t i c a l . Before discussing how the above information can be used i t i s appro-pr iate to digress b r i e f l y with the observation that the carbon-13 R-j-values in Table 3.5 c lea r l y show that the motion of the phenyl carbon-proton internuclear vectors of the benzoate substituent is anisotropic. As has 59 been observed for other benzene der ivat ives , the para carbon relaxes s i g n i f i c an t l y faster than e i ther of the ortho or meta carbon atoms. The carbon-13 Revalue of C-l and that C-ortho or C-meta are very nearly i d e n t i c a l ; the small d i fference ismost probably due to a s l i g h t l y shorter 2 C-H bond length for the sp -hybridized aromatic carbon re l a t i ve to that 3 of the sp -hybridized a l i pha t i c carbon C-l or C-2. And in th i s case the dif ference in the R^-values can be accounted for by a shortening of about 0 3 0.02 A, which i s not unreasonable because the C-H bond length of a sp -o 2 hybridized carbon is generally about 1.10A while that of a sp -hybridized carbon i s about 1.08A. Hence i t may be inferred from these data that there i s very l i t t l e internal or segmental motion between the.two rings across the bonds that separate them. This inference suggests that the b icyc lo -heptenol der ivat ive as a whole tumbles an i so t rop ica l l y . This i s not too surpr is ing because the general shape of th i s molecule may be described by an e l l i p s o i d and the formalism describing the anisotropic motion of a r i g i d 54 e l l i p s o i d i s now generally known. To a good approximation the tumbling Theoret ica l l y , the n.O.e. factor for a carbon-13 nucleus receiving com-plete dipolar re laxat ion contr ibut ion from a d i r e c t l y bonded proton(s) i s ( 1 + Y c / 2 Y H ) i . e . 2.987, assuming the molecule is tumbling in the extreme narrow region. - 86 -motion of 1_ can be described by a symmetric r i g i d e l l i p s o i d * with the C-H bond of the para carbon pa ra l l e l or nearly pa ra l l e l to the pr inc ipal axis of the e l l i p s o i d as shown in F ig. 3.8 below. Fig. 3.8 The symmetric e l l i p s o i d a l representation of the tumbling motion of 1_, where the D's are the rotat ional d i f fu s ion constants defined in Chapter 2, Section 2.4. Since only the para carbon shows an exception in i t s Revalues i t may be inferred that the angles between the pr inc ipa l axis of rotat ion and a l l the other C-H vectors are very s im i l a r . This leads us to the assumption that the reor ientat ion time of the three interproton relaxat ion vectors between H- l , H-2 and H-3 are very s im i l a r , i . e . , as far as s p i n - l a t t i c e interact ion between these three protons i s concerned the molecule tumbles " i s t r o p i c a l l y " . Assuming that the C-H bond of the para carbon is pa ra l l e l to the pr inc ipa l rotat ional axis of the r i g i d e l l i p s o i d , the C-H bonds of the meta and ortho carbon make angles of 60° and 120°, respect ive ly, with the pr inc ipa l o ax i s , and using a C-H bond length of 1.08 A, the ra t i o D||/Dj_can be c a l -culated according to eq. [2.37]. For the carbon-13 Revalues of the aromatic Further discussion on th i s r i g i d e l l i p s o i d model w i l l be given in Chapter 5. - 87 -r ing given in Table 3.5, the ra t i o D||/Dj_for 1_ i s calculated to be 2.02, which corresponds to a ra t i o of the major axis to the minor axis of the e l l i p s o i d of 2.13.* This value i s not unreasonable and compares favourably with a value of about 2.3 obtained from a molecular stereomodel. The inference here is that, although i t i s important to consider the ef fect of anisotropic motion th i s may not a f fect distance measurement when the i n te r -nuclear vectors make somewhat s im i l a r angles with the axis of ro ta t ion . 3 That th i s i s also so for the sp -hybridized protons of T_ w i l l be demonstrated in the next section. 3.7 Evaluation of Interproton Distances Having proven that a l l of the relaxat ion of 1_ accords with the dipole-dipole mechanism and obtained the magnitudes of a l l of the p..-values, the rat ios of the interproton distances can be calculated according to r.. p.- 1/6 = [3.4] r i j p i k provided x^. = r^. [3.5] For a molecule tumbling i s o t r o p i c a l l y , eq. [3.4] i s always true, but for one tumbling an i so t rop i ca l l y , i t i s only true when both T.. • and x ^ have the same angular dependence. We shal l assume, for reasons given in the preceding section that the reor ientat ion times of the three internuclear vectors, r^,, and ^ 3 a r e *The formulation necessary for th i s ca lcu lat ion is given in Chapter 5. - 88 -are e f f ec t i ve l y ident ica l and proceed to ca lcu late the interproton distance rat ios according to eq. [3.4] using the p...-values given Table 3.3. These rat ios are summarized in Table 3.6. Table 3.6 Ratios of the Interproton Distances 9 for H- l , H-2 and H-3 of 1 from Various Sources. Source of Ratios of Interproton Distances Data r ! 2 r 23 r 13 r 23 r 13 r 12 Relaxation Rates 1. Double- and S ingle-Select ive 1. ,27±0.02 1.65+0.12 1. 30±0.09 2. Non-Selective 1 .27±0.01 1. 66+0.05 1. 3U0.04 3. S ingle-Select ive 1 .27±0.01 1. 63+0.04 1. 28±0.04 4. T r i p l e - and Non-Selective 1 .26±0.04 1.91+0.80 1. 52+0.64 Calculat ion Dreiding b Stereomodels 1 .27±0.01 1.62+0.01 1. ,28±0.01 Computer Simulation 1.26 1.61 1.28 a Er ro r s given here are standard errors calculated according to eq. [9.6] (See Chapter 9, Section 9.2). Two sp -hybridized are arranged in the ecl ipsed conformation. C a l c u l a t e d with a computer program COORD(previously ava i lable in th i s l a b o r a t o r y u s i n g the 0 fo l lowing input parameters: bond lengths, C-H = 1.10 A, C-C = 1.54A; bond angles, 109.5°; dihedral angles, 0° . 89 -It now remains to evaluate the interproton distance rat ios in terms of actual geometry of ]_. In the absence of an independent experimental evaluation of these interproton distance rat ios given in Table 3.6 ( l ine 1 to l i ne 4), two reference sets of distance rat ios were obtained by i n -d i rec t means; the f i r s t , by measurements of Dreiding molecular models and the second, by computer s imulation. That the agreement between these data and those obtained from the re laxat ion data (see Table 3.6) i s as good as i t appears to be, augurs well for future appl icat ions of th i s approach. One reason for measuring interproton distances as rat ios i s because the cor re lat ion times of the interproton vectors cannot be d i r e c t l y deter-mined but can be shown to be equivalent, i . e . , i so t rop ic . If one of the interproton distances is known from another source, i t i s possible to evaluate a l l the interproton distances v ia the ra t io s . This i s demonstrated o for 1_ below. If i t i s assumed that r ^ = 1.80 A,* then the interproton distances for H- l , H-2 and H-3 can be determined as shown in Table 3.7. The excel lent agreement of r ^ - va lues between those obtained from relaxation and those calculated (see Tables 3.6 and 3.7) further supports the assumption that x^-va lues for the interproton relaxat ion vectors ( r ^ » »"i3> ^23^ °^ — a r e s i m i l a r -* I t i s reasonable to assume that the interproton distance of a geminal proton of a sp carbon i s 1.80 A. In Chapter 4 one such distance i s determined by neutron d i f f r a c t i on to be 1.80 ± 0.01 A. - 90 -Table 3.7 Interproton Distances (A) Between H- l , H-2 and H-3 of 1_. Interproton Distances 3 Source of Data r l 2 r l 3 Relaxation Rates 1. Double- and Single-Select ive 2.29+0.04 2.99±0.22 2. Non-Selective 2.29±0.02 3.02+0.09 3. S ingle-Select ive 2.29±0.02 2.93+0.07 4. T r i p l e - and Non-Select ive 2.27±0.07 3.4±1.4 Calculat ion Dreiding Stereomodels b 2.28+0.02 2.92±0.02 Computer S imulation 0 2.27 2.90 "Calculated using ^ 2 3 = 1 , 8 0 A ' t h i s b e i n 9 t n e v a l u e obtained by both methods of ca l cu la t ion . bSee footnote ' a ' Table 3.6. cSee footnote ' b ' Table 3.6. - 91 -3.8 Dynamic Range of the Method The data in Table 3.6 imply that the and distances should be determinable with high accuracy (note the standard errors in the rat ios r 12^ r 23 < ^ w n e r e a s * n e r i 3 distance should be less accurate (note the standard errors in the rat ios r-j3/^12 o r r i 3 ^ r 2 3 > 10^)"» ^he calculated distances in Table 3.7 c l ea r l y confirm the above expectation. The large error in determining r ^ is to be expected because of the large dynamic range between the H-l and H-3, and H-2 and H-3 interact ions brought about v ia the r ^ dependence. This s i tuat ion is summarized in Fig. 3.9 from which i t i s seen that = 4.0 p ^ whereas = 17.5 p^-The general inference one can make from Fig. 3.7 is that errors are pro-gressively magnified as one proceeds along the r . ./r . . versus p n--:/P• u p lot . IK 1J l J IK In th i s spec i f i c instance, the error made in measuring p ^ i s magnified by 17.5 times in p^> in addit ion to other systematic errors. It can also be inferred from the data shown in Tables 3.6 and 3.7, and the plot of F ig. 3.9, that the accuracy with which the r. .-values can be determined from the double- and t r i p l e - s e l e c t i v e pulse w i l l f a l l o f f more rapidly ( l ine 1 and l i ne 4 in Table 3.7) than in the case for the non- and s ing le - se lect i ve pulse ( l i ne 2 and l i n e 3 in Table 3.7). Although the above dynamic range problem c lea r l y l im i t s the r e l a t i ve - 6 accuracy with which interproton distances can be determined, the r dependence also provides the experimentalist with a tangible advantage - -i t results in an overal l reduction of the error in the r a t i o of the p..-values by a one s ix th factor. This was i l l u s t r a t e d in F ig. 2.3 (see Chapter 2, Section 2.12 ). - 92 -Fig. 3.9 Diagrammatic representation of the inverse s ixth power dependence of d ipo lar interproton interact ion on interproton distances. Setting p j j = P23 and using r-jj-values obtained through computer simulation (Table 3.7) i t i s readi ly seen that the H-l and H-3 interact ion is a very small f ract ion of H-2 and H-3, and p 2 3 = 4 . 0 PI2, P23 = 1 7 - 5 P l 3 * - 93 -3.9 Transient Nuclear Overhauser Enhancement The internal consistency of the various p. .-values obtained via the U above proton relaxat ion experiments can be independently evaluated by considering the effects of the se lect ive pulses on the nonresonant spins. Using the p. .-values in Table 3.3 the equations of motion for the magneti-zations of H- l , H-2 and H-3 can be e x p l i c i t l y obtained by solving eq. [3.1] for the various i n i t i a l condit ions; the relevant i n i t i a l conditions are summarized below. 3.9.1 S ingle-Select ive Pulse There are three independent s ing le - se lect i ve pulse experiments which involve H- l , H-2 and H-3 i nd i v i dua l l y . Consider the effects of a se lect ive 180° pulse which inverts the magnetization of H-2 at t=0 to - l ^ ^ ) while those of H-l and H-3 remain at +M. («>), i=1 and 3, respect ively. Using the p. .-values calculated from the non-selective pulse experiment ( l ine 2, Table 3.3) and the above i n i t i a l condit ions, eq. [3.1] can be solved for the motion of the unperturbed spins, H-l and H-3, as a function of time. This is depicted by the s o l i d curves in F ig. 3.10. The closed c i r c l e s (•), for H- l , and the closed tr iangles (A ) , fo r H-3, are experimental points; each of which i s the average of four measurements. The enhancement in the i n tens i t i e s of H-l and H-3 with time as a resu l t of nonequilibrium con-d i t i on in H-2 i s due to the cross-relaxat ion in teract ions , and o^y In p r i n c i p l e , the i n i t i a l slopes to these enhancement curves should give a measure of for H-l and f ° r H ~3 ; however, because of the small dynamic range of these transient n.O.e. curves,* a pract ica l evaluation of As was discussed in Chapter 2, Section 2.9, the transient n.O.e. curves for a homonuclear spin system cannot exceed a maximum 50% of i t s equi l ibr ium value. - 94 -Fig. 3.10 Changes in i n tens i t i e s of H-l and H-3 of compound 1 as a resu l t of a se lect ive 180° pulse applied to H-2. The closed c i r c l e s (©), fo r H- l , and the closed t r iang les (A), fo r H-3, are exper i -mental points; each of which is the average of four measurements The s o l i d curves are obtained through eq. [3.1] using p-jj-values derived from the non-selective pulse experiment (Table 3.3). The equations for the so l id curves are: H - l : [ M . ( t ) - M . ( c o ) ] / M . ( - ) H-SrCM.UJ-M.Hl/M.W = (0.0220e~ u - u y 4 y i )+(0.9530e" U ' ^ / b t ) - ( 0 . 9 7 5 0 e " ° - 5 8 7 6 t ) Note that the sum of the coef f i c ient s in each of the above equations i s zero, th i s being the i n i t i a l condition of the experiment. = ( 0 . 3 0 9 0 e - ° - 0 9 4 9 t ) - ( 0 . 1 8 9 5 e - ° - 2 2 7 5 t ) - ( 0 . 1 1 9 5 e " ° - 5 8 7 6 t ) - 95 -a.|2 and from these curves would be highly inaccurate. As i s shown in the calculated curves (Fig. 3.10), the increased intens i ty of H-l and H-3 r i ses to a maximum, and subsequently decreases as H-2 reverts to i t s equi l ibr ium state. 8 1 2 t(sec) 1 6 2 0 24 Fig. 3.11 The same curves as in Fig. 3.9 with t extended to larger values, The e f fect of cross-relaxat ion on H-2 and H-3 as a resu l t of a se lect ive pulse applied to H-l i s shown graphical ly in Fig. 3.12, while Fig. 3.1 3 depicts the e f fect of cross-re laxat ion on H-l and H-2 as a resu l t of a s i ng le - se lec t i ve inversion of the magnetization of H-3. 3.9.2 Double-Selective Pulse The transient n.O.e. induced into one resonance of simultaneous appl icat ion of a se lect ive 180° pulse to the other two resonances are described in Figs. 3.14 to 3.16. These transient n.O.e. data c l ea r l y provide further evidence that the p^-values determined for 1_ represent an accurate descr ipt ion of the rates of internal energy transfer between the three protons fol lowing the appl icat ion of se lect ive exc i tat ion pulses. - 96 -Fig. 3.12 The changes in the i n ten s i t i e s of H-2 and H-3 of compound 1_ as a resu l t of a se lect ive 180° pulse applied to H- l . The opened c i r c l e s (o), for H-2, and the closed tr iang les (A), for H-3 are experimental points; each of which is the average of four measurements. The so l id curves are obtained through eq. [3.1] using p^-j-values derived from the non-selective pulse experiment (Table '3.3). The equations for the so l i d curves are: H-2 : [M i ( t ) -M i ( - ) ]/M. (» ) = ( 0 . 3 0 9 0 e - ° - 0 9 4 9 t ) - ( 0 . 1 8 9 5 e " 0 - 2 2 7 5 t ) - ( 0 . 1 1 9 5 e ' ° ' 5 8 7 6 t ) H-3 : [M . ( t ) -M . (» ) ] /M.H = - ( 0 . 1 3 8 5 e - ° - 0 9 4 9 t ) + ( 0 . 2 3 6 6 e - ° - 2 2 7 5 t ) - ( 0 . 0 9 8 1 e " ° ' 5 8 7 6 t ) - 97 -F ig. 3.13 The changes in the i n ten s i t i e s of H-l and H-2 as a resu l t of a se lect ive 180° pulse applied to H-3. The closed c i r c l e s (•), for H- l , and the opened c i r c l e s (o), for H-2, are experimental points; each of which i s the average of four measurements. The so l i d curves are obtained through eq. [3.1] using the p...-values derived from the non-selective pulse experiment (Table J 3.3) . The equations for the s o l i d curves are: H-l : CM^tJ -M -Hj /M^-) = - ( 0 . 1 3 8 5 e - ° - 0 9 4 9 t ) + ( 0 . 2 3 6 6 e " 0 ' 2 2 7 5 t ) - ( 0 . 0 9 8 1 e " ° - 5 8 7 6 t ) H-2 : [ f V t J - M . H ^ . H = ( 0 . 0 2 2 0 e - ° ' 0 9 4 9 t ) + ( 0 . 9 5 3 0 e " ° - 2 2 7 5 t ) - ( 0 . 9 7 5 0 e ' ° - 5 8 7 6 t ) - 98 -3.14 The change in in tens i ty of H-2 as a resu l t of a se lect ive 180° pulse applied simultaneously to H-l and H-3. Each of the experimental points (o) i s the average of four measurements. The so l i d curve is obtained through eq. [3.1] using the Pii-va lues derived the non-selective pulse experiment (Table 3.3). The equation for the s o l i d curve i s : [M^tJ-M^-n/M^-) = ( 0 . 3 3 1 1 e - ° - 0 9 4 9 t ) + ( 0 . 7 6 3 4 e - ° ' 2 2 7 5 t ) - ( 1 . 0 9 4 5 e " ° - 5 8 7 6 t ) - 99 -3.1 5 The change in intens i ty of H-3 as a resu l t of a se lect ive 180° pulse applied simultaneously to H-l and H-2. Each of the experimental points (A) i s the average of four measurements. The s o l i d curve is obtained through eq. [3.1] using the p-jj-values derived from the non-selective pulse experiment (Table 3.3). The equation for the so l i d curve i s : [M i (t ) -M i (^)]/M.(co) = - ( 0 . 1 1 6 4 e - ° - 0 9 4 9 t ) - ( 1 . 1 8 9 5 e _ 0 - 2 2 7 5 t ) - ( 1 . 0 7 3 1 e " ° - 5 8 7 6 t ) - 100 -3.16 The change in intens i ty of H-l as a resu l t of a se lect ive 180° pulse applied simultaneously to H-2 and H-3. Each experimental points (o) i s the average of four measurements. The s o l i d curve is obtained through eq. [3.1] using p-jj-values derived from the non-selective pulse experiment (Table 3.3). The ' equation for the so l i d curve i s : [ M . t - M . M I / M . H = ( 0 . 1 7 0 6 e " ° - 0 9 4 9 t ) + ( 0 . 0 4 7 0 e ~ 0 > 2 2 7 5 t ) - ( 0 . 2 1 7 6 e " ° - 5 8 7 6 t ) - 101 -3.10 Conclusion The data reported here have demonstrated for the f i r s t time that se lect ive proton s p i n - l a t t i c e re laxat ion rates can provide a quant itat ive measure of the solut ion geometry of diamagnetic molecules. - 102 -CHAPTER 4 PROTON SPIN-LATTICE RELAXATION RATES MEASURED AT 400 MHz: A QUANTITATIVE DETERMINATION OF THE GEOMETRY OF DIAMAGNETIC MOLECULES IN SOLUTION. 4.1 Introduction The preceding chapter has c l ea r l y demonstrated that proton sp in-l a t t i c e relaxation rates can provide a convenient method for probing the solution geometry of a complex organic molecule. This chapter w i l l now provide further confirmatory evidence to support that contention. According to the formalism of the dipole-dipole mechanism shown in eq. [ 4 . 1 ] 4 0 2 2 (assuming (to.+oj.) T . . << 1), the relaxat ion contributions made by a deu-teron (I.=l) to an adjacent proton should be M5% of that of a proton 3 (I.=1/2) located at the same pos i t i on , i . e . 2 HH 6 Yjj = 0.063 31 -33 Thus, comparison of the proton R^-values of a "normal" organic mole-cule with those of i t s s p e c i f i c a l l y deuterated analogs should provide a d i rect method for ident i fy ing and measuring indiv idual interproton relaxa-t ion contr ibut ions, the p. .-values. This chapter w i l l i l l u s t r a t e how th is approach can be used to quan-t i t a t i v e l y evaluate interproton relaxation contributions and hence i n t e r -proton distances for a complex spin system. The accuracy, v a l i d i t y and - 103 -l im i t a t i on of th i s deuteration technique w i l l be compared with those of 61 neutron d i f f r ac t i on . Furthermore, i t w i l l be shown that th i s deuteration procedure ve r i f i e s the method of se lect ive pulse perturbation discussed previously in Chapter 3. The molecules chosen for th i s purpose are 1,2, 3.4- tetra-0_-trideuterioacetyl-B-D_-arabinopyranose (2_), the corresponding 5.5- dideuterio der ivat ive (3_) and a mixture of the isomeric 5-deuterio * derivatives (4,5) . D 3 C0C0 2 R = H-5a; R' = H-5e 3 R = D-5a; R1 = D-5e 4 R = H-5a; R' = D-5e 5 R = D-5a; R' = H-5e From the 100 MHz proton n.m.r. spectrum of 2_ shown in Fig. 4.1, i t i s c lear that a simple f i r s t order treatment of the relaxation of the pro-tons in 2_ cannot be readi ly applied because several of these protons are t i g h t l y coupled (J/6 >0.2) at th i s frequency. Presently, there i s no e x p l i c i t theory avai lable for a quant itat ive analysis of the relaxation of a complex mult ispin spectrum such as the one shown in Fig. 4.1. Although 3_,4 and 5_ are drawn as the D_-isomer here for convenience, they were synthesized as the L-isomers (for deta i l s see Experimental section in Chapter 9). As far as" n.m.r. studies are concerned, th i s difference has no s i gn i f i cance. - 104 -Fig. 4.1 100 MHz proton n.m.r. spectrum of a 0.1 M solut ion of 2_ in deuteriobenzene; experimental parameters were: SW = 1000 Hz, AT = 4 sec, NT = 4, PD = 30 sec, PW (90°) = 65 ysec, SE = 4 sec. Measurement made with a Varian XL-100 (15) spectrometer at 35°C. For assignments of the proton resonances, see Fig. 4.3. Fortunately at 400 MHz (Figs. 4.2) the indiv idual resonances for the protons of compounds 2_ to 5_ are s u f f i c i e n t l y sh i f ted such that the condi-t ion J/5 <, 0.2 (Table 4.1) i s f u l f i l l e d and hence an e f fec t i ve R.-value can be defined for each of these protons. The f ine structures of the various resonance l ines are shown in Figs. 4.3 and 4.4. - 105 -Fig. 4.2 400 MHz H n.m.r. spectra of (a) ?., (b) 3, and (c) 4 and 5_. Spectral parameters were: ( a j SW = 1800 Hz, AT = 9, PD = 30 sec, PW(53°) = 5 ysec, NT = 40, LB ( l ine broadening) = 0.0 Hz; (b) and (c) as in (a) except NT = 64. Measure-ments performed on a Bruker WP-400 spectrometer at 30°C. - 106 -Fig. 4.3 400 MHz H n.m.r. spectrum of 2 measured in the pulse F.t. mode with resolution enhancement to show the long-range sp in-spin couplings ( 0 . 5 Hz); the free induction decay ( f . i . d . ) was mul t ip l ied by exp (-JK), where j = 0 to n-1 for an n-point f . i . d . , K = TT.LB/2.SW, LB = -0.6 Hz. Other spectral parameters were as in F ig. 4.2 (a). - 107 -10 Hz Fig. 4.4 400 MHz 'H n.m.r. spectra of 3^ , 4_ and 5_ measured in the pulse F.t. mode to show longe-range spin-spin couplings and deuterium induced i sotopic s h i f t s ; the f . i . d . was mul t ip l ied by s in ( i r j/n) where j = 0 to n-1 for an n-point f . i . d . - the s ine-be l l method of resolut ion enhancement. Other spectral parameters were as in Figs. 4.2 (b) and (c). Top, the spectrum of 3^  and bottom that of a mixture of 4 and 5* - 108 -Table 4.1 Chemical Shifts and Coupling Constants Data for the Protons of Compound 2_ Measured at 400 MHz in Deuteriobenzene Solvent (0.10M) at 30°C. Protons i , j 1.2 2.3 3.4 4.5a 4.5e 5a.5e J 1 > j ( H z ) « 3.5 10.8 3.4 1.5 2.1 13.2 401.3 65.8 59.4 732.4 790.8 58.4 J . ./6. , C 1 ,J 1 ,J 0.0087 0.16 0.057 0.0020 0.0027 0.23 ° Coupling constants between protons i and j ; + 0.15 Hz; long range couplings, not shown, are MD.5 Hz. b Chemical sh i f t s between protons i and j expressed in Hz; + 0.15 Hz. c A lso, J 2 3 / 6 3 4 = 0.18 From Fig. 4.4, i t can be seen that at the high f i e l d used, the magni-tudes of the deuterium-induced isotope sh i f t s were s u f f i c i e n t to ensure the separate resolut ion of the t rans i t ions of the H-3 resonances of com-pounds 4_ and 5_. As we w i l l see l a t e r , th i s induced s h i f t i s pa r t i cu l a r l y important with regard to the evaluation of interproton relaxation c o n t r i -butions for 2_. The numerical values for the deuterium-induced proton chemical sh i f t s in compounds 3_ to 5_ are given in Section 4.9. - 109 -4.2 Evaluation of p-.-values from Deuteration Experiment The non-selective Revalues for the protons of 2_ to 5_ were measured 21 using the two-pulse inversion-recovery sequence as shown in Fig. 4.5 for 2_. These values are summarized in Table 4.2. Table 4.2 Non-Selective Spin-Latt ice Relaxation Rates 3 (10~ 3 s e c - 1 , + 5%) for Compounds 2_ to 5_ Measured at 400 MHz in Deuteriobenzene Solution (0.1 M) at 30°C. R O C O C D 3 2, R = H-5a; R' = H-5e — — . / 3 3. R - D-5a; R' = D-5e D3C0C0 O C O C D 3 -^-0C0CD 3 2 4, R = H-5a; R = D-5a; R' = D-5e R' = H-5e Compound H-l H-2 H-3 H-4 H-5a H-5e 2 201 210 283 402 1119 973 3 174 187 191 170 - -4 ., h b 264 k 310 -5 181 203° 211 288° - 186 c ' I n i t i a l slope values determined between 0.001 and t sec of the magnetiza-t ion recovery curve (semi-log p l o t ) , with t taken to: 2_, 0.60 sec; 3_, 3.00 sec; 4 and 5_, 1.40 sec. The errors are taken as twice the largest standard error (2.5%) in the least-squares f i t of the experimental curve. ""Only average Revalues for these resonances of the two isotopomers could be evaluated because not a l l the ind iv idual t rans i t ions were separately resolved. - 110 -30.0 J.JL . 5.0 JUL JJL 2.5 0.8 f— 04 T V 0 0 1 s e c Fig. 4.5 P a r t i a l l y relaxed H n.m.r. spectra (400 MHz) of 2_ depicting the inversion-recovery sequence of measuring non-selective Ri - v a l u e s . Experimental parameters were: SW = 1800Hz, AT = 9 PD = 30 sec, Pl(90°) = 8.5 M sec , P2(180°) = 17 P s e c , NT = 4, LB = 0.0 Hz, A l = 1, Temperature = 30°C and the various t-values are shown on the r ight of the respective spectra. sec, - I l l -From the non-selective Revalues given in Table 4.2, the various p. .-values for 2 can be calculated with the help fo eq. [4.2]. Consider the interproton relaxation contr ibution of protons i and j in a molecule. Then f ^ i H - j + p i other protons } + p i = R l < n s ' ^ I f proton j i s replaced by a deuterium eq. [4.3] becomes p i D - j + f p i other protons + = RJ (ns, D-j) [4.4] Equations [4.2] to [4.4] can now be combined to give P . . = 0.6959 R^ns, H-j) - R^(ns, D-j) [4.5] As an example of the use of th i s expression, consider the ca lcu lat ion of p 5a5e ' Subst itut ing the Revalues of H-5a of compound 2 and compound 4^  -3 -1 into eq. [4.5], one obtains in units of 10 sec , p5a5e = 5 6 3 ± 4 0 S imi la r l y the R-j-values of H-5e of 2_ and 5_ gives, p5e5a = 5 4 8 * 3 4 Since P 5 a 5 e = p 5 e 5 a ' ^ ""s o n 1 v reasonable to use the mean of these two values, i . e . P 5 a 5 e = 555 ± 26 Without going into deta i l s the other appropriate p^-values where i = 1 to 4 and j = 5a and 5e can be obtained s i m i l a r l y . These values are summarized in Table 4.3. - 112 -Table 4.3 The p . . - v a l ue s 3 (10 sec" ) where i = 1 to 5a or 5e and j = 5a ^ 3 and 5e fo r Compound 2_. Protons i , j P i j 1, 5a 14 + 8 2, 5a c 8 ± 5 3, 5a 50 ± 8 4, 5a d 8 1 + 6 5e, 5a 555 ± 26 1, 5e 5 ± 12 2, 5e c 8 ± 5 3, 5e b 14 ± 8 4, 5e 81 ± 6 9 The propagation of errors in p . --values was calculated based on a 5% error in the measured Revalues. b A l l 1,3 ax ia l -equator ia l relaxat ion assumed equal; a reasonable assumption in view of the experimental errors . c d ' Only an average value for p 2 5 g and P25e> a n d P45a a n d could be calculated because of degenerate t rans i t i ons . - 113 -Table 4.3 only l i s t s p. ^ va lues where i = 1 to 5e or 5a and j = 5a and 5e. The p..-values for the set of protons {i,j> = (1 to 4} cannot be determined d i r e c t l y from th is pa r t i cu la r deuteration experiment. However, these values can s t i l l be evaluated in the fol lowing way. The p..-values for { i , j } = {1 to 4} is best calculated by examining ^ 3 the ^ -va lues of 3. Before performing these evaluations, i t i s useful to make the fol lowing observations. The re la t i ve d i spos i t ion of the four protons is "symmetric" such that one would expect the R^-values of H-l and H-4, and those of H-2 and H-3 to be very nearly i d e n t i c a l . This i s summarized in Fig. 4.6 below. -3 -1 Fig. 4.6 The non-selective R e v a l u e s of 3_ in units of 10 sec . Rigorous analysis (e.g. see eq. [2.47]) cannot be applied here because the system is underdetermined; a to ta l of s i x p^ -va lue s to be extracted from a set of four experimentally measured R e v a l u e s . However an examina-t ion of the geometry of 3^  can lead to some s impl i fy ing assumptions which w i l l then permit the evaluation of the relevant p. .-values. Of the s i x p.j ..-values i t i s very reasonable to assume that P ^ % 0 and that p-^ % P-^ £ p35 e- Remembering that ^ s already determined (Table 4.2), a l l that is needed now is the evaluation of p ^ , p^^ and p ^ from the four exper i -mental Revalues. As an example, consider the evaluation of P . ^ from the - 114 -non-selective Revalue of H-4 in 3. The relaxation contributions that H-4 give r i se to R^ ~ (ns) in 3_ can be wr itten as f ( P 3 4 + P 2 4 > + p4D-5a + p4D-5e = R ? ~ 4 ( n s ) [ 4 - 6 ] where p^ % p 3 5 e ' a n d p4D-5a a n c l p4D-5e c a n b e o b t a i n e c l f r o m p 4 5 a a n d P 4 5 e by using eq. [4.2]. The values for P 3 5 E > P ^ 5 A a nd p ^ Q are given in Table 4.2. Equations s im i l a r to [4.6] can be wr itten to evaluate the P 2 3 - and p-| 2-values using the non-selective Revalues of H-3 and H-2, respect ive ly, and the value of p . ^ determined from eq. [4.6]. These p '^.-values are summarized in Table 4.4. Table 4.4 - 3 -1 p.--values (10 sec ) Compound 3_. for ( i ,j} = {1 to 4} Calculated from p12 p 23 p34 p 13 p24 93 ±17 18 ±14 93 ±9 14 ±8 14 ± 8 4.3 Proof of Isotropic Motion Before the various p. . -values can be used for distance calculat ions i t i s important to perform a qua l i ty control experiment to estimate the tumbling motion of 2^  and i t s deuterated analogs. The carbon-13 R^-values of 2 are summarized in Table 4.5. - 115 -Table 4.5 Carbon-13 n.m.r. Parameters 9 for 2_ in Deuteriobenzene (0.76M) at 35°C. C-l C-2 C-3 C-4 C-5 6(ppm, ±0 .1 ) b 90.7 67.4 67.6 68.9 62.9 R ^ l O ^ s e c " 1 , ±6%) C 1320 1240 1260 1320 2630 13 c _ { 1 H } n.0 .e . , (%, ± 8 ) d 102 102 101 101 100 Measurements made with a varian CFT-20 spectrometer. Experimental para-meters were: for chemical s h i f t s and relaxation measurements, SW = 4000 Hz, DP = 8K, AT = 1 sec, NT = 200, PW(90°) = 20 ysec, PD = 4.0 sec, SE = -0.4 sec Al = 1, for n.O.e. measurements a l l parameters as above except NT = 600. The carbon-13 resonances were assigned unequivocally through se lect ive proton decoupling; the chemical s h i f t values were referenced to CfiD set at 128.1 ppm downfield from internal TMS. The erros were taken to be twice the largest standard error (3.0%) in the least-squares semi logarithmic l i nea r f i t of the experimental data (10 data points) . Measured with the gated decoupling technique. - 116 -The n.O.e. data given in Table 4.5 indicate that the s p i n - l a t t i c e relaxa-t ion of a l l the protonated carbons occurs exclus ively v ia the dipole-dipole mechanism. Although the two carbons (C-1 and C-4) having equator ia l ly oriented protons appear to relax faster than the other two carbons (C-2 and C-3) having a x i a l l y oriented protons, the rate enhancements are neg l ig ib ly small and hence, i t can be safely inferred that 2_ tumbles i s o t r op i c a l l y . This contention is further supported by the fact that a l l the C-H bond lengths for the s i x C-H vectors of the pyranose r ing are very nearly ident ica l as shown in Table 4.6 Table 4.6 The C-H Bond Lengths ^rui^), f°r Compound 2 s from Neutron D i f f ract ion Measurement.°1 Bond r C H ( A , + 0.01) C-H (1) 1.10 C-H (2) 1.09 C-H (3) 1.11 C-H (4) 1.11 C-H (5a) 1.11 C-H (5e) 1.11 Mean 1.10 Neutron d i f f r a c t i on measurements were made on 1,2,3,4-tetra-0_-acetyl-B-D-arabinopyranose. - 117 -Thus, using the mean r e v a l u e of 1.10 + 0.01 A and the mean R^-value - 3 -1 of (1295 + 37) X10 sec , the i sot rop ic corre lat ion time for 2_ in a 0.76 M solut ion of deuteriobenzene at 35°C is calculated to be (6.37 + 0.18) X10 " 1 1 sec r a d - 1 . 4.4 Evaluation of Interproton Distances Having established that 2_ tumbles i s o t r op i c a l l y the p. .-values calcu-3 lated in Tables 4.3 and 4.4 can now be used to calculate interproton d i s -tances. Since the relaxation of H-5a and H-5e i s the most e f f i c i e n t , p5a5e W ^ ^ e u s e d t 0 n o r n i a l ' ' z e a 1 1 t n e other p^.-values. j U _ = ^ a 5 e ^ { i , j } = {l to 5aand5e} [4.7] 5a5e p i j The values calculated according to eq. [4.7] are l i s t e d in Table 4.7. These values are compared to those obtained by neutron d i f f r a c t i on in Table 4.8. The data in Table 4.8 show that the calculated interproton distances f o r 2 are in close agreement with those obtained in the s o l i d state by neutron d i f f r a c t i o n . This suggests that 2_ in deuteriobenzene at 30°C favours e s sent ia l l y the same ^ - con f o rma t i on as i t does in the s o l i d s tate. Parenthet ica l l y , i t i s worth noting that the v i c i na l 1H-^H couplings of 2 are also consistent with the conclusion as shown in Fig. 4.8. - 118 -Table 4.7 The Ratio of Interproton Distances, r../Tr ^ , for Compound 2 as Calculated from eq. [4.7]. 1 J b a b e Protons i , j r. . r5a5e r. . (A) a i j ' 2,5a 2,5e 2.03 ± 0.21 b 3.65 ± 0.38 3,5a 1.49 ± 0.04 2.68 ± 0.07 3,5e 1.85 ± 0.18 3.33 ± 0.32 4,5a 4,5e 1.38 ± 0.02 b 2.48 ± 0.04 l,5e 2.19 ± 0.88 C 3.9 ± 1.6 1,2 1.35 ± 0.04 C 2.43 ± 0.07 2,3 1.77 ± 0.23 C 3.19 ± 0.41 3,4 1.35 ± 0.02 c 2.43 ± 0.04 a ° Calculated by assuming that i " 5 a 5 e = 1.80 A b Only the average value could be determined for these protons because the i r resonances were not separately resolved for the isotoDomers and 5_. Calculations based on the assumption that p n ^ = p0A = p Q see Table - 119 -Table 4.8 Comparison of Interproton Distances (ft) fo r Compound 2 as Obtained from Proton R,-values and from Neutron D i f f ract ion Measurements. Protons o Interproton Distances, r. -(A) i ,J i , j From R-j-values 9 From Neutron D i f f b % Di fference 2,5a 3.97 -8 2,5e 3.65 ± 0.38 3.99 -9 3,5a 2.68 ± 0.07 3.64 +2 3,5e 3.33 ± 0.32 3.81 -13 4,5a 2.38 +4 4,5e 2.48 ± 0.04 2.53 -2 1,5e 3.9 ± 1.6 4.06 -4 1,2 2.43 ± 0.07 2.49 -2 2,3 3.19 ± 0.41 3.08 +4 3,4 2.43 ± 0.04 2.45 -1 5a,5e - 1.80 -1,5a 3.65 -9 2,4 3.33 ± 0.32 d 3.85 -14 9 From Table 4.7 b Neutron d i f f r a c t i on measurements were made on 1,2,3,4-tetra-0-acetyl-3-D_-arabinopyranose with an estimated error of ±0.01 A. ~ - 120 -Expressed as a % difference from the neutron d i f f r a c t i on value. It was assumed p 1 5 a = p^ = p 3 5 e i ^ r 1 5 a = = r 3 5 e in order to derive p. .-values for { i , j } = {1 to 4}. F ig. 4.7 The v i c i na l H- H couplings of 2 measured at 400 MHz. Thus the couplings ^ a r | d ^3 4 a r e charac te r i s t i c of the gauche or ienta-t i o n , J . and J . r are typ ica l of the D-arabino configuration while the H,ba 4,oe — large value of 3 i s a c lear ind icat ion that H-2 and H-3 have a trans-d iax i a l d i spos i t ion . 4.5 S ingle-Select ive Pulse and Proof of Dipole-Pi pole Mechanism Following the procedure given in Chapter 3, intercomparison of the i n i -t i a l s lope, non-selective R^-value for the H-l resonance of compound 2_ H-l - 3 - 1 {R-|" (ns) = 201 x 10" sec" } with the s ing le - se lect i ve value H-l % - " 3 - 1 {R-j (H-l) = 134 x 10 "sec ), gave a precise ra t io of 1.50. This served to confirm that H-l and, by inference, the other protons a l l relax exclus ively v ia the d ipole-dipole mechanism. The s ing le - se lect i ve inversion of the H-l t rans i t ions i s shown in F ig. 4.8. Furthermore, s im i l a r intercomparison H-l -3 -1 for the H-l resonances of compounds 4 and 5 {R, (ns) = 181 x 10 sec , - 121 -1 Fig. 4.8 Proton n.m.r. spectrum (400 MHz) of 2_ showing the se lect ive inversion of the H-l t rans i t i ons . This spectrum was obtained at time t = 0.01 sec a f te r the appl icat ion of the se lect i ve 180° pulse (13 msec, decouple attenuation -29 dB); SW = 2000 Hz, AT = 4 sec, NT = 4, PW = 8.5 ysec (90° monitoring pulse), LB = 0 Hz, A l = 1 . - 122 -F^ - 1(H-1) = 120 x 1 0 " 3 s e c - 1 } , giving a ra t io of 1.51, not only provides addit ional support for the above conclusion but also suggests that the protons at C-5 contribute very l i t t l e relaxation to H- l . 4.6 Evaluation of p..-values v ia Double-Selective Pulse Measurements. LJJ z = It i s evident from Fig. 4.2a that compound 2_ i s pa r t i cu l a r l y suited for a demonstration of the v a l i d i t y of the use of double-selective pulse in ident i f y ing interproton relaxat ion contr ibutions. This i s important because this method can be used to measure di rect ly some of the interproton relaxation contributions of 2_, e.g. p-, ^ a ndp-| y which could only be i nd i r e c t l y estimated vi a the deuteration method. Thus, the double-selective R-j-values for H-5a, H-5e; H- l , H-2; and H- l , H-3 are summarized in Table 4.9; the experiments themselves are t yp i c a l l y i l l u s t r a t e d in F ig. 4.9. Table 4.9 Double-Selective Revalues ( 1 0 " 3 s e c _ 1 , ± 5%) for Some of the Protons of 2. Experiment Proton H-i H-l H-2 H-3 H-4 H-5 R" 1 (H - l ,H - 2 ) a 175 191 - -R " - i (H - l ,H - 3 ) a 136 200 -Ry" 1 (H-5a,H-5e) - 986 912 a I n i t i a l slope: 0.01 < t < 1.6 sec b I n i t i a l slope: 0.001 < t < 1.0 sec - 123 -a 0.01 sec - I J U L 0.01 sec 3 1 V 0.001 sec Fig. 4.9 These spectra show the double-selective inversion of (a) H-l,H-2; (b) H-l,H-3; and (c) H-5a,H-5e of compound 2 at 400 MHz. Experi-mental parameters were: (a) Select ive pulse centred at 6-j ^/2t 14 msec, modulated at 200 Hz with attenuation set at ' -22 dB; (b) se lect ive pulse centred at S-| 3/2, modulated at 233 Hz and the other values as in (a); (c) se lect ive pulse centred at 6 5a 5 e / 2 ' 2 " 6 m s e c ' " 1 7 d B attenuation; a l l other parameters as in Fig. 4.8, and the t-values are shown on the r ight of the spectra. - 124 -From the double- and non-selective R,-values, the p. . -values can be ca lcu-lated according to eq. [4.8], p i j = 1 {R\(~i>^ ' 2 [ R J ( n s ) - R J ( i , j ) ] } + \ C R ^ ( i J ) - 2[R 1(ns) - RJ ( i , j ) ] } [4.8] and these values are l i s t e d in Table 4.10. Table 4.10 The Pn-.-values Calculated from the Double-Selective Pulse Experiment for Compound 2_. Protons p.. ( 10 " 3 sec _ 1 ) i , j 1,2 92 ± 14 1,3 13 ± 15 5a, 5e 503 ± 70 Comparison of the data of Table 4.10 with those of Table 4.4 shows that the p ^ _ and p^ -va lue s obtained from the d i rect double-selective experiments are in excel lent agreement with those obtained from a simple analysis of the non-selective proton R e v a l u e s of the 5,5-dideuterio der ivat ive, 3_, despite the large error in p ^ - This not only supports the v a l i d i t y of the method used in deriving the various p^ -va lues l i s t e d in Table 4.4 but also serves to ver i fy the correctness of the interproton distances, r.. for { i , j } = {1 to 5a and5e), given in Table 4.7. More - 125 -importantly, the Pg a g g -value obtained from the double-selective pulse experiment is in good agreement with that derived from the deuteration -3 -1 experiment; the double-selective p 5 a 5 e " v a l u e (503 x 10 sec ) i s only -3 -1 ^10% lower than that from the deuteration experiment (555 x 10 sec ). This experimental d i f f e r e n t i a l i s equivalent to a ^1.7% difference in the interproton distances determined by these two methods. This observation provides d i rect support for the v a l i d i t y of the use of se lect ive pulse experiments in i dent i f y ing interproton relaxat ion contr ibut ions. The e f fect of an off-resonance f i e l d on resonances that are close to the se lect ive pulse w i l l now be considered. In p r i n c i p l e , for weak pulses such as the se lect ive pulses used in th is thes i s , the actual bandwidth (in Hz) of the pulse i s approximately given by A v * T [4.9] P where i p i s the duration (in sec) of the pulse. Since the se lect ive pulse i s normally arranged such that the chemical s h i f t of the spin to be i r rad ia ted is at the midpoint of the bandwidth of the pulse, any resonance that i s within ±Av/2 Hz from the pulse would be expected to experience an off-resonance f i e l d a r i s ing from the se lect ive pulse. In p ract i ce , due to the occurrence of "harmonics", the off-resonance f i e l d extends beyond Av/2 Hz from the pulse. From the author's experience th i s e f fect generally becomes undetectable for resonances 1/xp Hz away from the pulse. On this basis the pract ica l l i m i t used in th i s thesis for the exclusion of off-resonance f i e l d ef fects was taken to be + 1/ T D Hz from the pulse. Further discussion on the choice of Xp-values w i l l be given in Chapter 9, Section 9.1. For the se lect ive inversion of H- l , H-2 and H- l , H-3 in th i s study, the duration of the se lect ive 180° pulse used was 14 msec ( i . e . Av = 71 Hz). - 126 -Since the chemical s h i f t differences for H-2, H-3 and H-4 are ^60 Hz (see Table 4.1), some off-resonance f i e l d e f fect could have occurred. An experimental check for th is was made by monitoring the changes in the inten-s i t i e s of those t rans i t ions close to the se lect ive pulse. Thus, when H-l and H-2 were se lec t i ve l y perturbed, a small (^5%) decrease in the "equi -l i b r ium" intens i ty of H-3 (but none for H-4) was observed in spectra measured not too long a f te r the appl icat ion of the se lect ive pulse. This implies that a small off-resonance perturbation had been experienced by H-3 but not by H-4. For the. double-selective inversion of H-l and H-3 a s im i l a r change in the "equi l ibr ium" i n tens i t i e s for both H-2 and H-3 was observed; with a decrease of ^1% for H-2 and a decrease of ^4% for H-4. On the basis of the data reported here, i t appears that such small off-resonance per-turbations do not introduce any unacceptably large systematic errors in the determination of and admittedly, the error in p ^ i s large. Since the H-5a and H-5e resonances experience substantial chemical sh i f t s from the other resonances (>700 Hz, see Table 4.1), se lect ive inver-sion of those resonances could be conveniently performed with a s ingle but more intense se lect ive 180° pulse centred about the midpoint of the i r chemical s h i f t d ifference ( i . e . 5e 7 2 ^ " T ' 1 U S W 1 ' t ' 1 a 5 e 1 e c t i v e pulse duration of 2.6 msec ( i . e . Av% 385 Hz) a l l the t rans i t ions for H-5a and H-5e were su i tably inverted without any detectable off-resonance f i e l d e f fec t on any of the other resonances. 4.7 Evaluation of P. .-values v ia T r ip le -Se lect i ve Pulse Measurements. L3 y  It i s c lear from the chemical s h i f t data of Table 4.1 and the preceding discussion (section 4.6) that double-selective inversion of any two of the three spins H-2, H-3 and H-4 cannot be carr ied out without an appreciable - 127 -off-resonance e f f e c t . However, since the chemical sh i f t s of these three protons are quite close 60 Hz) to each other and the i r resonances are resonably separated (> 400 Hz) from those of the other protons, i t should be possible to invert the i r t rans i t ions with a s ingle and intense se lect ive 180° pulse as used for the se lect ive inversion of H-5a and H-5e. Accord-ing ly , the t r i p l e - s e l e c t i v e Revalues for H-2, H-3 and H-4 were measured (Fig. 4.10) with x = 2.6 msec ( i . e . Av ^385 Hz), and these values are summarized in Table 4.11. Table 4.11 The Tr ip le -Se lect i ve Spin-Latt ice Relaxation Rates ( 1 0 " 3 s e c _ 1 , +5%) for H-2, H-3 and H-4 of Compound 5. Experiment H-2 H-3 H-4 R ^ V l . H ^ S ) 177 242 345 From the non-selective (Table 4.2) and the t r i p l e - s e l e c t i v e (Table 4.11) R,-values of H-2, H-3 and H-4 the various p..-values relevant for these three protons can be calculated according to eqs. [4.10] 1 1 0 p 23 RH" 2 1 0 1 p24 _ 2 3 RH" 3 [4.10a] 0 1 1 p34 RH- 4 where R "^1* = R^ 1 (H-2,H-3,H-4) - 2[R l, ," i(ns) - R^-1' (H-2,H-3,H-4)] [4.10b) for H-i = H-2, H-3, H-4. - 128 -u mn Fig. 4.10 Proton n.m.r. spectrum (400 MHz) of 2 showing the se lect i ve inversion of the H-2, H-3 and H-4 t rans i t ions ( t r i p l e - s e l e c t i v e pulse). The se lect ive 180° pulse was centred at <5_ J2, duration 2.6 msec, attenuation -17 dB; other spectral parameters were: SW = 2000Hz, AT = 8 sec, NT = 8, PW = 8.5 (90° monitoring pulse), LB = 0.2 Hz, Al = 1, t = 0.01 sec. - 129 -These results are summarized in Table 4.12. Table 4.12 The p.^-values (10~ 3 sec _ 1 ; ±25) for H-2, H-3 and H-4 of Compound 2_ Calculated from eqs. [4.10]. p 23 p 24 p 34 13 ± 25 61 ± 25 93 ± 25 \ Comparison of the data of Table 4.12 and those of Table 4.4 reveals that one of the p^ -va lue s ( P 2 4 ) derived from the t r i p l e - s e l e c t i v e pulse experiment i s in considerable e r ro r . One obvious source for th i s error i s the influence of an off-resonance f i e l d and, as expected, the "equ i l ibr ium" in tens i ty for H-l was found to be decreased by ^20% for times close to the appl icat ion of the se lect ive pulse. No intens i ty changes were observed for H-5a and H-5e. A s im i l a r , but smaller, error i s also observed in the -3 -1 p ^ 3 -values; a value of 13 x 10 sec being derived from the t r i p l e --3 -1 se lect ive pulse data as compared to a value of 18 x 10 sec obtained previously. Note however, that the estimated errors for the t r i p l e -se lect ive pulse experiment are very much larger than those of s ing le- and non-selective pulse experiments. Nevertheless, i t i s interest ing to note that th i s off-resonance f i e l d has no detectable e f fect on the relaxation interact ion of H-3 and H-4; the P 3 4 -value calculated from the t r i p l e -se lect ive pulse experiment i s in excel lent agreement with that obtained -3 -1 previously, both values being 93 x 10 sec . This i s not surpr is ing because both H-3 and H-4 receive very l i t t l e relaxation contr ibution from H-l which, being much c loser to H-2, i s the major contr ibutor to - 130 -the relaxation of H-2. Thus, any non-equilibrium condition which occurs in H-l would have a s i gn i f i can t influence on the relaxation of H-2 and consequently p. .-values involv ing H-2 would be expected to be in er ror . 4.8 "Dynamic range" Limitations Although the propagation of experimental errors in the d ipolar relaxation rates through the inverse s ixth root ca lcu lat ion works in favour of the experimental ist, the determination of interproton distances by the relaxat ion method can suf fer from "dynamic range" l im i ta t i on s . Thus the mutual relaxation between H-5a and H-5e i s so much more e f f i c i e n t than those interact ions which are of the same magnitude as p^^ o r weaker, that the accuracy with which these weaker interact ions can be determined experimentally, suffers accordingly. The s i tuat ion is depicted in Fig. 4.11. From this f igure and the p. .-values determined e a r l i e r i t can be ' J seen that p. . -values which are about 10 times smaller than p . ^ , can be I j D a oe determined accurately, while p..-values that are 25 times smaller than p,, ,- , can only be determined with poor accuracy. This i s a serious l im i t a t i on which, unfortunately, cannot beavoided. Of course, such l im i ta t ions are not present in s o l i d state s t ructura l studies by the neutron d i f f r a c -t ion technique. 4.9 Deuterium-induced Proton Chemical Shi fts A further advantage of making measurements at 400 MHz was that the deuterium-induced changes in the chemical sh i f t s of many of the protons could be accurately measured (see Fig. 4.4.). Aside from f a c i l i t a t i n g the conformational assignment of 2_, these values have a s igni f icance in t he i r own r i ght , and the i r numerical values are summaried in Table 4.13. 131 iikA 0.5h 0' 4.11 J i ' j i i i J i i i i I i J I I L 20 25 Plot of some representative rat ios of interproton distances ( r i k / r i j ) versus the inverse rat ios of interproton relaxation contributions {pi^/pi^) for compound 2_ showing the "dynamic range" of d ipolar i n te ract ion . The points for p-^, P34 and p45e ^ n 0 * s n o w n a r e between b and c; while other weaker interac-tions are beyond the point d. Table 4.13 Deuterium Isotope-Induced Chemical Shifts of Proton- i , A6j(± 0.15 Hz, or ± 0.004 ppm) a, fo r the Deuterio Compounds 3, 4_ and 5_ Relative to Those of the Prot io Compound 2 Measured at 400 MHz T30°C). Deuterium Isotope Shifts Compound Hz H-l ppm H-2 Hz ppm H-3 Hz ppm H-4 H-5 Hz ppm Hz ppm H-5e Hz ppm 3 2.4 0.0060 2.7 0.0067 2.1 0.0052 4.4 0.0110 -4 0.8 0.0020 1.0 b 0.0025 b 0.4 0.0010 2.2 0.0055 6.3 0.0157 -5 1.4 0.0035 1.5 b 0.0037 b 1.5 0.0037 1.9 0.0047 5.8 0.0145 a AS. = 6. (protio) - &. (deuter io); hence a l l the values given here correspond to h i gh - f i e l d s h i f t s . b May be interchanged. - 133 -In every instance, the introduction of a deuterium substituent at carbon-5 resulted in a s h i f t to h i g h - f i e l d . Without going into a detai led discuss-ion of these resu l t s , several intercomparisons are noteworthy. Especial ly in terest ing i s the f inding that the sh i f t s are add i t i ve ; those of the d i -deuterio derivatives 3_ are e s sent ia l l y the same as the sum of those of the mono-deuterio derivatives 4_ and 5_. Also noteworthy i s the induction of a s h i f t of 0.0012 ppm into the H-2 resonance by a proton-deuterium i n te r -change 4.0 A away and the fact that deuteration at H-5a induces a bigger s h i f t into H-3a than does i t s counterpart at H-5e; th i s l a t t e r observation implies a distance dependence which corresponds to the re la t i ve ordering of the other induced s h i f t s . However, there is no ind icat ion for the existence of a simple re lat ionship between the sh i f t s induced in a proton and i t s separation from the deuteron causing this "isotope e f f e c t " ; see Table 4.14. 4.10 Conclusion The proton relaxation studies described in th is chapter and the previous one suggest that proton R e v a l u e s can y i e l d remarkably accurate information concerning the solut ion geometry of complex organic molecules. Since the method i s best applied to molecules having e s sent ia l l y f i r s t order spectra i t provides a useful complement to studies of molecules p a r t i a l l y oriented by a nematic phase l i q u i d c r y s t a l , for which high i n t r i n s i c molecular symmetry i s a general prerequis i te. - 134 -Table 4.14 Comparison of Deuterium Isotope-Induced Chemical Shifts of Proton-i and the Internuclear Separations Between Proton-i and the Deuteron for Compounds 4 and 5_. Proton Compound 4 Compound 5_ i A6. (ppm)a A6. (ppm)a 1 0.0020 4.06 0.0035 3.65 2 0.0025 3.99 0.0037 3.97 3 0.0010 3.81 0.0037 2.64 4 0.0055 2.53 0.0047 2.38 a ±0.0004 ppm (see Table 4.13). The proton-deuteron distance i s assumed to be the same as the proton-proton distance; ±0.01 A (see Table 4.8). - 135 -CHAPTER 5 STUDIES OF MOLECULAR ROTATIONAL DIFFUSION OF CARBOHYDRATES IN SOLUTION 5.1 Introduction As part of th i s work to develop the measurement of proton s p i n - l a t t i c e relaxat ion rates (Revalues) as a ve r sa t i l e method for estimating i n t e r -proton distances for organic molecules in solut ion we have already shown that i t i s imperative to have an experimental protocol to establ i sh whether or not such derivatives tumble i s o t r o p i c a l l y . In th is chapter the use of carbon-13 s p i n - l a t t i c e relaxat ion rates to probe the rotat ional d i f fus ion in aqueous solut ion of several mono- and di-saccharides w i l l be given in 38 34 d e t a i l . Although Grant et a l . and Void et a l . have recently developed sophist icated relaxation experiments that can lead to a more complete 62 descr ipt ion of rotat ional d i f f u s i on , the conventional measurement of proton-decoupled carbon-13 spectra described here appears to provide relaxation data which are en t i r e l y adequate for most semi-quantitative studies of organic molecules; i t i s also relevant to note that most molecules have spectra 38 34 which are too complex for the techniques proposed by Grant and Void. The carbon-13 s p i n - l a t t i c e relaxation rates of the fol lowing mono-and di-saccharides in aqueous ^ O ) solution have been determined at 21 20 MHz by the conventional two-pulse inversion-recovery sequence : a- and B-D-glucopyranose (6), a- and 3-D-gal actopyranose (7_), methyl a-D-galactopyranoside (8), methyl 3-D-galactopyranoside (9_), a - and 3-lactose {4-0_-(3-D_-galactopyranosyl )-a-D_-glucopyranose and 4-0-(e-D_-galacto-pyranosyl )-B-D_-glucopyranose} (JOJ, a- and 3 -cel lobiose {4-0-(g-D-glucopy-ranosyl )-a-D-glucopyranose and 4-0-(3-D-glucopyranosyl)-3-D-glucopyranose} ( U J , a - and 3-maltose {4-0_-(a-D-glucopyranosyl)- a -D-glucopyranose and - 136 -4-0_-(a-D_-glucopyranosyl )-3-D-glucopyranose) (1_), methyl 3-D-lactoside {methyl 4-0-(3-D-galactopyranosyl )-3-D-glucopyranoside} (_3), methyl 3-D-cel 1 obioside {methyl 4-0_-(-3-D-glucopyranosyl)- 3-D-glucopyranoside} (14), a ,a-trehalose{a-p_-glucopyranosyl-a-D-glucopyranose} {)5), 6-0- (3-D-glucopyranosyl )-a-D-galactopyranose-6 ,6-d2and6-0-(3-D-glucopyranosyl )-3-D-galactopyranose-6 ,6-d^ (1_ ) , l a c t i t o l {4-0-(3-D_-galactopyranosyl )-D_-glucitol} (20), and ma l t i to l {4-0-(a-D-glucopyranosyl )-D-glucitol} (2_). These data have been interpreted in terms of the motional corre lat ion times and rota-t iona l d i f fus ion constants using Woessner's rotat ing r i g i d e l l i p s o i d 54 model . For both the mono- and di-saccharides the a and 3 anomers appear to tumble with approximately the same rates. But whereas some of the monosaccharides appear to tumble i s o t r o p i c a l l y , or nearly so, the d i s -accharides tumble an i so t rop ica l l y with the ra t i o of the two pr inc ipa l rotat ional d i f fus ion constants (D||/Dj_) varying between 1.37 for a-maltose and 2.03 for a- lactose. These rat ios appear to be in good agreement with 51 calculat ions based on the Perrin-Stokes-Einstein-Debye hydrodynamic d i f fus ion method. As w i l l be seen, i t was found that the use of carbon-13 s p i n - l a t t i c e relaxation rates as a motional probe can suf fer from certain l imi tat ions and as a resu l t a complementary probe was sought. This w i l l bring the discussion of th i s chapter to a consideration of quadrupolar s p i n - l a t t i c e relaxation of deuterons as a measure of the rotat ional d i f fus ion of molecules in so lut ion. * The carbon-13 Revalues of th i s compound were not measured because th-sample was too d i l u t e ; only i t s carbon-13 chemical s h i f t s were measu - 137 -5.2 General Theory I: Carbon-13 Spin-Latt ice Relaxation and Molecular Reorientation 6 3 It i s now well documented that the s p i n - l a t t i c e relaxation of most carbons bearing hydrogen substituent(s) occurs exc lus ive ly via the dipole-dipole mechanism. Although the s p i n - l a t t i c e relaxation of proton-coupled carbon-13 resonances can in p r inc ip le be complicated by nonexponential behaviour (due mainly to cross-relaxat ion with the proton(s)) the re laxa-t ion of most f u l l y proton-decoupled resonances i s known to be exponential*. It i s a t r i v i a l matter to prove experimentally (e.g., by gated proton decoupling^ 8) whether or not the relaxat ion of a pa r t i cu la r carbon resonance is mediated exclus ively via the dipole-dipole mechanism; i f i t i s , and i f the molecule is tumbling i s o t r op i c a l l y in the extreme narrowing reg ion** , then the relaxation rate of that carbon nucleus has the form shown in eq. [5.1] 2 2 2 R i ( i 3 c ) = V W L T C H [ 5 J ] rCH where the meanings of the various symbols have already been given in eq. [2.68] in Section 2.13 of Chapter 2. Thus, i f there are no var iat ions in C-H bond lengths and no addit ional degrees of internal motion for any * Another contr ibution to nonexponential behaviouris mult ispin (or cross-) corre lat ion between two d ipolar relaxation vectors e.g. between the two C-H relaxat ion vectors in a methylene carbon (>CH2), or between a C-H and an H-H relaxation vector where the proton that relaxes the carbon-13 nucleus i s being relaxed by other proton(s) in the molecule. Fortunately th is mult ispin corre lat ion can be compensated for by monitoring the evolution of the tota l in tens i ty of the magnetization of the resonance in question (see Chapter 2). * * 13 1 Support of th i s assumption comes from the facts that (a) the C-{ H} n.O.e. i s 100% and (b) the motional corre lat ion time for a l l the molecules studied here are in the range 10-12 < T „ < 10_9 s e C s and w r = 20 MHz, a) H = 80 MHz. L H L - 138 -part of the molecule, there should be a d i rect re lat ionship between the observed relaxation rate and the number of d i r e c t l y bonded protons (e.g. the relaxation of a methylene carbon should be twice as fast as that of a methine carbon). The experimentally determined R-j-value can be converted to the motional cor re lat ion time ( i sot rop ic ) by subst i tut ing in eq. [5.1] appropriate values of a l l of the constants. Thus for a C-H bond length of 1.10 & the re lat ionsh ip i s 2 ' 0 3 2 V 1 3 C > . n 10 H - l r , ? 1 iru = — J x 10 sec rad L5.2] un n |_| In the l i m i t of rotat ional d i f fus ion the corresponding i so t rop ic rotat ional d i f fu s ion constant can be readi ly calculated according to D = 1/6T c h [5.3] For a molecule which is tumbling an i sot rop ica l l y the s i tuat ion i s considerably more complex and fo r a proper understanding of the carbon relaxation rates i t i s necessary to refer to the prescient paper by 54 Woessner . He derived an e x p l i c i t expression that can be applied to the d ipolar carbon-13 s p i n - l a t t i c e relaxation rate (measured under conditions of complete proton decoupling) of a molecule shaped as a r i g i d e l l i p s o i d and undergoing anisotropic rotat ional d i f f u s i on , in terms of the three pr inc ipa l rotat ional d i f fu s ion constants, D x, D y and D_, given previously in Section 2.4 of Chapter 2. Although th i s model i s i dea l l y suited in many ways for the molecules under consideration here th i s author has chosen for a number of reasons to use a somewhat s imp l i f i ed treatment, also 54 • •, proposed by Woessner in which the molecule i s now regarded as a symmetrical r i g i d e l l i p s o i d , for which the rotat ional d i f fus ion constants (Dj_) about - 139 -two axes are i d e n t i c a l , but d i f fe rent from that about the th i rd axis (D|j). The reasons for the choice of th is simpler model are as fo l lows: 1. The model based on three d i f fe rent d i f fus ion constants requires more independent experimental measurements than are avai lable from the sugars of in teres t here and the calculat ions require complex computer f i t t i n g procedures. Furthermore, even when s u f f i c i e n t data are avai 1 able for a complete numerical so lu t ion , there i s no independent method or model whereby the chemical meaning of the d i f fus ion constants could be assessed; and the pr inc ipa l interest of the present study i s not so le ly to obtain numerical data. 2. In contrast, the ca lcu lat ion of the two-parameter model can be performed with a simple computer program or manually, and the mono- and di-saccharides of interest provide s u f f i c i e n t data fo r e x p l i c i t numerical analyses. Furthermore, the overal l chemical v a l i d i t y of the d i f fus ion constants obtained by th i s method can be checked by independent calculat ions based on various hydro-dynamic d i f fus ion models, thus enabling some chemical ins ight to be incorporated into the study; and th i s l a t t e r point i s regarded as a mandatory one. Woessner's equation for the rotat ing r i g i d e l l i p s o i d model with D, = D„ = Dw i D, = D M i s given in eqs. [5.4] for a C-H vector: - 140 -A = 1 (3 c o s V l ) ' 2 . 2 B = 3 cos esin 9 3 • 4, C = J s in e (6D±) •1 x B= (D,,+ BD^)" 1  T = (4D,,+ 2 0 ^ [5.4b] [5.4c] [5.4d] [5.4e] [5.5f] [5.4g] where a diagrammatic representation of the d ipos i t ion of the C-H bond with respect to the three pr inc ipa l axes i s given in the in se r t . Note that th i s expression (eq. [5.4a]) includes in addition to the usual parameters of the dipole-dipole relaxation mechanism, three corre lat ion t imes*, x^, x D , x r , which are defined in terms of the two rotat ional d i f fu s ion con-D C stants (D M, Dj_) as given in eqs. [5.4e] to [5.4g], and e , which i s the angle enclosed by the C-H vector and the pr inc ipa l axis of rotat ion. ^ t T ^ h e difference between Woessner's de f i n i t i on of cor re lat ion times and that of the more conventional one that i s used in th is thes i s , see Section 2.4 of Chapter 2. - 141 -Inspection of eqs. [5.4] immediately reveals an alarming potential l im i t a t i on to the carbon-13 method for probing i so t rop ic motion. I f a l l  the e-values for a molecule happen by chance to be ident i ca l then the carbon-13 R^-values w i l l be ident ica l even i f the molecule is tumbling an i so t rop i ca l l y , assuming there i s no var iat ion in the C-H bond lengths. As w i l l be seen l a t e r , certa in disaccharides exh ib i t precisely th is l i m i t a t i o n . Furthermore, i t can be inferred from eqs. [5.4] that carbon-13 R-j-values would be s i g n i f i c an t l y less sens i t ive to anisotropic reor ienta-t ion for certain values of e. For example, when 6 = 90° the B-term of eq. [5.4a] vanishes and thus reduces the s e n s i t i v i t y of the carbon-13 method as a measure of anisotropic motion. The dependence of carbon-13 59 Revalues on the values of 9 have been studied by Anet et a l . and the i r results are reproduced in F ig. 5.1. F ig. 5.1 Calculated carbon-13 R-| rat ios as a function of the tumbling or spinning ra t i o DM/DJ_ for four values of e [54.7° (magic angle), 60°, 90°, and 109.5°]. - 142 -However, i f the various C-H bonds of the molecule do subtend two or more d i f fe rent angles to the pr inc ipa l axis of rotat ion then i t i s possible to solve eq. [5.4a] e x p l i c i t l y in terms of a l l three unknown quant i t ies , D||, Dj_ and 6. Since the angles are usually not known(which i s the case that pertains to the carbohydrate systems), the most sensible approach i s to a r b i t r a r i l y assign the d i rect ion of the pr inc ipa l axis (and hence the e-angles) and to numerically ca lculate values for D^and D .^ These calculat ions can be repeated for various values of e and the outcome of these calculat ions can be displayed graphical ly as in F ig. 5.2 which i s a p lot of the ra t io D||/Dj_ versus e. As w i l l be discussed l a t e r , one of the pr inc ipa l l im i ta t i ons of th i s approach i s the i n s e n s i t i v i t y of Djj/rjj_ to changes in e for the carbohydrate systems studied here. An independent evaluation of the value of D||/Dj_ derived from the carbon-13 R-j-values can be obtained by ca lcu lat ion based on various hydrodynamical models fo r rotat ional d i f fu s i on . The use of the Debye-51 Stokes-Einstein-Perr in hydrodynamic model for rotat ional d i f fus ion with " s t i c k " boundary condition w i l l now be discussed. The rotat ional d i f fus ion constant about the i t h pr inc ipa l axis (D..) can be related to the f r i c t i o n constant (£.) of the hydrodynamic drag on an e l l i p s o i d a l body rotat ing about that axis in a viscous medium according to D. = I1 , i = x, y , z [5.5] where k i s the Boltzmann constant and T i s the absolute temperature. If a l l three semi-axes of the e l l i p s o i d are of d i f fe rent lengths a, b, c the ^ are functions of e l l i p t i c i n tegra l s ; these expressions can be found 54 54 in Woessner's paper . For an a x i a l l y symmetric e l l i p s o i d where b = c, one finds - 143 -8-i 1 1 1 1 1 1 0 10 20 30 40 50 £(C-H e q u o t o r i a|) (degrees) Fig. 5.2 P lot of D||/Dj_versus (C-He), the angle subtended between the equator ia l ly oriented C-4'-H-4' bond and the pr inc ipa l axis of rotat ion for methyl B-D-lactoside (13), based on the Woessner equation (eqs.[5.4]) with _ the assumptions that r C H = 1.10 A, and that the sum e(C-He) and e(C-Ha) i s 109°28' (see eq. [5.8]). [Note that D||/Dj_ is e s sent ia l l y indeterminate for 6 > 45°; further discussion w i l l be given l a te r in the tex t . ] - 144 -S = 5 = 327rnb2(a2-b2) [ 5 - 6 a ]  z 1 1 6a-3b^S s [ 5 . 6 b ] wi th 3(2a -b^)S-6a .2 u2Ni< - in { ^ 2 _2,J_ 5 = - ^ ^ *  a + ( a - b Y 2 >» a > b [5.6c] .2 , 2 X % b S - 2 , , t a n " 1 ! <b I a ^ }, b > a [5.6d] (b 2 - a 2 p a where n is the shear v i scos i ty of the l i q u i d . Although i t i s now known that th i s theory overestimates the drag coef f i c ient s by an order of 64 magnitude in many cases and various other improved theories have been proposed, i t appears to be a reasonably adequate model for the tumbling motion of mono- and oligo-saccharides in aqueous solut ion because of the presence of strong solute-solvent intermolecular interact ion through hydrogen bonding. Hence, th i s simple model w i l l be used here. 54 Equations [5.5] to [5.6] can now be combined to give : b 1 - (D„/DL ) 4 (D | |/D L) 2[1-(D | |/D 1) 2 - = ~ / 5 L5.7aJ 9 [2-(D||/DL)^]S'-2 2-(D||/DLrS' where S1 = a S. [5.7b] Equation [5.7a] i s graphical ly presented in Fig. 5.3. Observe that for b/a > 1 (disk-shaped molecules) D||/Dj_ exhib its only a small var iat ion with large changes in b/a. - 145 -Fig. 5.3 Plot of the ra t i o D||/Dj_ versus b/a for a r i g i d e l l i p s o i d a l body (shown in the insert ) rotat ing in a viscous medium as described by the Debye-Stoke-Einstein-Perrin hydrodynamic model. - 146 -5.3 Results and Discussion I: Carbon-13 Spin-Latt ice Relaxation The same experimental protocol was applied to a l l the substances 13 1 studied. The C- H nuclear Overhauser enhancement factors of a l l carbon resonances were determined using the gated decoupling technique of Freeman et a l w i t h integrat ion to give signal i n ten s i t i e s . The spectra in F ig. 5.4 of methyl B-D-lactoside (1_3) are typ ica l examples of 13 1 C- ; H} n.O.e. measurements; in fact integrat ion was performed on i n d i v i -13 1 dual resonances, e.g., the measurement of C-{ H} n.O.e. for C-l and C - l ' of 1_3 i s shown in F ig. 5.5, and the n.O.e. values for the other resonances were obtained in the same way. It was convenient to measure a l l of the carbon-13 relaxation rates using the two-pulse inversion-recovery sequence and Fig. 5.6 shows spectra which are typ ica l of the general qua l i ty that were obtained. The Revalues were calculated using the same semi logarithmic l i near least-squares f i t as was used for the calculat ions of proton R^-values. 13 1 The Reva lues , the C-{ H> n.O.e. factors and the chemical sh i f t s (6) for several series of mono- and oligo-saccharides (1.0 molar) in aqueous ^ 0 ) solut ion at 35°C are summarized in Tables 5.1 to 5.4 and t he i r proton-decoupled carbon-13 n.m.r. spectra are shown in Figs. 5.7 to 5.11. A l l chemical s h i f t values are quoted as being downfield from external tetramethylsi lane (TMS); they were measured with respect to internal acetone, the chemical s h i f t of which was set as being 31.1 ppm downfield from external TMS. - 147 -Fig. 5.4 Proton-decoupled 20 MHz carbon-13 n.m.r. spectra of methyl 3-D-lactoside (1.0M) in D20 at 35°C; top, with 13c-{lH} n.O.e.; boT/tom, without 1 3 C-{ 1 H} n.O.e. Both spectra were obtained with a Varian CFT-20 spectrometer using the fol lowing i n s t ru -mental parameters: SW = 2000 Hz, AT = 0.5 sec, PW (90°) = 20 ysec, NT = 1200, PD = 5.0 sec, SE = -0.4 sec, Al = 1. - 148 -1.1' Fig. 5.5 C-{ H} n.O.e. measurements for C-l and C - l 1 of compound 13. These spectra are es sent ia l l y those o f Fig. 5.4, showing only the region around C-l and C - l ' . Due to poor resolut ion the n.O.e. for C-l and C-T have been measured together. - 149 -Fig. 5.6 P a r t i a l l y relaxed 20 MHz carbon-13 n.m.r. spectra of methyl 8-D-lactoside (1.0M) in D2O at 35°C showing use of the two-puTse inversion-recovery sequence (180°-t-90°) for measurement of s p i n - l a t t i c e relaxat ion rates. These spectra were obtained with a Varian CFT-20 spectrometer using the fol lowing parameters: SW = 2000Hz,AT =2 sec, TT (180°-pulse) = 40 ysec, PW (90°-pulse) = 20 psec, NT = 300, PD = 0 sec, SE = -0.4 sec, Al = 1, and the t -values are shown on the r ight of each spectrum. Table 5.1 Carbon-13 Chemical Shifts, 6(ppm, ±0 .1 ) a , Spin-Lattice Relaxation Rates, (10" sec" , ±50), and ^C-^H} Nuclear Overhauser Enhancement Factors (in Parenthesis, %, +8) for Monosaccharides in Aqueous Solution (1.0 M) at 35°C. C-l C-2 C-3 C-4 C-5 C-6 0CH3 Compound a B 6 92.8 96.6 72.2C 74.8 73.5 76.4 70.3d 70.3d 72.2C 76.6 61.4 61.5 D-Glucopyranose (6) R l 970 830 910 870 980 940 940 940 910 920 1640 1720 (n.O.e.) (99) (99) (97) (99) (99) (100) (98) (98) (97) (102) (98) (98) 6 93.0 97.1 69.1 72.6 69.9 73.5 70.0 69.4 71.1 75.8 61.9 61.7 D-Galactopyranose ~ n ) R, 810 870 830 860 910 900 920 1010 890 920 1600 1370 (n.O.e.) (98> ( 9 8 ) ( 9 8 ) ( 9 7 ) ( 9 9 ) ( 1 0 0 ) ( 9 9 ) ( 1 0 0 ) ( 9 9 ) ( 9 7 ) ( 9 8 ) ( 1 0 0 ) Methyl c-D- 6 1 0 0 - 4 6 9 ' 3 7 0 , 5 7 0 ' 3 7 1 , 7 6 2 " 3 5 6 J galactopyranoside R l 960 980 970 960 990 1470 360 Methyl a - £ - 6 104.9 71.8 73.8 69.7 76.2 62.0 58.2 galactopyranoside — — — — (i) R1 840 910 890 1090 980 1550 380 - 151 -Table 5.1 (cont 'd) Chemical sh i f t s referenced to internal acetone set at 31.1 ppm downfield from external TMS. For assignment of carbon-13 resonances, see refs . 65 and 66. b The n.O.e. for compounds 8 and 9_ were not measured; i t i s safe to assume that the relaxation mechanism for the carbons of these two compounds i s completely d ipo lar . c,d These resonances overlapped. Table 5.2 Carbon-13 Chemical Shifts, (ppm, ±0 .1 ) a , Spin-Lattice Relaxation, (10 3sec , ±200), and C-{ H} Nuclear Overhauser Enhancement Factors (in Parenthesis, %,±8) for Five 1,4-Linked and One 1,1-Linked Disaccharide in Aqueous Solution (1.0 M) at 35°C. Compound C-T C-2' C-3' C-4' C-5' C-6' C-' 1 C-2 C-3 C-4 C-5 C-6 0 C H 3 a B a B a B a B a B a B 6 104.0 72.1 73.7 69.7 76.4 62.2 92.9 96.9 72.3 75.0 72.6 75.5 79.7 79.6 71.2 75.9 61.3 B 61.3 B Lactose (10) RT (n.O.e.) 4120 (99) 4050 (97) 3920 (102) 4730 (100) 3970 (97) 5010 (100) 5180 (98) 3510 (102) 3920 4020 (99) (100) 3650 3850 (102) (97) 3720 (101) 4010 (100) 3820 (100) 3860 (97) 7810 7810 (100) (100) 6 103.3 73.9 76.3 70.3 76.7 61.4 92.6 96.5 72.0 74.7 72.1 75.1 79.6 79.5 70.9 75.5 60.9 C 60.9 C Cellobiose (ID R ] (n.O.e.) 3700 (102) 3600 (100) 3680 (99) 3800 (100) 3630 (101) 6380 (98) 4890 (100) 3260 (100) 3730 3730 (98) (98) 3970 3810 (98) (101) 4200 (99) 4200 (99) 3750 (100) 4020 (100) 7880 7880 (97) (97) 6 100.5 73.4 73.7 70.2 72.5 61.4 D 92.6 96.6 72.1 74.7 73.9 76.9 78.3 78.0 70.7 75.3 61.4 D 61.4 D Maitose (n,0.e.) 3770 (100) 3750 (101) 3820 (100) 3740 (99) 4110 (98) 5630 (101) 4210 (99) 2860 (99) 3830 3230 (99) (100) 3350 3480 (99) (98) 4000 (100) 3640 (100) 3480 (100) 3470 (100) 5630 5630 (101) (101) Methyl 6  B-D-103.5 71.5 73.1 69.1 75.9 61.6 103.6 73.4 75.0 79 .1 75 .3 60.8 57.8 lactoside (13) R1 (n.O.e.) 4010 (100) 4030 (102) 4040 (100) 4900 (100) 4250 (98) 5670 (98) 3970 (100) 4130 (98) 3960 (98) 4180 (100) 4000 (100) 7600 (97) 1150 (IOO-Methyl s e-£-103.4 74.0 76.4 70.3 76.8 61.4 103.9 73.7 75.5 79 .6 75 .2 60.9 SS.o cellobio- R-j (n.O.e. 4430 ) (100) 4730 (100) 4290 (102) 4410 (100) 4270 (103) 8210 (100) 4250 (102) 4230 (99) 4210 (100) 4680 (100) 4380 (100) 9190 (100) 1290 (97) a ,a- 6 94 .2 72.2 * 73.6 70 .9 73 .1 61.7 Trehalose M (n.5]e. ) 4570 (100) 4420 (100) 4670 (100) 4570 (98) 4680 (99) 7420 (100) - 153 -Table 5.2 (cont 'd) a Chemical s h i f t s referenced to internal acetone set at 31.1 ppm downfield from external TMS. For assignment of carbon-13 resonances, see refs. 66 to 69. Note that the carbon-13 resonances for the non-reducing ring are degenerate (corresponding to the a and £ anomers at the reducing carbon atom). b,c,d Overlapping resonances. Table 5.3 Carbon-13 Chemical S h i f t s , 6(ppm, ± 0 . 1 ) a , Sp in -Lat t ice Relaxation Rates, R . ( l O ' ^ e c " 1 ' ±200) , and 1 3 C-{ ] H} Nuclear Overhauser Enhancement Factors ( in Parenthesis, %, +8) for Three l ! 6-Linked Disaccharides in Aqueous Solut ion (1.0 M) at 35°C. Compound C - l ' C '4 ' C -1 C-2 C- 3 C-4 C-5 C-6 C-2' C-3 1 C '5 1 C '6 ' a 8 a e a 8 a 8 a 8 a 8 6 103.4 73.8 76.6 d 71. l f 76.4 d ' S 61.6 92.8 96.7 73.5 74.8 73.7 76.4 e 7 0 . 3 f ' 9 70.3 f* 5 7 2 . 2 75.6 69.41 69.4 h tienti oDiose (J6) R l (n.O.e, 2970 .) ( 9 8 ) 3030 (100) 2900 (102) 3360 (100) 2910 (100) 5530 (100) 3120 (101) 3290 (102) 3590 3410 (100)(98) 3430 (99) 2910 (100) 3370 (98) 3370 (98) 3190 3610 (102)(99) 6360 (99) 6360 (99) 6 98.9 69.9 1 70.2 j 69.2 71.6 61.8 92.9 96.8 72.1 74.8 73.7 76.6 6 9 . 9 i , k 70.2^ 70.8 1 , k75.0 66.6 1 66.6 1 Melibiose (11) R l (n.O.e. 2920 ) (100) 3210 (98) 3600 (100) 3600 (100) 3480 (102) 3680 (98) 2980 (102) 3150 (100) 3130 3170 (100)(102) 3350 (98) 3140 (102) 3210 (98) 3600 000 ) 3420 3440 (100)(98) 5980 000) 5980 (100) 18 b 6 103.4 73.9 76.4 70.4 76.7 61.6 93.1 97.2 69.0 72.6 69.8 73.4 70.0 m 69.6 7 0 . l n 74.5 7 0 . f 70.0 m R1 (n.O.e. 2110 j (101) 1890 (100) 2080 (99) 2120 (100) 2140 (98) 3950 (100) 2190 (102) 1890 (99) 1970 1920 (98) (98) 1880 (100) 1910 (97) 2750 (100) 2090 (100) 2590 2130 O00K97) 2590 (100) 2750 (100) 103.3 73.9 76.4 70.4 76.7 61.5 93.1 97.2 69.0 72.5 69.7 73.4 69.9 69.6 70.1 74.4 - 155 -Table 5.3 (cont 'd) a Chemical sh i f t s referenced to internal acetone set at 31.1 ppm down-field from external TMS. For assignment of carbon-13 resonances see: ]6_, ref. 68; 17, ref. 70 - th is reference gave a very poor assignment for 1_7, thus many of the resonances were reassigned here by comparison with the other sugars; 18 and 19_, assigned here for the f i r s t time. Note that the carbon-13 resonances for the nonreducing r ing are degenerate (corresponding to the a and B anomers at the reducing carbon atom). b Compounds 1_8 are the a and 6 anomers of 6-0_-(B-D-glucopyranosyl )-D-galactopyranose. The carbon-13 R,-values of 1_8 —were measured at 0\5 M; estimated error ±150 x 10~3sec~^ , c Compounds 1_9 are the a and 3 anomers of the 6,6-dideuterio (reducing r i ng ) analogs of 1_8. Only chemical sh i f t s were measured for th is compound because the sample was too d i lu te (^ 0.1 M) for carbon-13 relaxation measurements. d, f,k May be interchanged. e, g,h,i,j,1,m,n Overlapping resonances. Table 5.4 Carbon-13 Chemical Shifts, 6(ppm, ±0.1 ) a , Spin-Lattice Relaxation Rates, R1(10"3sec" , ±200), and 13 1 1 C-{ H) Nuclear Overhauser Enhancement Factors (in Parenthesis, %, ± 8 ) for Lactitol and Maltitol in Aqueous Solution (1.0 M) at 35°C. Compound c-r C-2' C-3 ' C-4 ' C-5' C-6' C-l" C-2" C-3" C-4" C-5" C-6" 6 104.1 7 2 . 3 7 3 . 6 6 9 . 8 76.1 62 .1 6 3 . 8 7 2 . 2 7 0 . 6 8 0 . 4 7 3 . 3 6 3 . 2 Lactitol ( 2 0 ) R 1 (n.O.e.) 3690 ( 1 0 2 ) 3360 ( 9 7 ) 3840 ( 1 0 0 ) 4140 ( 1 0 0 ) 3640 ( 1 0 1 ) 4000 ( 1 0 0 ) 4670 ( 9 8 ) 3050 ( 9 8 ) 3910 ( 1 0 2 ) 4010 ( 1 0 1 ) 3460 ( 1 0 0 ) 5220 ( 1 0 2 ) 6 1 0 1 . 6 7 3 . 8 7 4 . 0 7 0 . 6 7 2 . 7 B 6 1 . 6 6 4 . 0 7 2 . 7 B 7 1 . 6 8 2 . 9 7 3 . 6 6 3 . 5 Maltitol ( i i ) RT (n.O.e.) 3810 ( 1 0 0 ) 3670 ( 1 0 2 ) 3790 ( 1 0 2 ) 3 8 9 0 ( 1 0 0 ) 3620 ( 1 0 2 ) 6 6 5 0 ( 1 0 2 ) 3920 ( 1 0 0 ) 3620 ( 1 0 2 ) 3520 ( 1 0 0 ) 3570 ( 1 0 1 ) 3830 ( 9 8 ) 4 1 3 0 ( 9 8 ) Chemical shifts referenced to internal acetone set at 31.1 ppm downfield from external TMS. For assignment of carbon-13 resonances, see:2i, ref. 71; 20, assigned here for the f i rs t time. - 157 -CHjOH SB 150 Hz 150 Hz OCH> 2i.O Hz OCH 3 Fig. 5.7 Proton-decoupled 20 MHz carbon-13 n.m.r. spectra of (a) D-glucopyranose, (b) D-galactopyranose, (c) methyl a-D-galactopyranosideT a n d ( d) methyl B-D-"ga1actopyranos'ide in aqueous (D90)~so1ution (1.0 M) at 35°C. These spectra were obtained with a Varian CFT-20 spectrometer using the fol lowing parameters: SW = 2000 Hz, AT = 1 sec, PW(90°) = 20 ysec, NT = 200, PD = 3 sec for (a) and (b), and 10 sec for (c) and (d), SE = -0.4 sec, Al = 1. - 158 -Fig. 5.8 cont 'd - 159 -5.8 Proton-decoupled 20 MHz carbon-13 n.m.r. spectra of a series of 1,4-1 inked disaccharides in aqueous (D2O) solut ion (1.0 M) at 35°C; (a) lactose, (b) ce l lob iose, (c) maltose, (d) methyl 8-D_-cellobiosides and (e) a,otrehatose (a 1,1-linked disaccharide). These spectra were obtained with a Varian CFT-20 spectrometer using the fol lowing parameters: SW = 2000 Hz,AT= 2 sec, PW(90°) = 20 psec, NT = 300 for (a) to (d), 200 for (e), PD = 0 sec, SE = -0.4 sec, Al = 1. For the spectrum of methyl g-D-lactoside, see Figs. 5.4 and 5.6. ~~ - 160 -5'*3B 1P 180 Hz 4' 4o+4p 60 + 6P 3'* 4$ 13 6Q»6P Fig. 5.9 Proton-decoupled 20 MHz carbon-13 n.m.r. spectra of a series of 1,6-linked disaccharides in aqueous (D2O) solut ion (1.0 M) at 35°C; (a) gentiobiose and (b) melibiose. These spectra were obtained with a Varian CFT-20 spectrometer using the fol lowing parameters: SW = 2000 Hz, AT = 2 sec, PW(90°) = 20 ysec, NT = 600 for (a) and 300 for (b), PD = 0 sec, SE = -'0.4 sec, Al = 1. - 161 -. 5.10 Proton-decoupled 20 MHz carbon-13 n.m.r. spectra of (a) 6-0_-((3-D-glucopyranosyl )-D-galactopyranose (0.5 M) and (b) 6-0_-(S-TJ-glucopyranosyl )-TJ-galactopyranose-6,6-0^ (^0.1 M) in aqueous (D^O) solut ion at 35°C. Both spectra were obtained with a Varian CFT-20 spectrometer and the parameters used were: (a) SW = 2000 Hz, AT - 2 sec, PW(90°) = 20 ysec, NT = 800, PD =. 0.25 sec, SE = -0.4 sec, Al = 1; (b) SW = 1500 Hz, AT = 1 sec, PW(90°C) = 20 ysec, NT = 47000, PD = 0 sec, SE = -0.4 sec, Al = 1. - 162 -CH2OH 230 Hz 2% 5' CH20H 220 Hz Fig. 5.11 Proton-decoupled 20 MHz carbon-13 n.m.r. spectra of (a) l a c t i t o l and (b) ma l t i to l in aqueous (D2O) solut ion (1.0 M) at 35°C. These spectra were obtained with a Varian CFT-20 spectrometer using the fol lowing parameters: (a) SW = 2000 Hz, AT = 1 sec, PW(90°) = 20 ysec, NT = 300, PD = 1 sec, SE = -0.4 sec, Al = 1; (b) as in (a) except, SW = 4000 Hz and NT = 200. - 163 -The f i r s t questions to be answered were "whether there i s any substan-t i a l d ifference between the overal l rotat ional d i f fus ion constants of mono- and di-saccharide der ivat ives " and "whether the a and 6 forms of a sugar behave i d e n t i c a l l y " . These comparisons were most simply made by recasting the R^-values given in Tables 5.1 to 5.4 as average Revalues for the appropriate sugars as l i s t e d in Tables 5.5 to 5.8. Table 5.5 Average Carbon-13 Revalues ( lCf^sec" , ±50) for Monosaccharides as Calculated from the R,-values in Table 5.1. Compound Average 9 Carbons Having Equatorial. C-H Bonds C-l C-4 a 933 970 . -D-Glucopyranose = ( i ) 3 890 a 877 810 920 D-Galactopyranose = a) „ 888 1010 Methyl a-D-960 galactopyranoside 980 960 (8) Methyl e - ID-gal actopyranoside ( i ) 905 - 1090 a 0n ly the r ing carbons are considered in the averaging; Ri-values of over-lapping resonances involv ing a and £ anomers, and Revalues of carbons having an equatorial hydrogen substituent ( l i s t ed separately) are not included in the averaging. - 164 -Table 5.6 Average Carbon-13 Revalues (10 sec , ±200) for 1,4-Link D i -saccharides as Calculated from the R] values in Table 5.2. Reducing Ring Non-Reducing Ring Compound Average 9 Carbons t o r i a l Having Equa-C-H Bond Average 9 Carbons to r i al Having Equa-C-H Bond C-l C-4 C - l ' C-4' a Lactose (10) 3 3778 3850 5180 -4015b 4015b - 4730b 4730b a Cellobiose ( l i ) B 3817 3705 4890 -- - 3682b 3682b a Maltose (12) 3 3665 3336 4210 — 3855b 3855b 3770b 3770b -Methyl 3-D-l a c t o s i d e -(11) 4048 - - 4082 4900 -Methyl 3-D-cellobiosTde ( l i ) 4350 • - - 4426 - -a ,a-Trehalose c (15) 4585 4570 - - - -a 0n ly the r ing carbons are considered in the averaging; R-j-values from unresolved resonances are not included in the averaging. bNote that these values are from unresolved resonances of the a and 3 anomers. a,a-Trehalose i s a 1,1-linked disaccharide; due to symmetry the carbon-13 resonances of the two rings are i d e n t i c a l . - 165 -Table 5.7 Average Carbon-13 Revalues (10 sec , ±200) for 1,6-Link Disaccharides (1.0 molar) as Calculated from the Revalues in Table 5.3. 1 Reducing Ring Non-Reducing Ring Compound Average Carbons Having Equa-a t o r i a l C-H Bond C-l C-4 Average' Carbons Having Equa-t o r i a l C-H Bond C-l C-4' Gentiobiose (16) a 3403 3 3437 3120 3000L 3000 Melibiose (IZ) a 3240 3 3225 2980 3480L 3480t 2920L 2920t 3600L 3600 6-0 r 3-£-Glucopyranosyl-D-galactopyranose = (18) a 1875 1988 2190 d 2090 2086 2086 Only the r ing carbons are considered in the averaging. Revalues of unresolved and ambiguous resonances are not included in the averaging. Note that these R]-values are from unresolved carbon-13 resonances of the a and 3 anomers. At 0.5 molar in aqueous so lu t ion , ±150. C-4a and C-63 resonances overlapped. - 166 -Table 5.8 Average Carbon-13 R-|-values (10 sec , ±200) for Lac t i to l and Ma l t i t o l as Calculated from the Revalues in Table 5.4. Carbons Having Equatorial C-H Bonds Compound Average 3 C-T C-4 Lac t i to l 3632 - 4140 (20) Ma l t i to l 3783 3810 ( i i ) Only the r ing carbons are considered in the averaging. For reasons that w i l l become apparent l a te r on in the discuss ion, these average R-j-values only include carbons having axia l hydrogen subst ituents, while carbons having equatorial hydrogen substituents are separately l i s t e d ; and in both cases only the pyranose r ing carbons are considered. It can be seen that there is a substantial (^ 4- fo ld at 1.0 M concen-t r a t i o n , by comparing the average R-j-values given in Tables 5.5 to 5.8) difference between the overal l tumbling rates of the mono- and o l i go -saccharide derivat ives in an aqueous medium. Also, at f i r s t s ight, the a and 3 anomers of each sugar appear to behave i d e n t i c a l l y . It should be noted, however, that the interpretat ion of the data for the disaccharides such as lactose, ce l lob iose, e t c . , presents a new problem, because each of - 167 -the carbon resonances of the nonreducing rings is degenerate (corresponding to the a and 3 anomers at the reducing carbon atom), and, hence those r e -values need to be treated with some caution. The inference that one can make from the close s i m i l a r i t y in the tumbling rates of the a and 3 anomers fo r each sugar is that the R-j-values of the degenerate carbon resonances of the nonreducing rings of these disaccharides may s t i l l provide a r e a l i s t i c descr ipt ion of the motional behaviour of these molecules in so lut ion. We w i l l return to a discussion of th is l a te r . The next, and major considerations is whether or not these various sugars are tumbling i s o t r op i c a l l y . Consider f i r s t the Revalues (Table 5.1) for the indiv idual carbon atoms of D_-gl ucopyranose, D-gal actopyranose, methyl a-D_galactopyranoside and methyl 3-D-galactopyranoside. If we accept that a r e a l i s t i c estimate of the experimental error on any indiv idual value i s ^5% (twice the largest standard error in the semi 1ogarithmic l i nea r least-square f i t of the experimental data), which is equivalent to -3 -1 +50 x 10 sec , then the deviations from the mean R^-values for these mono-saccharides, as l i s t e d in Table 5.9, appear to suggest that these systems tumble i s o t r op i ca l l y or very nearly so. However, a c loser examination of the deviations l i s t e d in Table 5.9 shows that the R-j-values for C-4 resonances of 3-D-galactopyranose and methyl 3-D-galactopyranoside are enhanced (greater than twice the experimental error) re l a t i ve to the R-j-values of the other r ing carbons. There are two possible explanations for these observed enhanced relaxation rates; e i ther there i s a shortening in the appropriate C-H bond lengths or the molecules are tumbling an i so t rop ica l l y . Let us consider the f i r s t and simplest explanation for the enhanced relaxation rates of the C-4 resonances of 3-D-galactopyranose and methyl - 168 -Table 5.9 The Deviations from the Mean Revalues (10 sec" ) for the Ring Carbons of D-Gl ucopyranose, D_-Gal actopyranose and the Methyl D-GalactopyFanosides as Calculated from Tables 5.1 and 5.5 C-l C-2 C-3 C-4 C-5 Compound ct g a B a g a B a g D-Glucopyranose 37 -60 -23 -20 47 50 7 7 -23 30 = (6) D-Galactopyranose -67 -18 -47 -28 33 12 43 122 13 32 = (Z) Methyl a-D-Galacto- _ 2 Q 0 _ 1 0 _ 2 0 1 0 pyranoside" (8) Methyl B-D-Galacto- _ 6 5 5 _ 1 5 1 8 5 7 5 pyranoside (9) g-D-galactopyranoside: namely, that the C-4-H-4 bond lengths in both these two molecules are shorter than the other C-H bonds. It follows from 13 the inverse sixth-power re lat ionship between R-j ( C) and r ^ , i m p l i c i t in eq. [5.1] for an i so t rop ic tumbler and summarized graphical ly in Fig. 5.12, that the observed enhancements of 14% and 20%*. respect ive ly, fo r the C-4 resonances of B-D-galactopyranose and methyl B-D-galactopyranoside would Calculated with respect to the mean R-i-values. - 169 -5.12 Plot of per cent enhancement in carbon-13 Reva lues, AR-|/R-|, as a function of per cent shortening in a C-H bond, A r CL|/ r CL|> for an i sot rop ic tumbler in the extreme narrowing region. - 170 -require a 2.15 and 3.00% shortening of these C-H bonds; i t i s then a question of deciding i f a shortening of such magnitudes i s reasonable. According to the published neutron d i f f r a c t i on data for mono- and di-saccharides (Table 72 5.10) kindly provided by Professor G.A. Jeffrey of the University of 72 Table 5.10 Comparison of C-H Bond Lengths from Neutron D i f f ract ion Data Structure Anomeric^ C-H in Range of non-C-H in K •anomeric Ref. a-D_- Gl ucopyranose 1.095 1.092 - 1.107 73 B-L-Arabi nopyranose 1.102 1.092 - 1.102 74 Methyl a-D-Gl ucopyraTTOside 1.109 1.092 - 1.095 75 Methyl a-D-Mannopyrancside 1.102 1.101 - 1.105 75 Methyl a-D-Altropyrandside 1.105 1.094 - 1.105 76 Methyl g-D-Xylopyranoside 1.095 1.092 - 1.102 74 g-Maltose Monohydrate 1.106 1.107 - 1.111 77 - 171 -Pittsburgh Crystallography Laboratory the maximum var iat ion detected exper i -mentally does not exceed 0.02 & about the mean value of 1.10 & 1.8% va r i a t i on ) . Furthermore these var iat ions in C-H bond lengths for the 78 carbon atoms of the sugar ring are not systematic . Accordingly, the second and more plaus ib le a l ternat ive explanation was sought. Attention w i l l now be directed to methyl 3-D-lactoside and methyl 3 -D-cel lobios ide. It seems log ica l that these two compounds, which d i f f e r so le ly in the configuration at C-4 1 , should have s im i l a r tumbling motions and i t i s l i k e l y that th i s motion should have some anisotropic component. Evidence for th i s l a t t e r poss ib i l i ty i s immediately obvious in the C-4' resonance of the lactoside which, uniquely, bears an equator ia l ly oriented -3 -1 proton; i t s R e v a l u e of 4900 x 10 sec i s subs tant ia l l y higher 20%) than the mean of the R-j-values of e i ther the other carbons of the same sugar -3 -1 r i ng , 4082 x 10 sec , or of the other carbons of the other sugar r i ng , - 3 - 1 4048 x 10 sec (see Table 5.6). In contrast, the data for the ce l lob ios ide der ivat ive show no s i gn i f i c an t departures from the mean, the largest var iat ion being for C-2 ' , ^7% higher than the mean value of the carbons in the same sugar r ing or ^9% higher than that of the carbons in the other r ing . An explanation for the enhanced relaxation rate of C-4' resonance of methyl 3-D.-lactoside i s possible in terms of the Woessner model, summarized in eqs. [5.4], with several reasonable assumptions and approximations: 1. We assume that methyl 3-D-lactoside tumbles as a r i g i d ent i ty with no independent l i b r a t i o n between the two sugar r ings. This may not be absolutely true, but the mean of the R e v a l u e s fo r the two sugar rings -3 -1 -3 -1 4082 x 10 sec for the nonreducing r ing and 4048 x 10 sec for the reducing r ing (see Table 5.6) are ident i ca l within exper i -mental error and are consistent with that assumption. - 172 -2. To a f i r s t approximation we assume that the shape of methyl B-D-lactoside i s such that a l l the a x i a l l y oriented C-H vectors subtend the same angle e(C-Ha) with the pr inc ipa l axis. If we further assume that the r ing carbon atoms a l l have precisely tetrahedral bond angles then e(C-Ha) + e(C-He) = 109°28' [5.8] where e(C-He) is the enclosed angle between an equatorial C-H bond and the pr inc ipa l axis. A diagrammatic representation of the posit ions of the pr inc ipa l axes i s shown in F ig. 5.13. Fig. 5.13 A diagrammatic representation of the positions of the molecule-f ixed p r inc ipa l axes of methyl B-D-lactoside. 3. I t seems i n t u i t i v e l y reasonable that the pr inc ipa l axis of rota-t ion should l i e somewhere along the length of the molecule, and Fig. 5.13 shows this axis a r b i t r a r i l y directed between C-4 1 and C - l . Let us now consider eqs. [5.4]. Note that f o r each carbon atom there are e s sent ia l l y three unknowns e, D| | and associated with the motional cor re la t ion time of the molecule, and one experimentally determinable quantity, - 173 -13 R-j ( C) ... an impasse! Fortunately, for methyl g-JJ-lactoside we have two types of carbon, each having a d i s t i n c t relaxat ion rate and value for e, and i f we are j u s t i f i e d in assuming that eq. [5.8] i s v a l i d , this e f fec t i ve l y eliminates one of the unknowns; furthermore, i f we chose to a r b i t r a r i l y assign values for e we can calculate for each a value for both D| ( and Dj_. Adopting this approach gives a series of values for these two D-values and i t i s then a question of attempting to decide which value for e is the most appropriate one and, preferably of obtaining an independent check of th i s conclusion. The most revealing approach to the f i r s t of these objectives i s to plot the ra t io D||/Dj_ versus e as already shown in Fig. 5.2. It i s c lear that th i s re lat ionship has three d i s t i n c t regions and th i s has extremely important implications both for the outcome of other studies in th i s area as well as of the assumptions upon which the whole of this treatment has been predicated. In the f i r s t region corresponding to 0° < e < 30° the value of D^/ Dj_ i s e s sent ia l l y independent of 6 , and hence i t i s e s sent ia l l y impossible to determine an accurate value for e with any confidence. And by the same token any systematic errors introduced by the assumption of precise ly tetrahedral angles are of l i t t l e importance. In the second region for 0 > 45°, the value of D||/Dj_ varies so rapid ly with e as to be indeterminate. F ina l l y there i s an intermediate region for 30° < e < 45° where there i s a reasonable re lat ionship between Dj|/Dj_ and 6 . In the l i g h t of assumption 3 i t follows that methyl B-D-lactoside f a l l s into the f i r s t of these three categories and hence i t i s impossible to determine a precise value fo r e. A r b i t r a r i l y assigning 6(C-He) =19 028' and e(C-Ha) = 90°, and using the Revalues of the non-reducing ring (Revalue of 4900 x 10 " 3 sec _ 1 for C-4 1 and mean Revalue of 4082 x 1 0 " 3 s e c _ 1 - 174 -for the other carbons having axia l hydrogen subst ituents, see Table 5.6), 9 the calculated values for D (j and are respectively 1.01 x 10 and 0.67 x 9 -1 10 rad sec , and the ra t i o Dj(/Dj_ = 1.5. The rotat ional d i f fus ion con-stants can be converted to the rotat ional corre lat ion times according to T i = 6TJ7 ' [5.9] (see also eq. [2.29] in Chapter 2, Section 2.4) giving - 1.65 x 10~ 1 0 and = 2.47 x 1 0 " ^ S ec rad~^. Essent ia l ly the same values were obtained when the average Revalue of the reducing r ing was used. These values imply that the molecule i s tumbling anisotropical ly and somewhat faster about the pr inc ipa l axis (D||> DjJ. Furthermore, neg l ig ib le internal motion occurs about the C-1 1-0-4-C-4 g lycos id ic centre. It i s now a question of deciding i f some independent check can be made of the v a l i d i t y of th is conclusion, which quite obviously involves several somewhat c y c l i c a l steps. In the absence of independent experimental evidence, the author has resorted to calculat ions based on the Debye-Stoke-51 E inste in-Perr in model , which was summarized in Fig. 5.3 in which the r a t i o D||/Dj_ was plotted as a function of the ra t i o of the dimensions of the molecuie (b/a). Thus i f the dimensions of the molecule can be measured e i ther from molecular stereomodels or a computer simulation program then an estimate of the ra t i o D||/Dj_ would be possible by using Fig. 5.3 or eqs. [5.7]. A computer simulation program (NEWCARTf which calculates the pr inc ipal x,y, z Cartesian coordinates for a molecule was used to estimate the dimension of methyl B-D-lactoside; and the values (in A) for two rotamers about the g lycos id ic centre are shown in Fig. 5.14. For deta i l s see Appendix II. - 175 -<j> = 0° * = 0° i> = 0° * = 180° 'CH3 2.7 9.5 11.0 Rotamer A Rotamer B Fig. 5.14 The two types of rotamer about the C -V -0 -4 -C4 g lycos id ic centre of a disaccharide; rotamer A: C - l ' - H - l ' and C-4-H-4 bonds are an t i - p a r a l l e l corresponding to the conformation cj> = 0 ° , = 0° used by Lees and Skeret t ? 9 ; rotamer B: C -V -H-V and C-4-H-4 bond are pa ra l l e l corresponding to <j> = 0 ° , = 180°79. The dimensions (A) shown here are the x,y,z pr inc ipa l axes (see text) for methyl B-D_-lactoside. Calculations based on the fol lowing assumed parameters: bond length (A), C-H = 1.10, C-C = 1.52, C-0 = 1.42; bond angles, tet rahedra l ; the subst ituents, -CH2OH and -OH, assumed as point masses centred about the atoms that are d i r e c t l y bonded to the sugar rings ( in r e a l i t y , the hydroxy! pro-tons are replaced by the deuterons in D2O); and the conformation of the methyl group is set such that the 6-CH3 bond i s between the C - l -H - l and C-l-0 (ring) bonds, i .e., 60° conformation is given Chapters 6 and 7). These two rotamers were chosen on the assumption that the most favoured conformation probably l i e s between those two l i m i t s . Two estimated values for b/a are possible for each rotamer, the ra t i o of "width" to " length" (y/z) and the ra t i o of "thickness" to " length" (x/z). For rotamer A y/z = 0.52, x/z = 0.43, and in terpo lat ion of these values using F ig. 5.3 gives values of D||/Dj_ = 1.8 and 2.2 respect ively. S im i l a r l y , rotamer B gives y/z = 0.45, x/z = 0.25, which on interpo lat ion give D||/Dj_ = 2.1 and 4.6 respect ively. Compare now these values with the value of 1.5 obtained from carbon-13 R-j-values. Two inferences can be made. F i r s t , the lower D||/Dj_ - 176 -ra t i o obtained from carbon-13 R e v a l u e s may suggest that the angle enclosed by the C-4'-H-4' bond and the pr inc ipa l axis of rotat ion i s f a i r l y large, say in the region 30° < e < 45°, see F ig. 5.2. (Recall that the value D||/Dj_ = 1.5 was obtained by assuming that the C-4 1 -H-4 1 bond subtends an angle of 19°28' with the pr inc ipa l axis of rotat ion.) Second, since the D||/D^  r a t i o obtained by carbon-13 R-j-values i s c loser to that calculated for rotamer A, methyl 3-D-lactoside probably assumes a rotamer conformation which gives a larger b/a ra t i o than e i ther rotamer A or B. These two points w i l l be considered further l a t e r together with the R-j-values of lactose. It also appears that, in evaluating the b/a r a t i o , ' b ' assumes the larger of the x or y value with ' a ' taking the value of z, the largest of the three. I n t u i t i v e l y , th i s i s very reasonable; and further hydrodynamic calculat ions w i l l be based on the two largest molecular dimensions. Turning b r i e f l y to the data for methyl 3-D-cel lobios ide, we immediately note a difference in the overal l pattern of the data, with the two rings -3 -1 having c losely s im i l a r mean relaxat ion rates, 4426 x 10 sec fo r the -3 -1 nonreducing r ing and 4350 x 10 sec for the reducing r i ng , with the largest rate enhancements (^ 1%) from the mean being found for C-2 1 (4730 x 10 sec ) and C-4 (4680 x 10 sec ). Neither of these enhancements i s as large as the value previously noted for C-4' in methyl 3-D-lactoside. We shal l now discuss the data for the 1-4-linked disaccharides (Table 5.2). One problem i s immediately obvious - the carbon-13 resonances of the nonreducing rings are a l l degenerate, each cons ist ing of the two t rans i t i on l ines corresponding to the a and 3 anomers at the reducing centre. S t r i c t l y then, i t i s not possible to properly determine the i r R-j-values and without these we only have the data for the carbons of the reducing r ing . Under these circumstances i t i s not poss ible, fo r any of these der ivat ives , to evaluate whether the two rings have the same rotat ional d i f fus ion constants or whether they are tumbling an i so t rop ica l l y . - 177 -Nevertheless, some progress can be made i f we make the assumption that the a and 3 anomer of the 1,4-linked disaccharides, including the reducing and nonreducing r ing of each anomer, have the same rotat ional d i f fus ion constants. I f th i s be so and i f , as before, we assume that a l l carbons have precise ly tetrahedral hybr id i zat ion , then we can combine the R e v a l u e s 54 of the two anomers to obtain a so lut ion to the Woessner model in much the same way as for the methyl 3 -D- lactos ide. As an example consider the Revalues of lactose. Support for the assumption that the a and 3 anomers do tumble i d e n t i c a l l y comes from the close s i m i l a r i t y of the mean R-j-values of the reducing rings of the two anomers (3778 x 10 " 3 s ec _ 1 f o r the a and 3850 x l O - 3 sec " 1 for the - 3 -1 3 anomer, see Table 5.6) and within experimental er ror (±200 x 10 sec ) these values are not too d i f fe rent from the mean combined R^-values of the - 3 -1 nonreducing rings (4015 x 10 sec ). Observe that the R^-value for C-la i s 5180 xl0-3 sec \ We conclude then that both anomers of lactose tumble at approximately the same rate with the equator ia l ly oriented proton of the -3 -1 a anomer inducing an enhancement in the R^-value of C-la of 1402 x 10 sec 37%). However, the R e v a l u e of C-4' at the nonreducing r i n g , also -3 -1 bearing an equator ia l ly oriented proton, i s only 4730 x 10 sec corres-ponding to ^18% enhancement in rate re la t i ve to the mean R e v a l u e of the other carbons in the nonreducing r ing. Let us now consider some of the possible reasons for the rather substantial (ca. two-fold) difference in rate enhancements between C-la and C-4' of lactose. On the basis of the bond length data given in Table 5.11 i t i s most un l ike ly that the observed rate enhancement d i f f e r e n t i a l in C-la and C-41 of lactose arises from a difference in the C-H bond lengths at these two centres. Thus th i s difference implies that the C-l-H-1 bond of the a anomer of lactose subtends a smaller angle with the pr inc ipa l axis of - 178 -rotat ion for the molecule than does the C-4 1-H-4' bond; see Fig. 5.15 for a graphical summary of th i s e f f ec t . Applying Woessner's relaxat ion model and employing the same assumptions as used e a r l i e r for methyl 3-D-lactoside one can obtain for lactose two sets of rotat ional d i f fus ion constants. Based on the R-j-values for the reducing r ing of a - lactose one finds D|, = 1.26 x 10 9 rad s e c " 1 , Dj_ = 0.62 x 10 9 rad sec " 1 and D,|/Dj_= 9 -1 2.03, while the data from the nonreducing r ing give D||= 1.01 x 10 rad sec , 9 -1 Dj_ = 0.70 x 10 rad sec and Dj|/D|_ = 1.44. Hydrodynamic calculat ions for a - lactose giving D||/Dj_ =1.7 for rotamer A-type conformation, and D||/Dj_ = 1.9 for rotamer B-type conformation, suggest that the pr inc ipa l axis of lactose l i e s c loser to the C - l -H - l ( a ) vector than the C-4 1-H-4 1 vector. This also further confirmed an e a r l i e r suggestion that the pr inc ipa l axis for methyl 3-D-lactoside i s making a f a i r l y large angle with the C-4 1-H-4 1 vector. S imi lar data analyses to those used for lactose can be readi ly performed for cel lobiose and maltose, and the monosaccharides (3-D-galactopyranose and methyl 3-D-galactopyranoside). The results of these calculat ions are summarized in Table 5.11. In doing these calculat ions the author has simply assumed that the pr inc ipa l rotat ional axis runs along the length of the molecule together with the re lat ionsh ip expressed in eq. [5.8]. The rotat ional constants given in Table 5.11 can be converted to molecu-l a r dimensions, a/b, the ra t i o of thelongest molecule-fixed pr inc ipal axis to that of the pr inc ipa l axis with intermediate length according to eqs. [5.7] or Fig. 5.3. These values are summarized in Table 5.12 together with those values calculated from simple geometrial calculat ions as in methyl 3-D_-lactoside. We may conclude that the difference in the a/b values between those measured from carbon-13 R^-values and those predicted from geometrical ca lculat ions i s most probably due to the unknown or ientat ion of the pr inc ipa l axis of rotat ion for these molecules. - 179 -8-. • j — | , 1 1 1 0 10 20 30 40 50 # ( C - H e q u a t o r i a l ) (degrees) Fig. 5.15 Plots of D||/Dj_ versus e(C-He), where in (a) 0 i s the angle subtended between the equator ia l ly oriented C- l -H- l bond and the pr inc ipa l axis of rotat ion for a - l ac to se , and in (b) e i s the angle subtended between the equator ia l ly oriented C-4'-H-4 1 bond and the pr inc ipa l axis of rotation for methyl 3-D-lactoside (see Fig. 5.2). These plots are based on the Woessnelr equation (eqs. [5.4]) with the assumption that r r u = 1.10 A, and that the sum of e(C-He) and e(C-Ha) i s 109°28' (eq. [5.8]). The or ientat ion of C- l -H- l of a- lactose is compared here with that of C-4'-H-4' of methyl 3-D-lactoside rather than that of C-4'-H-4' of lactose because the C-4"' resonance of lactose is degenerate, while in the lactos ide the C-4' resonance i s uniquely defined. Note that the ra t i o D||/Dj_ for a- lactose i s more sens i t ive to var iat ion in 6 because the C- l -H- l bond l i e s c loser to the pr inc ipa l rotat ional axis than the C-4'-H-4' of the lactos ide. - 180 -Table 5.11 Calculated Rotational Diffus ion Constants (loVad sec " 1 ) and the Corresponding Correlat ion Times (10-lOsec rad- l ) f o r Some Carbohydrate Derivatives in Aqueous Solution (1.0 Molar) at 3b L . D M D ± T | | T ± D l|/°± 3-D-Galactopyranose (7_) 4.39 3.30 0.38 0.51 1.33 Methyl B-D-Galactopyranoside (9_) 4.58 3.03 0.36 0.55 1 .51 Methyl 3-D- 3 lactoside -(13.) b 1.01 1.03 0.67 0.67 1.65 1.62 2.49 2.49 1.51 1.54 Lactose (10) ° ~ d 1.26 1.01 0.62 0.70 1.32 1.65 2.69 2.38 2.03 1 .44 Cel l obi ose Q l ) c 1.16 0.66 1 .44 2.53 1.76 Maltose (]_2)C 1.08 0.79 1.54 2.11 1 .37 a Using mean R^-value of nonreducing r ing . b Using mean R e v a l u e of reducing r ing . c Calculated for a anomer and using the R^-values for the reducing r ing only. ^ Calculat ion based on the Revalues of the nonreducing r ing only. - 181 -Table 5.12 Comparison of a/b Values Derived from Carbon-13 -values and Those obtained by Simple Geometrical Calculations for Molecules Given in Table 5.11. Compound Carbon-13 R-j-values Geometrical Calculations Rotamer A Rotamer B 3-D-Gal actopyranose (7_) 1.45 1.21 Methyl 3-D-Galactopyranoside (9_) 1.67 1.62 a 1.67b Methyl 3-D-Lactoside ( I D - 1.69° 1.94 2.24 Lactose (TO) 2.13 d 1.59e 1.82 2.04 Cel l obi ose (1J_) 1.89d 1.78 2.04 Maltose (12) 1.52 d 1.94 1.98 3 It was found that for th is molecule, y £ z = 4.7 A and x = 2.9 A, hence a/b was taken to be z/x. k Using mean R-|-value of non-reducing r ing. c Using mean R-j-value of reducing r ing. d Calculated for a anomer and using the Revalues for the reducing r ing only. e Calculat ion based on the Revalues of the non-reducing r ing only. - 182 -Let us now d i rect our attention to the carbon-13 R-j-values of the 1,6-l inked disaccharides (Tables 5.3 and 5.7) and the polyol der ivat ives of lactose and maltose (Tables 5.4 and 5.8). It i s immediately obvious that the overal l motion of these molecules can be complicated by the po s s i b i l i t y of addit ional internal motion. For example, the rat ios of the Revalues for C-6 to the mean R^-values for the reducing r ing of gentiobiose and of melibiose are 1.8*, somewhat less than the expected value of 2.0 for the absence of internal motion, and thus implying that there i s a small amount of internal motion about the C-5-C-6 bond. Internal motion of C-6 re la t i ve to the nonreducing r ing i s more d i f f i c u l t to determine because of addit ional segmental motion along the C-1'-0-6-C-6 bonds. A further discussion on internal motion w i l l be given l a t e r on. No rate enhancement was observed in any of the carbons for these systems, not even in C-l of the a anomer. This observation supports the conclusion that the rate enhancements detected for carbons bearing equatorial protons are due to a preferent ia l rotat ional motion for the molecule about an axis that i s s i tuated close to these C-H vectors rather than a shortening in the lengths of these C-H bonds. It also suggests that even i f the overal l motion of these molecules i s an isotropic, which is l i k e l y so, the anisotropic e f fect cannot be readi ly measured for two reasons. Either the presence of internal motion has rendered the pr inc ipa l axis of rotat ion somewhat undefined, or i f th i s axis i s present, i t i s s i tuated in such a way that a l l the C-H vectors subtend s im i l a r angles with i t , or a combination of these e f fec t s . The f i r s t point is demonstrated by the R-j-values of l a c t i t o l and m a l t i t o l ; i t can been seen that the R e -value for C - l " of l a c t i t o l has the largest rate enhancement ind icat ing _ It i s un l ike ly that this reduced value i s caused by the presence of anisotropic motion. - 183 -that th i s carbon is least affected by internal motion. The second point i s demonstrated by the R-j-values for a,a -trehalose, in that a l l the C-H bonds including the C- l -H- l (equatorial) bonds of th i s molecule subtend very s im i l a r angles to the pr inc ipa l rotat ional ax i s , and hence the carbons have c losely s im i l a r R^-values. (Note that the carbon-13 resonance for each carbon of a,a-trehalose is degenerate, each resonance l i ne corresponding to two ident ica l carbon atoms, one from each of the two sugar rings. It i s assumed as before that the rotat ional constants for the two rings are i dent ica l . ) Let us now consider in some deta i l the question of internal rotat ional motion about a s ingle bond. It can be ant ic ipated that the interpretat ion of the Revalues of the primary carbon atoms (C-6, C-6' and C - l " to C-6") of these derivatives i s add i t iona l l y complicated by the p o s s i b i l i t y of rotat ion about the C-C s ingle bond, which can cause departures from the "n^-rates" i m p l i c i t in eq. [5.1]. It should be noted that anisotropic motion can cause departures from the n^-rates as w e l l , and th i s w i l l be demonstrated at a l a t e r point. The data for the disaccharides reported here, allowing for the possible ef fects of anisotropic motion, imply that there i s l i t t l e such rotat ion for C-6 (about the C-6-C-5 bond), but C-6 1 (about the C-6 1 -C-5 1 bond) apparently can have a greater degree of rotat ional freedom. This i s understandable for the 1,6-linked disaccharides since C-6 i s part of the "br idge" between two very s im i l a r sugar rings for each disaccharide and each r ing would be expected to have an approximately equal "weight" on the motion of C-6. The s i tuat ion for the 1,4-linked disaccharides i s somewhat more complicated. An explanation can be offered on the basis of intramolecular hydrogen-bonding. Most probably the hydroxyl substituent on C-6 i s more extensively hydrogen-bonded to other substituents on the same molecule than C-6' thus reducing i t s rotat ional freedom. This s i tuat ion is i l l u s t r a t e d - 184 -for methyl B -D-cel l obioside in Fig. 5.16 which shows that two hydrogen-bonds H-->0< O C H 3 Fig. 5.16 Diagrammatic representation of intramolecular hydrogen-bonds involv ing the hydroxy! substituents on C-6 and C-61 for methyl B-D-cellobioside constructed from molecular Dreiding models. The hyrJrogen-bond between 0-5' and OH-3 (in DMSO) has been previously reported*^. are involved with 0-6 compared with one on 0 -6 ' , and hence the Revalue for C-6' (9190 x 10~ 3 sec _ 1 ) i s higher than that for C-6' (8210 x 10" 3 s e c " 1 ) . If the Revalues of methyl B-D-lactoside are compared to those of methyl B-D- c e l l obi oside, the Revalue for C-6' of the former suggests that the substituents on th i s carbon atom have more rotat ional freedom than those substituents on C-6' of the l a t t e r . Since these two molecules are s t ruc tu ra l l y very s im i l a r , except for the i r configurations at C-4 ' , th i s implies that an a x i a l l y oriented hydroxy! substituent at C-4' for methyl B-D_-lactoside does not favour hydrogen-bond formation with the hydroxy! substituent of C-6 ' , which permits the more rapid rotat ion about the C-6 ' -C-5 ' bond. The same d i f f e r e n t i a l i s observed for the Revalues of C-6 and C-6 1 of cel lobiose and lactose. Unfortunately the Revalues for C-6 and C-6' of maltose cannot be discussed because these resonances were not separately resolved (see F ig. 5.8 (c) ) . Returning now to the R-j-values - 185 -of the 1,6-1 inked disaccharides, the difference in the R-j-values fo r C-6' for gentiobiose and melibiose also suggests that an equator ia l l y oriented hydroxyl substituent at C-41 in gentiobiose favours an intramolecular hydrogen-bond with the hydroxyl substituent on C-6 ' . The a x i a l l y oriented hydroxyl substituent on C-4' in melibiose appears not to favour such hydrogen-bond formation so that the CH^ OH rotates more f ree ly about the C-5 '-C-6 ' bond resu l t ing in a lower relaxation rates on C-6 1 when compared to i t s counterpart on gentiobiose. This observation i s also consistent with the previous data fo r the lactose and cel lobiose der ivat ives. When the R e v a l u e fo r C-6 of a ,a-trehalose is compared to the R-j-values of C-6 and C-6' of methyl B-D-cel lobioside (since the r ing carbons of these two sugars have c losely s im i l a r R e v a l u e s ) , i t i s apparent that the C-6 of a,a-trehalose has more rotat ional freedom than C-6 or C-6' of methyl B-D-cell obioside because the C-6 of the former i s relaxing slower than C-6 and C-6' of the l a t t e r (see Table 5.2). For the monosaccharides, a l l C-6's have very s im i l a r rotat ional freedom except for B-D-galactopyranose. The reason for th i s exception i s not apparent at th i s point. Having examined the tumbling motion of carbohydrate derivat ives in aqueous solut ion i t was f e l t necessary to check the ef fect of a solvent change. Accordingly, the carbon-13 R^-values of three sugars, a-D-galacto-pyranose, lactose and ce l lob iose , were measured in hexadeuteriodimethyl sulphoxide (DMSO-dg) and these data are summarized in Table 5.13. The carbon-13 n.m.r. spectra for these compounds are shown in Fig. 5.17. The same rate enhancements are observed for the R-j-values of carbon atoms having equator ia l ly oriented hydrogen substituents as can be seen Table 5.13 Carbon-13 Chemical S h i f t s , (ppm, ± 0 . 1 5 ) a , and Sp in-Lat t ice Relaxation Rates, R, (10 sec , ± 8%) for One Mono- and Two Di-Saccharides in Deuteriodimethyl Sulphoxide (DMS0-dfi) Solut ion (1.0 M) at 35°C. Compound C - T C-2' C-3' C-4' C-5' C-6' C- 1 C-•2 C--3 C-4 C-5 C-6 cx 8 a 8 a 8 a 8 a 8 a 8 D-Galactopyranose - (Z) 6 92.8 69.1 69.3 69.7 70.6 60.9 R l 281 (97) 321 (98) 300 (98) 304 (98) 298 (102) 336 (97) Lactose (JO) 6 104.1 71.1 73.6 68.6 75.8 61.0 b 92.5 97.0 71.8 75.1 C 72.5 7 5 . l c 81.3 81.5 70.2 75.3 61.0 b 61.0" R l 1840 1700 1740 1950 1730 1800 2350 1740 1870 1830 1790 1830 1720 1910 1800 1710 1800 1800 Ce l l obiose (11) S 103.4 73.6 76.7 70.2 d 76.9 61.3 92.3 96.9 71.8 75.2 72.3 74.8 e 80.8 80.9 70.2 d 74.8 e 6 0 . 8 f 60.8 f R l 1720 1760 1770 1860 1700 2710 2360 1570 1740 1690 1740 1750 1780 1850 1860 1750 2920 2920 3 Chemical s h i f t s referenced to interna l DMS0-d5 set at 39.6 ppm downfield from internal TMS. Assignment of Carbon-13 resonances based on those in aqueous so lu t i on . Note that the carbon-13 resonances for the nonreducing r ing of the disaccharides are degenerate (corresponding to the a and 6 anomers at the reducing carbon atoms). b " 6 ve r l app i ng resonances. - 187 -H 0 CH70H , 180 Hz , 6'+6a+6P Fig. 5.17 Carbon-13 n.m.r. spectra of (a) a-D-galactopyranose, (b) lactose, and (c) cel lobiose in DMSO-dc (1-0~M) at 35°C. These spectra were obtained with a Varian CFT-20 spectrometer using the following parameters: (a) SW = 2000 Hz, AT = 1.5 sec, PW(90°) = 20 ysec, NT = 400, PD = 0 sec, SE = -0.4 sec, Al = 1; (b) as in (a) except AT = 0.5 sec and NT = 2000; (c) as in (a) except, AT = 0.35 sec and NT = 3000. - 188 -for C- la of both lactose and cel lobiose and C-4' of lactose (Table 5.13). No rate enhancement was observed for a-D_-gal actopyranose as was the case in aqueous so lut ion. The rotat ional d i f fus ion constants for lactose and cel lobiose in DMSO can be analyzed as before and these data are given in Table 5.14. Comparison of the data in Tables 5.11 to 5.14 for the 1,4-8 -1 Table 5.14 Rotational Diffus ion Constants, Dj j and Dj_ (10 rad sec ) and the Corresponding Correlat ion Times, T and x (10-10sec rad~l) The Values for a/b Are Also Included. D,, Dj_ T m x ± DH/DL a/b a 2.53 1.38 6.59 12.08 1.83 1.92 Lactose (]0) b 2.17 1.71 7.68 9.75 1.27 1.39 Cellobiose (11) a 2.67 1.37 6.24 12.17 1.95 2.08 a Calculations based on the Revalue for C-la and the mean R i -va lue for carbons having axia l protons of the reducing r ing of the a anomer; only resolved resonances are considered. b Calculations based on the R,-value for C-4' and the mean Revalue for the other carbons of the non-reducing r ing. l inked disaccharides (lactose and cel lobiose) indicates that these systems behave very s im i l a r l y e i ther in an aqueous or in an organic medium with regard to anisotropic motion. In order to seek out any i r r e gu l a r i t y in the ef fect of solvent on R e -values, the carbon-13 R-j-values for a-D-galactopyranose, lactose and - 189 -cellobiose in DMSO and in water are compared as shown in Table 5.15. It can readi ly be seen from the R^-values of the r ing carbons of these molecules that they tumble more rapidly in water than in DMSO which results in enhancement of the relaxation rates for these carbons in DMSO-dg; about 3.5 times for 3-D-galactopyranose and four to f i ve times for lactose and cel lobiose (Table 5.15). That these molecules tumble more slowly in DMSO than in water i s mainly because DMSO i s a much more viscous solvent than water. For the pure l i q u i d s , DMSO i s 2.3 times more viscous that 81 water at 35°C . The observed increase in R-j-values of much greater than 2.3 times suggests that a 1.0 M solut ion of these sugars in DMSO is e f f e c t i ve l y much more viscous than a 1.0 M, solut ion of these same sugars in water. Returning to the data in Table 5.15, the Revalues for C-6 appear to be less affected by the solvent change. This suggests that for a f ree ly rotat ing group, rotat ion about i t s internal axis may be independent of the solvent medium; and the R-j d i f f e r e n t i a l for such a group in d i f fe rent solvents arises mainly from a dependence on the solvent of the overal l tumbling rate of the i n te rna l l y rotat ing group. Unfortunately none of the -CF^OH groups studied here are f ree ly rotat ing and hence the above point w i l l not be pursued any further. The preceding discussion on the rotat ional d i f fus ion of carbohydrate systems in solut ion i s n ice ly summarized by the carbon-13 Revalues of methyl 3-0-deuterioacetyl-4,6-0-benzylidene-2-deoxy-g-D-ribo-hexopyranoside (22) shown in Fig. 5.18. The carbon-13 n.m.r. for th is compound is shown in Fig. 5.19. Table 5.15 Ratios of (R,-va1ues in DMSO)/(R,-values in D„0) for Compounds ]_, ]Q_ and C-l C-2 C T C °' C 3' C 4' C 5 ' C G 1 C-3 C-4 C-5 C-6 a 6 a 6 a 8 a 8 a 8 a 8 a-D-Galacto-pyranose (7_) 3.47 3.87 3.30 3.30 3.35 2.10 Lactose (10) 4.47 4.20 4.44 4.12 4.36 3.59 4.54 4.96 4.77 4.55 4.71 4.17 4.62 4.76 4.90 4.75 2.30 2.30 Cel lobiose (Jl) 4.65 4.89 4.68 4.89 4.81 4.25 4.83 4.82 4.54 4.59 4.66 4.20 4.24 4.40 4.96 4.69 3.71 3.71 - 191 -1.687 O C 0 C D 3 Fig. 5.18 Carbon-13 Ri-values (10 sec ) of methyl 3-0-deuterioacetyl-4,6-0-benzylidene-2-deoxy-a-Il-ribo-hexopyranoside (22) in deuteriobenzene so lut ion (0.94 M) at 35°C. The experimental errors in these Revalues are taken to be ±4% (twice the largest standard error observed in the l i near least-squares f i t of the experimental data points) . I t can be seen from Figs. 5.18 and 5.19 that the carbons (C-l and C-3) having equator ia l ly oriented protons are relaxing more rapidly than the carbons (C-4, C-5 and C-7) having ax ia l protons. The molecule i s tumbling an i so t rop ica l l y with the phenyl group rotat ing rapidly about i t s C^-symmetry axis (C-7-C-8 bond). Although the methyl group i s also rotat ing rapidly about i t s ^-symmetry axis interpretat ion of th i s fact i s complicated by addit ional rotat ional motion about the C-l-0-1 glycosidic bond. The overal l rotat ional d i f fus ion constants for 22_ in deuteriobenzene (0.94 M) at 35°C can be calculated according to the "tumbling, r i g i d 54 e l l i p s o i d " model of Woessner . I f i t i s assumed that the pr inc ipa l axis of rotat ion for 22_ l i e s along the " length" of the molecule inthe general 9 -1 d i rect ion of the C-l-H-1 bond, one gets D| | = 4.75 x 10 rad sec , D, = 3.62 x 10 9 rad s e c - 1 and D||/Dj_ = 1.31. (In th i s ca l cu l a t i on , i t i s - 192 -14 10 11 OCH3 ococDa I / \ I \4 15 .C6D6 4 3 5 16 t 1 ' ' 1 1 20 0 15 0 1 i ' l ' I i I T — I 1 I 1 I 1 1 • I ~~T 15 I 100 5 0 ppm Fig. 5.19 Proton-decoupled carbon-13 n.m.r. spectrum (20 MHz) of methyl 3-0_-deuterioacetyl-4,6-0-benzylidene-2-deoxy-a-D-ribo-hexopyranoside in deuteriobenzene (0.94 M) at 35°C. Instrumental parameters are: SW =4000 Hz, AT = 1 sec, PW(90°C) = 20 psec, NT = 200, PD = 20 sec, SE = -0.4 sec, Al = 1. - 193 -assumed that the three C-H axia l bonds of C-4, C-5 and C-7 are perpendicular to the pr inc ipa l rotat ional axis while the C-l-H-1 bond makes an angle of 19°28' with i t . ) It i s also possible to estimate the internal rotat ional d i f fus ion constant (D^^.) for the motion of the phenyl r ing about the C-7-C-8 bond. The relevant formulations for the ca lcu lat ion of D..^ are also given by Woessner (see eq. [8]-[9] and [15] in Woessner's paper, ref. 82). The ca lcu lat ion of D^ n t f o r a group rotat ing about an axis within an e l l i p s o i d i s very tedious and i s best done with the aid of a computer program. This was cer ta in ly found necessary for the evaluation of D ^ for the phenyl r ing of 22. I f the C-2-axis of the phenyl r ing i s assumed to subtend an angle of 19°28' with the major axis of the e l l i p s o i d , i t e r a t i ve computation, using the R-j-value of C-9 and C-13 (the ortho-carbons) and the previously calculated values of D| | and Dj_, gives D. t = 5.33 x 1 0 ^ rad sec which i s an order of magnitude larger than e i ther D| j or Dj_. In th is ca lcu lat ion i t i s assumed that a l l the carbons of the phenyl r ing have bond angles of 120° and that the C-H bond lengths for these carbons are 1.08A\ The R-j-value of the ortho-carbons i s used in the ca lcu lat ion of D. , rather than that of the meta-carbons because the ortho-carbons i n t are the slowest relaxing ones. It i s not c lear why the meta-carbons relax somewhat fas ter than the ortho-carbons although at f i r s t s ight they are expected to have ident i ca l R^-values. The R^-value of the para-carbon (C-11) having i t s C-H bond s ituated along the rotat ion axis i s not affected at a l l by internal motion. I f the carbon-13 Revalues of the methylene carbons (C-2 and C-6) of 22^  are compared with those of the methine carbons ( C - l , C-3, C-4, C-5 and C-7), the rat ios of these two sets of R-j-values are e i ther greater or less than 2.00 implying that 22 i s tumbling an i so t rop ica l l y (assuming a l l the C-H bond lengths for these carbons are i d e n t i c a l . - 194 -5.4 General Theory II: Deuterium Spin-Latt ice Relaxation and Molecular  Moti on The s p i n - l a t t i c e relaxat ion of a deuterium nucleus i s almost always dominated by the interact ion between i t s quadrupole moment and the e l e c t r i c f i e l d gradient at the nucleus. In the l i m i t of rapid motion (or extreme narrowing) the contr ibution of the quadrupolar mechanism to the 40 83 s p i n - l a t t i c e relaxat ion rate of a deuteron, R-j (D) i s given by ' 2 2 M D ) - f ( l (^)SD [5-10] where e qQ/h is the quadrupole coupling constant (in units of Hz), i s the asymmetry parameter of the f i e l d gradient along the C-D bond and i s the rotat ional cor re lat ion time of the C-D f i e l d gradient vector. For a C-D fragment n i s very close to zero and may be eliminated from M eq. [5.10] which then, to a f i r s t approximation s imp l i f i e s to R,(D) = | ( ^ ) 2 , C D [5.11] In order to calculate the rotat ional corre lat ion time of the C-D vector a knowledge of the quadrupolar coupling constant i s required. The deuterium quadrupolar coupling constants of C-D groups are generally in the range of 150-250 kHz and may be obtainable from known sources*. The expressions that can be used to describe the angular dependence of the rotat ional motion of a C-D bond are ident i ca l with those used to express the angular dependence * See, e^g_., Table 13 of ref. 83. - 195 -of the rotat ional motion of a C-H bond given in eqs. [5.4]; these expressions w i l l not be repeated here. On this basis though, i t appears that deuteron R-j-values may suf fer from the same l imi tat ions as carbon-13 R-j-values as probes for anisotropic motions in carbohydrate systems. For further deta i l s on the appl ications of quadrupolar relaxation to studies of aniso-t rop ic molecular reor ientat ion the reader is referred to the work of 53 Huntress Because of the ident i t y of the motional cor re lat ion time in eqs. [5.1] and [5.11] i t i s readi ly seen for a molecule undergoing i so t rop ic reor ienta-t ion t h a t 8 3 ' 8 4 2 2^2 f U 1 3 C ) = ITT ^ 9 ? R l ( D ) [ 5 - 1 2 ] where has been set equal to zero. Given the carbon-13 s p i n - l a t t i c e 13 1 relaxation rate in a C -H moiety, eq. [5.12] provides an i nd i rec t estimate of the s p i n - l a t t i c e relaxation rate of the deuteron in the same moiety, providing that the quadrupolar coupling constant (e qQ/h) i s known and the asymmetry parameter (n ) i s zero. Another use of eq. 13 [5.12] i s that i f R-j ( C) and R-j (D) are known under ident i ca l experimental condit ions, these quantit ies may be used to calculate the deuterium quadru-84 polar constant i f that is not already known. 5.5 Results and Discussion II: Deuterium Spin-Latt ice Relaxation The R-|-values for the deuterons of methyl 2,3,4,6-tetra-O-acetyl-a -D-glucopyranoside-2,3,4,6,6 '-d 5 (23) and methyl 2,3,4,6-tetra-0-acetyl-e -D-glucopyranoside-2,3,4,6,6'-dg (24_) were measured by the conventional 21 two-pulse in vers ion-recovery procedure i l l u s t r a t e d in Fig. 5.20 for 2A_. - 196 -Fig. 5.20 P a r t i a l l y relaxed deuterium n.m.r. spectra (61.42 MHz) of compound 24_ in acetone (0.075 M) at 25°C, depicting the two-pulse inversion-recovery sequence^ for measurement of s p i n - l a t t i c e relaxation rates. Experimental parameters were: SW = 400 Hz, AT = 1.25 sec, Pl = 31.0 psec, P2 = 15.5 ysec, NT = 32, PD = 1.0 sec, LB = 0.0Hz, Al = 1. The t-values (sec) are shown to the r ight of the respective spectra. - 197 -The deuterium Revalues for 24^  were measured in acetone (0.075 M) while those of 2^ 3 were measured both in acetone and in benzene (0.075 M in both so lvents) . The deuterium n.m.r. spectra for ,23 in acetone and benzene are shown in F ig. 5.21. The deuterium n.m.r. parameters for 2_3 and 24_ are summarized in Table 5.16. I f the quadrupolar coupling constants for the deuterons of 23_ and 2_4 are i d e n t i c a l , the fol lowing inferences can be made regarding the relaxation data given in Table 5.15. The rather s im i la r deuterium Revalues fo r 2_3 and 24 in acetone suggest that these two molecules may have the same rotat ional behaviour. The close s i m i l a r i t y of the ind iv idual R e -values for the r ing deuterons D-2, D-3 and D-4 for each compound indicate that both 23 and 24_ tumble i s o t r op i c a l l y in so lut ion. The larger var iat ion in the relaxation rate of D-5 i s most l i k e l y due to a greater systematic error in the evaluation of th i s value. The difference between the deuterium R e v a l u e s of 23 in acetone and in benzene is mainly a r e f l ec t i on of the more viscous nature of benzene as a solvent. (For the pure l i q u i d s , benzene 81 i s twice as viscous as acetone at 26°C .) F i na l l y , since the R-j-values for D-6 and 0-6' are very nearly the same as those for D-2, D-3 and D-4, for both 23_ and 2_4, there i s very l i t t l e , i f any, rotat ion about the C-6-C-5 bonds in these two molecules. Even i f anisotropic reor ientat ion was present in the rotat ional motion of 23 and 24, i t i s un l ike ly that the R-j-values for the r ing deuterons of the molecules w i l l detect th i s e f f e c t . This i s because the C-D bonds for these deuterons would have very nearly ident i ca l or ientations with respect to any molecule-fixed ax i s , as these bonds are a l l a x i a l l y oriented with respect to the pyranose r ing . Thus, unless the presence of an equator ia l ly oriented deuteron indicates otherwise, the data reported here suggest that the two pyranose sugars tumble i s o t r op i c a l l y in so lut ion. - 198 -6 5 4 ppm 3 2 Fig. 5.21 Deuterium n.m.r. spectra (61.42 MHz) of 23_ (a) in acetone (0.075 M), and (b) in benzene (0.075 M), at 26°C. Experimental parameters for both spectra were: SW = 400 Hz, AT = 1.25 sec, PW(90°) = 15.5 ysec, NT = 16, PD = 1.0 sec, LB = 0.0 Hz, Al - 1. - 199 -Table 5.16 Deuterium Chemical Sh i f t s , <5(ppm, ±0.015) and Spin-Latt ice Relaxation Rates, R,(10-3sec"l, ±3%) D for Compounds 23 and 24 26°C. 1 ~~ OCH, OCH, 23 R = COCH, 24 R = COCH, Compound D-2 D-3 D-4 D-51 D-6 D-61 23 x l fe 4.77 9410 5.01 13440 5.36 9340 5.80 13690 4.96 9110 5.26 14030 3.91 10510 3.76 15330 4.13 8990 4.21 13530 4.02 9280 4.02 13550 24 4.82 9850 5.17 9530 4.94 9910 3.86 9180 4.18 9370 4.04 9910 Chemical sh i f t s referenced e i ther to internal acetone (C2H5DO) set at 2.03 ppm down-field from internal tetramethyls i lane, or to internal benzene (C5H5D) set at 7.17 ppm downfield from tetramethyls i lane. b Experimental errors are taken to be ±3% (twice the largest standard error in l i nea r least-squares f i t of the experimental data points ) . The intens i ty of th is t rans i t i on i s considerably weaker (see Figs. 5.20 and 5.21) than others and hence the Revalue for th is deuteron contains larger systematic error (±6%). Reason for the weaker intens i ty of D-5 w i l l be given in Chapter 6, Section 6.3. ^ Measured in acetone. Measured in benzene. - 200 -If the quadrupolar coupling constants for the deuterons of 23_ and 24 are known, then the relaxation data given in Table 5.16 can be readi ly con-verted to the rotat ional d i f fus ion constants for these molecules. Since the quadrupolar coupling constants are not known i t would be of interest to measure these values using eq. [5.12]. Accordingly, the carbon-13 R-|-values of the prot io analogs of 23_ and 2_4, methyl 2,3,4,6-tetra-0_-deuterioacetyl-a -D-glucopyranoside (25) and methyl 2,3,4,6-tetra-0_-deuterioacetyl-6-D-glucopyranoside (26) were measured in deuterioacetone (0.10 M) at 30°C. The carbon-13 relaxation data are summarized in Table 5.17. Since no s i gn i f i c an t rate enhancement is observed for C-l of 25, which bears an equatorial hydrogen subst ituent, the reor ientat ion of 25_ may be regarded to be i so t rop i c . It can be further inferred that 26^  tumbles i s o t r o p i c a l l y as w e l l . This observation i s in agreement wi th the results of the R-|-values for the deuterons of 2_3 and 2_4. The R^-value for C-6 of 25 appears to indicate that i t has more rotat ional freedom about the C-6-C-5 bond than i t s counterpart in 26_. However, the R-j-values fo r D-6 and D-61 do not appear to indicate a d i f f e r e n t i a l in the rotat ional rate for C-6 of 23 and 2_4. The reason for th i s apparent disagreement i s not c lear . I f i t i s now assumed that the experimental conditions used to obtain the data given in Tables 5.16 and 5.17 were e s sent ia l l y ident ica l (actual ly there was a difference of ^4°C in temperature and of ^0.025 M in concentration), then these data can be converted to the quadrupolar coupling constants of the various deuterium according to P2nO nHR,(D) h 4 V ^ = 3 . 7 0 H ' x 10 4 Hz [5.13] h R 1( 1 JC) o Equation [5.13] i s derived from eq. [5.12] by assuming r^ H = 1.10 A. The calculated quadrupolar constants are l i s t e d in Table 5.18 - 201 -Table 5.17 Carbon-13 Spin-Latt ice Relaxation Rates, R] (10" sec" ,±10%) a for Compounds and 26_ i n Deuterioacetone (0.10 M) at 30°C. Compound C-l C-2 C-3 C-4 C-5 C-6 25 b 490 450 450 460 460 780 26 c 380 420 420 420 410 810 a Measurement done by Dr. K. Bock of the Department of Organic Chemistry, the Technical University of Denmark, using a Bruker HFX-270 spectrometer operating at 67.89 MHz for carbon-13 resonance. b Average R e v a l u e fo r C-l to C-5 i s 462 x 1 0 " 3 s e c _ 1 . r - 3 - 1 Average R,-value for C-l to C-5 i s 410 x 10 sec . - 202 -Table 5.18 Deuterium Quadrupolar Coupling Constants ,e qQ/h (kHz, ±9) as Calculated from Deuterium and Carbon-13 Spin-Latt ice Relaxation Rates. Compound D-2 D-3 D-4 D-5b D-6 D-6' 23 169 169 165 177 178 180 24 179 176 180 175 180 183 a Errors are calculated based on a 3% error in Rn(D) and a 10% error in i y 1 3 c ) . 1 b Errors for th is deuterium are s l i g h t l y higher, ±10 kHz. Within the estimated experimental errors the calculated quadrupolar coupling constants for the various deuterium of 23_ and 24 are very nearly equal, with 23 having an average of 173 kHz and 24 having an average of 179 kHz. These values can now be used to evaluate the i sot rop ic rotat ional cor re lat ion times (see Table 5.19) for 23 and 24 according to eq. [5.11]. These data w i l l l a t e r be used in Chapter 6. 5.6 Conclusion Although carbon-13 and deuterium R-|-values can provide valuable information concerning the way in which molecules tumble in so lut ion, l im i ta t ions to th i s approach can ar i se depending on the re la t i ve d i spos i t ion of the various relaxation vectors (C-H or C-D bonds). Two s i tuat ions commonly ar ise in carbohydrate systems. One, is when a l l the relaxation vectors have s im i la r or ientations in space with respect to the molecule; in such a case neither carbon-13 nor deuterium Revalues can be used to detect the presence of anisotropic motion. - 203 -Table 5.19 Calculated Rotational Correlat ion Times, tCDO° sec rad" ), and the Corresponding Rotational Diffus ion Constants, D(10_9 rad sec-1), fo r Compounds 23_ and 24. Compound TCD D a 2.10 ± 0.07 7.94 ± 0.27 23 b 3.10 ± 0.11 5.38 ± 0.19 24 c 3.10 ± 0.07 8.09 ± 0.27 a In acetone (0.075 M). Calculat ion based on e^qQ/h = 173 kHz, mean R, (D) = 9276 x 10-3sec-1 (for D-2, D-3 and D-4 only) 1 b In benzene (0.075 M). Parameters used for ca lcu lat ion as in ' a ' with mean R](D) = 13720 x 10-3sec-L c In acetone (0.075 M). Calculat ion based on e2qQ/h = 179 kHz, mean R, (D) = 9763 x 10-3sec-l (for D-2, D-3 and D-4 only) 1 On the other hand, in carbohydrate systems which have a x i a l l y and equator ia l ly oriented C-H relaxation vectors, anisotropic ef fects can be studied. However, because the re la t i ve d ispos i t ion of such vectors in these systems i s approximately tetrahedral (^109°), the R-j-values are not pa r t i cu l a r l y sens i t ive to the or ientat ion of the anisotropic axes of the molecule; th i s can severely l i m i t the s en s i t i v i t y of carbon-13 and deuterium Revalues as motional probes for these molecules. An important coro l la ry to th i s l a t t e r point is that proton Revalues are not s i g n i f i c an t l y affected by anisotropic motion i f the angles between the various interproton vectors are of the order of 90° (see Fig. 5.1); hence intercomparison of i n t e r -proton relaxation contributions (P . . -values) can s t i l l provide a quant itat ive measure of interproton distances. - 204 -CHAPTER 6 APPLICATIONS OF SELECTIVE AND NON-SELECTIVE PROTON SPIN-LATTICE RELAXATION RATES 6.1 Introduction To further document the v e r s a t i l i t y and also possible l imi tat ions of se lect ive and non-selective proton Revalues as "probes" for the geometry of diamagnetic molecules in so lu t ion , the proton R-j-values of several series of derivatives were evaluated. It must be emphasized at the outset that none of these ind iv idual studies was ever intended to be a comprehensive, or f i n a l , evaluation of a pa r t i cu l a r chemical system. Rather, i t was intended that these preliminary surveys would permit us to place the methodology described e a r l i e r in th is thesis into chemical contexts which were not a p r i o r i designed to be optimized for the relaxation method - e.g., systems having substantial anisotropic motion, systems having complex, second order spectra, and systems with conformational time-averaging. As w i l l be seen, some of these problems compromise the appl icat ion whereas others are s u f f i c i e n t l y amenable to chemical control that the relaxation method can be used to i t s f u l l po tent i a l . 6.2 Phenyl Derivatives A number of problems associated with the measurement of R n-values for protons of planar molecules w i l l now be discussed with respect to the proton R-j-values of l-trideuteriomethoxy-2,4-dinitrobenzene (2_7) and l-methoxy-2,4-dinitrobenzene (28). These values, obtained under various experimental condit ions, are summarized in Table 6.1; the proton n.m.r. spectrum of 27 i s shown in Fig. 6.1. - 205 -Table 6.1 Proton Relaxation Rates ( 1 0 ~ 3 s e c _ 1 ) a for Compounds 2_7b and 28 c in Deuteriobenzene (0.50 M, degassed) at 35°C. OR 0CD 3 OCH3 Experiment H-3(±10%) H-5(±5%) H-6(±5%) 0CH 3(±5%) _27 28 27 28 21 28 29 1. Non-Selective 12.1 13.5 74.1 76.9 76.3 181.2 359.7 2. S ingle-Selective 8.3 9.2 48.9 51.8 49.8 122.0 -3. Ratio 1/2 1 .46+0.21 1.47±0.21 1.52±0.11 1.48±0.11 1.53±0.11 1.49±0. 11 -Double-Selective 4. R] (H-l,H-2) 9.9 50.9 - -5. R^ H- l , H-3) 8.2 - 51.3 -6. R](H-2,H-3) - 67.0 73.0 71.0 146.5 343.6 7. R11(H-3,0CH3) - - 153.4 -a Measured with the two-pulse inversion-recovery sequence. C l  b I n i t i a l slopes for a l l protons: 0.1 ± t <_ 15.0 sec. c I n i t i a l slope for H-3: 0.1 1 t £ 15.0 sec; for H-5, H-6 and 0CH 3: 0.1 ± t <_ 3.0 sec 206 -H-3 O C D 3 H-5 100 Hz 1 1 H-6 Fig. 6.1 Proton n.m.r. snectrum (100 MHz) of compound 27 (0.50 M in deuteriobenzene at 35°C. Instrumental parameters used were: SW = 1000 Hz, AT = 4, NT = 4, PD = 600 sec, PW(90°) = 65 ysec, SE = 1.5 sec. - 207 -It was ant ic ipated that three d i s t i n c t problems would merit considera-t i on . F i r s t , since i t i s well known that phenyl der ivat ives tumble anisotro-p i c a l l y in so lu t ion , allowance for th i s would be necessary. Second,the re l a t i ve rat ios of the interproton distances were l i k e l y to impose serious dynamic range problems on the accuracy of the determination. And t h i r d l y , the proton flanked by the two n i t r o groups (H-3) i s so far from the other protons that i t seemed probable that i t would have to obtain a s i gn i f i c an t proportion of i t s relaxation from elsewhere - e i ther other solute or solvent molecules. Evidence for the anisotropic motion of phenyl der ivat ives can be obtained 6 3 from carbon-13 Revalues , and the values for 27., shown in Table 6.2, c lea r l y indicate that th is compound (and hence 28) i s tumbling an i sot rop ica l l y with the pr inc ipa l axis of rotat ion ly ing in the general d i rect ion of C-3-H-3 bond. This suggests that the motion of the interproton vector between H-3 and H-6 i s anisotropic re la t i ve to that of H-3-H-5 or H-5-H-6 and hence that H-3-H-6 relaxation interact ion should be considered separately from that of the other two interproton relaxat ion contr ibutions. I t i s reasonable to suggest that, because the angles subtended by the H-3-H-5 and H-5-H-6 vectors with the pr inc ipa l axis of rotat ion are nearly the same, the respective relaxation contributions w i l l be largely uninfluenced by any anisotropic motion. Furthermore, since the enclosed angle between the H-3-H-5 and H-5-H-6 vectors i s almost precisely 90°, these two interact ions (pg,- and pj-g) should be even more insens i t ive to anisotropic rotat ional motion of the molecule. (Compare with Chapter 5 for a discussion of th is 59 point and also Levy et a l . ) The second problem i s i m p l i c i t in the probable magnitudes of the three interproton distances, shown in Fig. 6.2. Remembering the discussion - 208 -Table 6.2 Carbon-13 Chemical Sh i f t s , 6, Relaxation Rates, R ], and C-{ H) n.O.e. Factors for the Carbons Bearing Hydrogen Substituents in Compound 27 a 0CD3 N02 N.M.R. Parameters C-3 C-5 C-6 6(ppm, ±0.1 ) b 121.4 128.4 113.3 c 249 168 246 R ^ l O ^ s e c " 1 , ±8%) d 238 171 243 Mean 244 170 244 1 3 C-{ 1 H)n.0.e. (%) e 100 ± 8 90 ± 15 92 ± 8 a Measurements made for a 0.50 M solut ion (degassed) of 27_ in deuteriobenzene at 35°C using a Varian CFT-20 spectrometer. b Carbon-13 resonances assigned by se lect ive proton decoupling and referenced to internal deuteriobenzene set at 128.1 ppm downfield from tetramethyls i lane. c 21 Using the two-pulse inversion-recovery sequence ; experimental parameters were: SW .= 1000 Hz, AT = 4 sec, NT = 400, PD = 40 sec, SE = -0.3 sec, Al = 1. d 85 Using the two-pulse fast inversion-recovery sequence ; experimental para-meters were as in ' c ' except PD = 0 sec. e 58 Measured with the gated decoupling technique . - 209 -- 6 r, 55 = 2.48 H-3 H-5 = 4.30 o Fig. 6.2 The calculated interproton distances (A] for 27 assuming the fol lowing86 : bond lengths, C-H = 1.08 A; C-C = 1.40 A; a l l bond angles = 120°; and the molecule is planar. given in Section 3.9 (Chapter 3) i t is obvious that the precis ion with which and p^ can be determined could be unacceptably poor due to dynamic range l im i t a t i o n . The th i rd problem is somewhat associated with the second, as that intermolecular interact ion may become an important re laxat ion mechanism for these protons, and espec ia l l y so for H-3 since i t i s s i tuated r e l a t i v e l y very far away from both H-5 and H-6 in the same molecule. Independent evidence for the occurrence of intermolecular interact ion involv ing 27 came from the observed changes in the chemical sh i f t s of the protons of 27 as a function of concentration, shown in Table 6.3. It i s c lear from these data that there i s an appreciable amount of solute-solute molecular associa-t ion which results in a downfield s h i f t of the proton resonances as the solute concentration i s increased. The largest e f fec t i s observed for H-6 while H-3 i s the least affected which indicates that th is intermolecular e f fect may be s t e r i c dependent. It can also be inferred that the solvent molecules (deuteriobenzene) also part ic ipate in such an association with the solute molecules although th i s e f fect cannot be measured d i r e c t l y here - 210 -Table 6.3 The Observed Change in the Chemical Sh i f t s , AS.(ppm) , of the Protons of 27 as a Function of Its Concentration in Deuteriobenzene, C (M), at 35°C. AS. AS. AS, ASCCDCH 6 5 0.10 0.50 1.00 •0.016 -0.076 -0.130 -0.025 -0.132 -0.234 -0.048 -0.243 -0.444 0.000 0.000 -0.004 a AS^  S.(0.025M) - 6.(C), where 6^(0 is the chemical s h i f t of proton-i at C M concentration of 27_. Negative values correspond to downfield s h i f t . Error = 0.0015 ppm. because the solvent molecules are present in large excess over the solute molecules . Bearing the above three problems in mind l e t us now return to the R e -values of Table 6.1. Following the prescr ipt ion given in Chapter 3, the relaxation data of Table 6.1 can be converted to the indiv idual pairwise interproton relaxat ion contr ibut ions, p. .-values, and these are summarized in Table 6.4 Although i t was possible to choose a solvent that did not part ic ipate in molecular association with the so lute, of the commonly ava i lable deuterated solvents, deuteriobenzene was chosen because i t provided optimal chemical s h i f t dispersion for the protons of 27 thereby f a c i l i t a t e s the se lect ive pulse experiments which const itute a c r i t i c a l aspect of th i s study. - 211 -Table 6.4 Calculated P. .-values for Compounds 27 and 28. ' vJ Experimental Source '35 '36 '56 J6CH-27 28 27 28 27 28 28 Non-Selective 5.4±1.8 3.7±6.4 2.6±1.8 5.3±6.4 44.0±1.8 47.5±6.4 S ingle-Select ive 5.8±1.8 3.5±6.4 2.4±1.8 5.7±6.4 43.0±1.8 48.3±6.4 Double-Selective b 3.6±3.8 1.4±3.8 39.3±6.0 45.7+11 63±20 C Deuterat ion 73 7' Calculated from 1 1 0 P35 " R H - 3 _ 1 0 1 p36 = k 0 1 1 where for non-selective pulse k = 2/3, R H-i n H- i \ ~ ' = R ' ^ 'Cns ) , i = 3 and 5 for 27 and 28, RH~6 = R ^ n s ) -2 M3CD, for 27, ,H-6 nH-6 1 - R-, (ns) - 2 P3QCH f o r — ' f o r s i ng1e - s e l e c t i v e pulse k = 1, ,H-i _ n H- i 1 = Re (H- i ) , i = 3 and 5 for 27 and 28, R H-6 _ n H-6„,^ 1 H-R^ (H -6 ) - p 3 C D fo r 27, Ru-6 = RH-6(H-6) - p for 28, 1 ~ , x l Average p 3CH3 = 6 8 1 P 3 CD 3 = 4-3 ±0.7. [R ? _ i (H - i ,H - j ) - R^H- i)] + [ R ^ V i , H ^ j ) - R ^ V j ) ] for { i , j } = {3,5,6} P3CH = 2t R ? " 6 (H-6,0CH 3 ) - R ! | I " 6 (H-6)] ,H-6, P 3 C H = 0.6959[R^"D(ns,0CH3) - R ^ n s , OCD3], see eq. [4.5] in Chapter 4. - 212 -It i s c lear from Table 6.4 that the accuracy with which the p. .-values can be determined decreases with increase in the dynamic range of the R e -values; the estimated errors in the evaluated p. . -values are larger for 28 than for 2_7 because the R-j-values for the protons of 2_8 span a much wider range than those for the protons of 2J_. Consider now the indiv idual p ^ -values for these two molecules. (As mentioned e a r l i e r , the p_ c -value w i l l not be considered because the H-3-H-6 interact ion i s expected to be prefer-e n t i a l l y enhanced by anisotropic reor ientat ion about an axis close to the r^g interproton vector.) Assuming that = x^g, the ra t i o ^ / i ^ g c a n be calculated from the s ixth-root of p , c / p , r . The various values for th i s bb ob ra t i o calculated from the non-selective and se lect ive pulse experiments, along with that predicted from simple geometrical consideration (see Fig. 6.2) are summarized in Table 6.5 for 27 and 28. These values are also compared with those obtained from l i q u i d crysta l n.m.r. studies of s t ruc tu ra l l y 87 s im i l a r phenyl derivatives (Table 6.5). I t i s immediately c lear that the ra t i o r35/ r55 derived from the interproton p^j-values i s considerably lower than expected. Two reasons for th i s can be given. 1. Since H-5 i s very e f f i c i e n t l y relaxed by H-6, the relaxation con-t r i bu t i on from H-3 i s a neg l ig ib ly small quantity which cannot be determined s u f f i c i e n t l y accurately; th i s i s a typ ica l dynamic range problem. 2. H-3 is s i tuated so fa r away from e i the r H-5 or H-6 on the same molecule (see Fig. 6.2) that a considerable amount of i t s re laxa-t ion contributions has to come from the magnetic spins of other nearby molecules, both solute and solvent, vi a intermolecular relaxation Let us consider in deta i l possible intermolecular relaxation contr ibu-tions to the relaxation of H-3. F i r s t of a l l , the mechanism for any - 2 1 3 -Table 6 . 5 Measured and Calculated ^ / ^ g Values for Compounds 2_7 and 28 along with Those for 1,4-Dibromo- and 1,4-Diiodo-benzene Obtained from Liquid Crystal Studies. 27 R = OCD, 28 R = OCH, Experimental 11 r r p r 1 2 r 2 3 2 8 Non-Selective 1 . 4 2 ± 0 . 0 8 1 . 5 3 ± 0 . 4 4 Single-Select ive 1 . 4 0 ± 0 . 0 7 1 . 5 5 ± 0 . 4 7 Double-Selective 1 . 4 9 ± 0 . 2 6 -Ca lcu la t i on 9 1 . 7 3 1 . 7 3 Liquid Crystal B r~0~ B r 1 . 7 2 3 ± 0 . 0 1 0 ~ o 1 . 7 5 1 ± 0 . 0 0 9 9 See Fig. 6 . 2 . - 214 -intermolecular s p i n - l a t t i c e relaxation of H-3, i f present, must be dominantly d ipolar as evidenced by the fact that the ra t i o R^" 1(ns)/R^~~ i(H-l) i s e s sent ia l l y 1.5 for both 27_ and 28_ (see Table 6.1). The same experimental evidence shows that th is "externa l " source of relaxation must be the " l i k e " spins, i . e . , the other protons of the nearby solute molecules; i f th is were H-l H-l ^ not so, the ra t io R-j~ (ns)/R-|~ (H-l) would be s i g n i f i c an t l y less than 1.5. Contributions from the benzene-d c solvent molecules w i l l be small because of the small gyromagnetic ra t i o of deuteron. The next question to consider i s the effects of intermolecular relaxation contr ibution to the R-j-value of H-3. This is best answered by comparing the calculated intramolecular interproton distances, and r ^ , to the preferred intermolecular distances found in s im i l a r planar systems. The values calculated for r^g and were n gg 4.30 and 4.96 A, respect ive ly, see Fig. 6.2. Bochynski studied the structure of l i q u i d benzene by X-ray d i f f r a c t i on and found that the preferred i n t e r -molecular distances between the centres of nearest neighbours are 4.11, 4.94 » 89 and 6.55 A. He also studied the intermolecular d i s t r ibut ions of l i q u i d nitrobenzene by x-ray d i f f r a c t i on and found preferred intermolecular distances at 4.10, 5.23 and 5.65 A. I f i t i s assumed that the intermolecular d i s t r i -butions of 2_7 or 28 in deuteriobenzene solut ion are very s im i l a r to those reported for l i q u i d benzene or l i q u i d nitrobenzene, then i t i s c lear that molecules of 2_7 and 28 can come s u f f i c i e n t l y close to each other that H-3 can receive relaxation contributions from magnetic spins of nearby molecules. Moreover, as indicated by the X-ray d i f f r a c t i on l i q u i d benzene model of 90 Narten , i t i s very probable that the intermolecular interproton separation i s much closer than 4.0 X, Ue.,< r 3 5 or r 3 6 . According to that model, the closest interproton distances between two benzene molecules can be estimated o as 3.19 A. Thus, on the basis of interproton distance considerations alone i t can be concluded that the Revalue of H-3 of 2_7 or 28 has two dipolar - 215 -components: intramolecular and intermolecular relaxation contr ibutions. It i s unfortunate that the intermolecular relaxation contr ibution cannot be eas i l y be separated from the intramolecular one, at least not by any com-bination of se lect ive and non-selective pulse perturbation experiments. This, and the l im i ta t i on in the dynamic range of the -values for protons of 27 or 28 c lea r l y precludes the determination of or p^g with any acceptable level of accuracy. Nevertheless, i t was s t i l l of interest to consider the accuracy with which the r^g distance could be determined from the p^g-values (Table 6.4) and the carbon-13 R,-values (Table 6.2). The e x p l i c i t re la t ion between r,.c l bb and Pgg for 27 or 28 i s given by eq. [6.1] 5.696 x x c c x 1011 1/6 r 5 6 = ( ^ ) [6.1] 0 0 p 56 In order to use th i s expression to determine r^g, i t i s f i r s t necessary to obtain an estimate of the motional corre lat ion time for the H-5-H-6 i n t e r -proton vector, Tgg. This value can be calculated from the carbon-13 R e -value of 27_, providing that the e f fect of anisotropic reor ientat ion i s taken into account. Using the procedure of Chapter 5 and assuming that the p r i n c i -pal rotat ional axis of 27 i s pa ra l l e l to the C-3-H-3 or C-6-H-6 vector, 54 ca l cu la t i on * according to Woessner's tumbling r i g i d e l l i p s o i d model gives D| | = 3.13 x 1 0 1 0 and Dj_ = 1.55 x 1 0 ^ rad s e c - 1 . Since i t i s assumed that the pr inc ipa l rotat ional axis i s pa ra l l e l to the H-3-H-6 vector, i t follows by inference that the angle (e) between r^g and the pr inc ipa l axis i s 30°. Subst itut ing these values for D||, Dj_ and 6 in eq. [6.2] In th is ca l cu l a t i on , i t i s assumed that r^u = 1.08 K, the mean R-j-value for C-3 and C-6 i s taken as 244 x lO-Ssec"" 1 and that for C-5 as 170 x lO-Ssec" 1 . Also the C-2-H-2 vector is assumed to be perpendicular to the pr inc ipa l rotat ional axis. - 216 -T56 = DJL [ ( 3 cos 29-1 )2/24 + 3 sin2eCos26/(5+D||/Dj_) + 3 sin4e/4(2+4D|,/DL)] [6.2] (see also eq. [2.37] in Chapter 2), gives = 9.67 x I O - 1 2 sec r a d " 1 . Using this value for and the p^g-values given in Table 6.4, the r e -values can be calculated according to eq. [6.1] and these values are summarized in Table 6.6. Although the r e v a l u e s given in Table 6.6 were obtained Table 6.6 The Calculated Intramolecular Interproton Distances for H-5 and H-6, r , K ( S ) , of 27 and 28 a . Experimental r56 Source 27 28 Non-Selecti ve 2.24 2.21 S ingle-Select ive 2.25 2.20 Double-Selective 2.28 2.22 Calculat ion 2.48 Errors are not estimated for these values because an unknown systematic error may have been introduced by the assumption that the pr inc ipa l rotat ional axis of the molecule is pa ra l l e l to the H-3-H-6 vector. using a number of assumptions, i t i s very encouraging to note that the derived values are only M0% lower than the expected value of 2.48 A. Two reasons w i l l now be offered to account for th is d i f ference. The f i r s t i s that a systematic error in the x^^-value i s l i k e l y since the e f fect of anisotropic motion has not been completely allowed for . The maximum value - 217 -of th i s error would cause the measured r c c - v a l u e to d i f f e r from i t s true 56 value is a factor of (D|J/DJ_) which in th is case i s M.12, corresponding to a 1^2% d i f ference, or er ror . The second reason could be that there i s a small amount of intermolecular relaxation to pcc such that the e f fec t i ve bb distance with which relaxation can take place appears to be smaller. And of course both these effects can operate simultaneously, causing the r^g-value derived from the measured Pgg-vaTue to be even smaller than i t s true value. It i s appropriate to consider now the conformation of the methyl group of the methoxy substituent. It i s c lear from the relaxation data of 2_8 that H-6 receives a substantial relaxation contribution from the methyl protons, which implies that the methyl group p re fe rent i a l l y assumes a conformation about the aromatic carbon-oxygen bond such that the methyl protons are r e l a t i v e l y close to H-6. The average CH^ -H-e distance, r g ^ can be estimated i f we make the fol lowing assumptions. 1. The e f fec t i ve distance between the protons of the CH^  group and H-6 can be taken from the midpoint of the t r iang le defined by the protons of the CH^  group to H-6. The use of th is "methyl proton 91 centroid" model has been shown to be a reasonable one for protons not d i r ec t l y adjacent to the methyl group as in th is case. Essent ia l ly the "centro id " model compensates for the rapid internal motion of the methyl group about i t s three-fo ld symmetry axis. 2. The e f fect i ve corre lat ion time between the methyl protons and H-6, T6CH ' c a n b e t a ' < e n t 0 D e ident ica l with that of the H-5-H-6 vector determined previously. -3 -1 Subst itut ing the average p g ^ -value of 68 x 10 sec and the e f fec t i ve T G C H -value of 9.67 x 10 sec rad into eq. [6.3]*, one obtains 3 * A three fac or is introduc d in eq, [6.3] (compare eq. [6.1]) because there are three methyl protons contr ibuting relaxation to H-6. - 218 -3 x 5.696 x T6CH3X 1 0 1 / 6  r 6 C H 3 ( P 6CH 3 } 6 ' 3 r g C H = 2.50 A, i . e . , the average CH3~H-6 distance in 28 i s 2.50 A. This value i s in excel lent agreement with the value of 2.49 A obtained from geometrical consideration i l l u s t r a t e d in Fig. 6.3, from which i t may be inferred that the approach adopted here in ca lcu lat ing the CH3~H-6 distance Fig. 6.3 The calculated distance from the centroid of the methyl protons to H-6. The ca lcu lat ion was performed by computer s imulation. The methyl carbon i s assumed to have sp3-hybridization whereas ^ the aromatic carbon and the methoxy oxygen are assumed to be sp -hybridized. The bond lengths used in the ca lcu lat ion are: aromatic, C-C = 1.40 A, C-H = 1.08 A, C-0 = 1.36 A; a l i p h a t i c , C-H = 1.10 A, C-0 = 1.43 A. The 0-CH 3 bond i s assumed to be coplanar with the aromatic r ing . in 28 i s not unreasonable. It can further be inferred that the methyl group e f f e c t i v e l y does not rotate about the aromatic C-0 bond. Two poss i -ble reasons why the methyl group could have the preferred conformation shown in Fig. 6.3 are as fol lows. F i r s t l y , th i s conformation may be favoured because of some pa r t i a l double-bond character in the aromatic C-0 bond. Secondly, s t e r i c hindrance with the n i t ro substituent on the ortho pos it ion probably forces the methyl group towards H-6, thereby minimizing the s t e r i c hinderance. - 219 -A number of general conclusions concerning proton R-j-values of phenyl derivatives can be derived from the relaxat ion data reported here for compounds 27 and 28_. We see here that intermolecular relaxation contributions to protons that are e i ther meta or para to each other in a phenyl r ing may be e f f i c i e n t enough that relaxation contributions from magnetic spins of other nearby molecules, cannot be neglected. In th is regard these systems may provide suitable models for future studies of intermolecular re laxat ion * , pa r t i cu -l a r l y i f th is occurs v ia the dipole-dipole mechanism. However, the re laxa-t ion between protons that are ortho to each other (e.g., H-5 and H-6) appears to be less sens i t ive to intermolecular e f fect s . In p r i n c i p l e , intermolecular relaxat ion contributions to protons a r i s ing from dipole-dipole interact ions can be minimized i f the measure-ment of Revalues i s performed at high d i l u t i on of the solute molecules and in a nonmagnetic solvent; in p rac t i ce , however, th is may not always be poss ible. At high d i l u t i o n , the low signal to noise ra t io for the n.m.r. signals may necessitate extensive time-averaging and for slowly relaxing spins (such as H-3) the measurement of Revalues may require such an extensive period of time that undesirable systematic errors due to long term i n s t a b i l i t y of the n.m.r. spectrometer may be introduced. The use of a nonmagnetic solvent i s generally not pract ica l because most n.m.r. spectrometers require a second set of magnetic nuclei in the sample to provide a resonance " f ie ld-frequency lock " . Deuterium resonances are very su itable in th is regard, which i s fortunate because the relaxation e f fect Although intermolecular relaxation experiments would provide information concerning the structure of l iqu ids and intermolecular forces, there i s at present considerable lack of experimental data; one possible reason for th i s i s the theoret ica l d i f f i c u l t i e s in treat ing intermolecular relaxation and the theory of l i q u i d mixtures. - 220 -of a deuteron i s reduced from that of a proton by y 2 f - j r = 0-063 [6.4] so that th is e f fect i s often s u f f i c i e n t l y small that for most pract ica l purposes i t can be ignored. In the present study proton relaxat ion data for 27_ and 28 were obtained at the rather high concentration of 0.50 M in deuteriobenzene solvent so that those data could be combined together with the carbon-13 R-j-values to give a quant itat ive measure of the interproton separations. In summary then we have shown that 27 and 28 tumble an i sot rop ica l l y and, having considered the e f fect of anisotropic motion on the measurement of interproton distances v ia the proton Reva lues , we conclude that a small anisotropic e f fect does not s i g n i f i c an t l y a f fect the overal l accuracy with which interproton distances can be derived. Clear ly though, i t would be of interest to further invest igate the ef fect of anisotropic motion on the measurement of interproton distances. Despite the many complications present in the systems studied here, a reasonable measure of the interproton distance of the two protons ortho o to each other was obtained; the average measured r ^ - va l ue of 2.23 A for o 27 and 28 is only 10% less than the calculated value of 2.48 A. Interest-ing l y , the average CH^-H-e distance in 28 was found to be 2.50 A, which is o in excel lent agreement with that calculated (2.49 A) on the basis of the centroid model. - 221 -6.3 Glucopyranose Derivatives This section w i l l demonstrate how an otherwise t i g h t l y coupled complex proton system can be chemically manipulated to become s u f f i c i e n t l y simple and loosely coupled that the various indiv idual pairwise interproton relaxat ion contr ibution can be measured v ia se lect ive pulse perturbation experiments. Furthermore, i t w i l l be shown that se lect ive pulse experiment can be used to separate intramolecular dipole-dipole interact ions between resonant and nonresonant spins. Fig. 6.4 (a) shows the 100 MHz proton n.m.r. spectrum of methyl 2,3,4, 6-tetra-0_-trideuterioacetyl-ot-D_-glucopyranoside (29_), from which i t i s c lear that the protons are so t i g h t l y spin-coupled that a simple f i r s t order analysis cannot be applied. On the other hand the spectrum of methyl 2,3,4,6-tetra-0_-trideuterioacetyl-a-D_-glucopyranoside-2,3,4,6,6 1 -dg (30) shown in F ig. 6.4 (b) is s u f f i c i e n t l y s imp l i f i ed that i t s proton resonances can be quant i tat ive ly studied. The proton Revalues for 30 and the corresponding 3 anomer, methyl 2,3, 4,6-tetra-0-tr ideuterioacetyl-B-D-glucopyranoside-2,3,4,6,6 ' -d 5 (3]_) were measured in deuterioacetone and deuteriobenzene, a l l at 0.10 M concentra-t ion and at 35°C. The proton n.m.r. spectra for 30 and 31_ in deuterio-acetone and in deuteriobenzene are shown in Fig. 6.5 and the R e v a l u e s obtained from various experimental sources are summarized in Table 6.7. Before we proceed to extract the geometrically relevant information from the relaxat ion data given in Table 6.7., one subsidiary problem con-cerning these compounds must f i r s t be considered. It i s immediately apparent from the spectra shown in Fig. 6.5a-d that for compounds 30_ and 31 the ra t i o of the integrated i n ten s i t i e s of the H-l resonance to that of the H-5 resonance i s not precisely 1:1; the measured value fo r 30 was 1:0.81 (H-l:H-5) and that for 3J_was 1:0.74 (H-1:H-5). This indicates - 222 -100 Hz O C H , A C H 2 O R . a O C H , R = COCD, R = COCD, Fig. 6.4 The 100 MHz proton n.m.r. spectrum of (a) methyl 2,3,4,6-tetra-0_-trideuterioacetyl-a-p_-glucopyranoside (29_) and (b) methyl 2,3, 4,6-tetra-0_-trideuterioacetyl-a-D_-glucopyranoside-2,3,4,6,6' -(30). Both spectra were obtainect in deuteriobenzene (0.10 M) at 35°C. - 223 -Fig. 6.5 The proton n.m.r. spectra (100 MHz) of 30, (a) in deuterio-actone and (b) in deuteriobenzene; and those of 3J_, (c) in deuterioacetone and (d) in deuteriobenzene. A l l spectra were obtained with 0.10 M solutions at 35°C. Table 6.7 Proton Reva lues ( l O ^ s e c - 1 , ±3%) a of Methyl 2 ,3 ,4 ,6 -Te t r a -O - t r i deu te r i oace ty l - a -D - g l ucopy ra^ 4 , 6 , 6 , - d 5 (30) and Methyl 2,3,4,6-Tetra-CI-tr ideuterioacetyl-|-D-glucopyranoside-7,3,4,6,6 - d 5 (31) l n Deuterioacetone and Deuteriobenzene, A l l at 0.10 M and at 35°C7 H-l H-5 0CH 3 Experimental 30 11 30 H 30 11 (CD 3 ) 2 C0 C 6 D 6 (CD 3 ) 2 C0 C 6 D 6 (CD 3) 2C0 C 6°6 (CD 3) 2C0 C 6 D 6 (CD 3) 2C0 C 6 D 6 (CD 3) 2C0 C 6°6 1. Non-Se lect ive b 108 145 213 317 71.2 102 178 275 360 459 347 474 2. S i n g l e - Se l ec t i ve 0 73.3 97.5 141 213 55.0 80.5 121 - - 448 - -3. Ratio 1/2 1.47 1.49 1.51 1.49 1.29 1.27 1.47 - - 1.02 - -Double-Select ive 4. R](H-1,H-5) Q 76.5 103 186 - 59.0 86.7 170 -- - - -5. RJ (H - l ,CH 3 ) e 106 143 176 - -- - - 358 461 - -6. RJ(H-5,CH 3 ) e - - - - 64.9 94.8 125 191 354 449 339 458 a I n i t i a l slopes were (t in sec) : b 0.1 < t < 2.4 c 0.1 < t < 6.0 for H-l & H-5, 0.1 < t < 2.4 f o r CH 3 d 0.1 < t _< 6.0 e 0.1 < t j< 2.4 - 225 -that some deuterium had been introduced at C-5 and hence the H-l resonance for e i ther 30 and 31 i s degenerate, corresponding to the overlapping resonances of the species depicted in formulae I and II for 30 or formulae III and IV for 3J_ OCH-III OCH-IV The existence of II and IV i s confirmed by the deuterium n.m.r. of 30 and 31 (as the protioacetate der ivat ives) shown previously in Figs. 5.20 and 5.21 of Chapter 5. That each of the relaxat ion measurements of the H-l resonances had to be made on an " i s o top i c " mixture was an unwanted complication but fortunate ly , as we sha l l short ly show, th i s did not ser iously compromise the v a l i d i t y or accuracy of the s t ructura l evaluation. It i s worth noting in passing that th i s deuteration at C-5 is not eas i ly expl icable (see Experimental sect ion). The composite R-j-value for the methyl protons is not expected to be affected by a degeneracy corresponding to the presence or absence of a proton at C-5 pos it ion because the mutual relaxat ion effects of the methyl protons are considerably more e f f i c i e n t than re laxa-t ion contributions from other spins. - 226 -Returning now to the relaxation data of Table 6.6, l e t us consider i i ^ f i r s t the values for the ra t io (ns)/R^(i) in l i ne 3. For H-l the values are e s sent ia l l y 1.5 for both compounds 30_ and 31_ in the two solvents used. This proves that H-3 relaxes exc lus ive ly via the dipole-dipole mechanism and furthermore implies that the correct i n i t i a l slopes have been used to extract the Revalues for H-l from the magnetization recovery curves. How-ever, a somewhat d i f fe rent s i tua t ion i s encountered fo r the relaxat ion of both H-5 and the methyl protons. Consider f i r s t the relaxat ion of H-5. H-5 H-5 ^ The ra t i o R-j (ns)/R.| (H-5) was again e s sent ia l l y 1.5 for the 3 anomer (31) in deuterioacetone; i t was not measured in deuteriobenzene because in th i s solvent the H-5 and the methyl proton resonances were not s u f f i c i e n t l y chemically sh i f ted from one another to allow for se lect ive inversion of the H-5 t rans i t ions without perturbing those of the methyl protons (see Fig. 6.5d). H-5 H-5 ^ In contrast, the ra t io R^ ~ (ns)/R-|~ (H-5) for the a anomer (30_) was substant ia l l y less than 1.5 in both the solvents used; the value found being ^1.3. A number of a l ternat ive reasons can be c i ted for th i s f ac t , including the p o s s i b i l i t y that an incorrect i n i t i a l slope had been used in extract ing the R^-values for H-5 of the a anomer. A more a t t rac t i ve and plaus ible a l ternat ive i s that since in the a anomer, H-5 i s s i tuated further away from the other protons i n the same molecule than i t i s in the 3 anomer, i t s intramolecular d ipolar relaxation contributions from " l i k e " spins ( i,e.protons) would be less e f f i c i e n t while those from "un l i ke " spins ( i . e . deuterons) would become correspondingly more s i g n i f i c an t . If th i s i s so, the ra t i o R^'^ns)/R^" 5(H-5) for the a anomer would be expected to be less than 1.5 and the tota l d ipolar relaxation contributions that H-5 received would be given by - 227 -5 2 [ R " 5 (ns ) - R " 5 (H-5)] f ( l i ke ) = ^ r - £ ^ [6.5] R^"5 (H-5) Note that eq. [6.5] is a special case of eq. [2.51] given e a r l i e r in Chapter 2. From eq. [6.5] and the data of Table 6.6 i t can be estimated that in deuterioacetone H-5 of the a anomer receives 59% of i t s relaxat ion con t r i -butions from other protons with the other 41% coming most probably from the nearby deuterons in the molecule. For the a anomer in deuteriobenzene, the above values were 53% and 47%, respect ively. These two sets of values were in good agreement with the calculated values of 53% and 47%, respect ive ly * . S im i l a r l y , H-5 of the 3 anomer in deuterioacetone receives 94% of i t s relaxation contributions from other protons with the remaining 6% coming from the deuterons in the molecule. These values were also in good agree-ment with those obtained from ca lcu lat ion which were 93% and 7% respect ively. From these percentages i t i s possible to evaluate the relaxation contr ibu-tions to H-5 of both the a and 3 anomer from the deuterons in the molecule; -3 -3 -1 these are respect ive ly, 23 x 10 and 7 x 10 sec (in deuterioacetone). In p r i n c i p l e , the relaxation contributions from the deuterons to H-5 should be ident ica l fo r both the a and 3 anomer; the observed difference (ca_. three-fold) is due to d i f f e r e n t i a l dynamic range effects in the two molecules. Calculat ion based on an idea l i zed C^i a-D-glucopyranose geometry and using the r~6 dependence of the dipole-dTpole mechanism. Input para 5 meters used in the ca lcu lat ion were: bond lengths, C-H(C-D) = 1.10 A, C-C = 1.52 K, C-0= 1.42 A; a l l bond angles = 109°28'. Due to the uncertainty in the or ientat ion of the deuterons on C-6, these c on t r i -butions were not included in the ca lcu la t ion . For further deta i l s see Chapter 5 and Appendix II. - 228 -CH CH ^ For the methyl protons, the ra t i o R-j 3 (ns)/R 1 3 (CH 3 ) was e s sent ia l l y unity for 30 in deuteriobenzene. This i s to be expected because the mutual relaxation between the methyl protons i s so e f f i c i e n t that re laxa-t ion contributions from other protons only const i tute a small f ract ion of the overal l re laxat ion. Inter a l i a th is then confirms the e a r l i e r sugges-t ion that the presence or absence of a proton at the C-5 pos it ion would have a neg l ig ib le e f fect on the R-j-value of the methyl protons. With th i s fact in mind further se lect ive perturbation of methyl protons was not performed. At th i s juncture, i t i s necessary to demonstrate that the R^-values for the H-l protons of both 30 and 31 contain no unacceptably large systema-t i c errors even though these resonances are "degenerate". The fact that H-l H-l ^ the ra t i o R^ ~ (ns)/R-|~ (H-l) i s e s sent ia l l y 1.5 indicates unequivocally that a l l the relaxation is d ipolar and originates from the other protons i n the molecule; relaxat ion from deuterium i s e x p l i c i t l y precluded, at least within experimental error. The results from the double- and s ing le -se lect ive pulse experiments provide further evidence. The relaxat ion contr ibution that H-l receives from H-5 i s given by P 1 5 = 2[R f j l ' 1 (H-l,H-5) - R^Vl)] [6.6] and that which H-5 receives from H-l i s given by P 5 1 = 2[R t 1 1 - 5 (H- l ,H^) - R ^ V B ) ] [6.7] In p r inc ip le p ^ 5 must be ident ica l to p 5 1 ( i . e . P 1 5 = )» and hence any dev iat ion, s i g n i f i c an t l y larger than the estimated experimental er rors , from th i s ident i ty should imply the presence of an unacceptably large systematic "e r ror " in the R-j-value of H- l . From the results summarized in Table 6.8, i t i s c lear that within the l i m i t of estimated experimental - 229 -Table 6.8 Calculated P. .-values 3 for H-l and H-5 of Compound 30 and 31 using eqs. [&.6] and [6.7]. Relaxation 30 H Contribution (CD 3) 2C0 C6D6 (CD 3) 2C0 C6°6 P15 6.4 ± 6.4 11 ± 8 90 ± 14 -p51 8.0 ± 4.8 12 ± 7 98 ± 12 -Mean3 7.2 ± 4.0 12 ± 5 94 ± g -3 Errors in the mean values are calculated according to eq. [9.6], see Section 9.2 of Chapter 9. errors P ^ = P^ -J which supports the e a r l i e r suggestion that the measured R^-values for the H-l protons of 30_ and 3_1 are e f f ec t i ve l y due to species having formulae I and I I I , respect ively. The above contention is further supported by the fact that the relaxation e f fect of a deuteron at C-5 on a proton at C-l ( i . e . 0.063 P ^ ) i s not a measurable quantity because th i s value i s smaller than the estimated experimental er rors , see Table 6.7. The most appropriate measure of the relaxat ion contr ibution between H-l and H-5 is the mean of the values of P-^ and P ^ given in Table 6.7 and hence the fol lowing general expression (derived e a r l i e r in Chapter 2, see eqs. [2.61] and [2.62]) can be used to evaluate th i s i n te rac t i on * : If PT5 and P51 as expressed in eqs. [6.6] and [6.7] are s i g n i f i c an t l y d i f fe rent as a resu l t of the H-l resonance being degenerate, then the relaxat ion interact ion between H-l and H-5 i s best evaluated by eq. [6.7] - 230 -P 1 5 = [ R ^ \ H - l , H - 5 ) - R 1 H - 1 ( H - l ) ] H R ! | , - 5 ( H - l , H - 5 ) - R y - 5 ( H - 5 ) ] [6.8] The relaxation contr ibution that H - l or H-5 receives from the methyl protons i s best evaluated by eq. [6.9]: p i C H 3 = 2 [R^ i (H - i ,CH 3 ) - R^ 'CH- i ) ] [6.9] where i = 1 or 5. The analogous expression, eq. [6.10], p CH 3 i = 2[R^ H3(H-i,CH 3) - R^H3(CH 3)] [6.10] would not be appropriate because the composite R^-value of the methyl protons is so dominated by the intra-methyl interact ions that i t i s generally insens i t ive to the small relaxat ion effects of other protons. Using eqs. [6.7] and [6.8] the spec i f i c interproton relaxat ion c on t r i -butions for the protons of 30_ and 3J_ can be evaluated and these values are summarized in Table 6.9. Interproton distances can be readi ly calculated from the relaxation contributions given in Table 6.9 according to the formalism (eqs. [6.1] and [6.3]) for d ipolar interact ions . These values together with those obtained from computer simulation of the " i dea l i z ed " geometry of 30 and 3]_ are l i s t e d in Table 6.10. It can be seen from the data fo r 30_ that the measured interproton distances are independent of the solvent used. It i s encouraging to note that the measured separation between H-l and H-5 is very close to the value obtained from computer s imulation. Let us now consider the conformation of the methyl group about the C-l-0-1 g lycos id ic bond. For 30_ the conformation of the methyl group which most c losely s a t i s f i e s the data given in Table 6.10 i s shown in Fig. 6.6. and that for the methyl group of 31_ i s shown in Fig. 6.7. - 231 -•3 -1 Table 6 9 Calculated Interproton Relaxation Contributions, P y ( 1 0 sec ), for Compounds 30 and 3J_ in Deuterioacetone, (CD^CO, and Deuteriobenzene, CgDg-Relaxation p15 5 CH 3 30 31 7.2 ± 4 . 0 1 2 + 5 94 ± 9 P 1 C H 65 ± 8 91 ± 10 70 ± 14 Contribution . . _ r n (CD 3) 2C0 C 6D 6 (CD 3) 2C0 C 6 D 5 20 ± 5 29 ± 7 8 ± 10 15 ± 14 a a Since the R 1j l" 5(H-5) value was not measured, th is quantity can only be determined from = , f { R ^ V 5 , C H 3 ) - 2 [R^ 5 (n s ) - R ^ B . C ^ ) ] } . 3 Table 6.10 Interproton Distances (A) for 30 and 3J_. 30 31 Interproton Distances Experimental 9 /"\mr\ t i "i- n v ^ Experimental 9 • • Pnmni IT*P V*^  (CD 3) 2C0 C 6 D 6 uullipUT-cr Simulation (CD 3) 2C0 C 6 D 6 Simulation r 15 3.44 ± 0.32 3.37 ± 0. 24 3.67 2.24 ± 0.04 - 2.40 r c  r l C H 3 2.86 ± 0.06 2.89 ± 0. 06 2.88 d 2.82 ± 0.10 - 2.82e r c 5CH3 3.49 ± 0.15 3.50 ± 0. 14 2.85 d 4.05 ± 0.84 3.90 ± 0.61 4.37e 9 These distances were evaluated according to eqs. [6.1] and [6.3] using P-jj-values given in Table 6.8 and T.j j - v a l ues of Table 5.18. For 3J_ in C5D5 i t was assumed that i t s motional corre lat ion i s ident ica l to that of 30_ in CgDg-b Calculated according to program NEWCART (see Appendix I I). c Using the centroid model discussed in Section 6.2. d See Fig. 6.6. e See Fig. 6.7. - 233 -C-2 H-1 0-5 <|> = 50° Exo-anomeric e f fect Fig. 6.6 The conformation of the methyl group of 30 including the pro-jec t ion viewed along the 0-1-C-l bond. For <|> = 50° the 0 calculated values of r i c H 3 a n c ' r5CH3 a r e a n c i 2 " ^ 5 ' respect ively. These values were obtained using the computer program NEWCART with the fol lowing input parameters: bond lengths92, C-H = 1.10 A, C-l-0-1 = 1.40 A, 0 - l -CH 3 = 1.42; bond angles assumed to be a l l tetrahedra l ; and the methyl proton's were approximated to the centroid model. - 234 -Anomer (31) C-2 0-5 CH 3 H-1 i> = 55° Exo-anomeric e f fect Fig. 6.7 The conformation of the methyl group for 31_ including the projection viewed along the 0-1-C-l bond. For <j> = 55°. the calculated values of r , r u and r , n , are 2.82 and I t r io bLrio 4.37 A, respectively. These values were obtained in the same $ay as those for 30 in Fig. 6.6 except for C-1-0-1 = 1.38 A92. - 235 -The conformations for the methyl groups of 30 and 3 1 as summarized in Figs. 6.6 and 6.7 appear to be consistent with the presence of the so-93 ca l led "exo-anomeric e f f ec t " in these systems. The exo-anomeric e f fect favours that conformation in which the methyl group of a glycopyranoside i s gauche to 0-5 and H- l . This exo-anomeric e f fect appears to be solvent dependent and in the next chapter i t w i l l be shown that aqueous medium compensates for th i s e f fect i f the methoxy substituent i s a x i a l l y oriented 9 3a as in 30_ - in accord with Lemieux's pred ict ion. It seemed of interest to make a check on the above conformations as fol lows. The calculated average separations between H-l and the methyl protons were set as close as possible to those obtained experimentally and the corresponding dihedral angles e were measured. Using those values the average separations between H-5 and themethyl protons in 30_ and 31 were then ca lcu lated, as shown in Table 6.9 and Figs. 6.6 and 6.7. It i s not completely c lear why the agreement between calculated and experimental values i s so close for 31 and so disparate for 30 (see Table 6.9). Obviously the excessive s imp l i c i t y of the various models used in these calculat ions cannot be expected to be en t i re l y adequate, but i t i s not immediately c lear why the i r l im i tat ions are quite so obvious for 30_. Since we sha l l return to a further discussion of glycoside conformation in Chapter 7 no conclusion w i l l be drawn at th i s juncture. 6.4 A Sucrose Derivative In the course of the preceding discussions we have so far seen three methods whereby ind iv idual interproton relaxation contributions can be quant i ta t i ve ly factor ized from the experimentally measured relaxat ion rates; these are, b r i e f l y , as fo l lows. - 236 -1. E x p l i c i t analysis of e i ther a s ingle set of non-select ive, or a combined set of s i ng le - se lec t i ve , R e v a l u e s of an i so lated three-spin system. 2. Extension of th i s method to include e i ther a double- or a t r i p l e -se lect ive equivalent in which the perturbing pulse is now applied se lec t i ve l y to any two or three resonances. 3. Comparison of the non-selective R-j-values of the normal compound with those of i t s s p e c i f i c a l l y deuterated counterpart. This section w i l l be concerned with the possible extension of the f i r s t method to systems having more than three spins, and in pa r t i cu la r to the problem of extract ing interproton relaxation contributions from jus t a s ingle set of non-selective Revalues. There are a number of ways of approaching this problem and the simplest and for many purposes the most powerful of these w i l l here be i l l u s t r a t e d with respect to the determina-t ion of the relaxation contributions which the anomeric proton of the galactopyranose residue of tetrachloro-tetramesyl galacto-sucrose der ivat ive (32) receives from the protons of the fructofuranose r ing. The non-selective proton R e v a l u e s of 32 were determined at 360 MHz and are summarized in Fig. 6 . 8 . At 360 MHz the n.m.r. spectrum of 32_ (see Fig. 6.9) shows that both the galactopyranose and the fructofuranose r ing protons are s u f f i c i e n t l y loosely spin coupled that the simple f i r s t 32 - 237 -Fig. 6.8 The non-selective R,-values (x 10 sec - ,±5%) for the protons of 32 measured at 360MHz in 0.10 M deuteriochloroform solut ion at 30°C. Fig. 6.9 360 MHz proton n.m.r. spectrum of a 0.1.0 M solut ion of 32 in deuteriochloroform (degassed), obtained by using a Bruker HX-360 i nstrument. - 238 -order analysis we have used so far can be applied to t he i r Revalues. The non-selective R e v a l u e s for the r ing protons of the gal actopyranose residue (see Fig. 6.8) can be formulated in terms of the various i n t e r -proton p -values, and as a resu l t of the inverse s ixth power dependence on distance, we need only consider nearest neighbour in teract ions , namely gauche interact ions (pg)> 1,3-diaxial interact ions ( p a a ) and for the anomeric proton, the i n te r - r i n g contr ibution ( p - j n ^ e r _ r - j n g ) • S t r i c t l y we cannot ignore the v i c i na l (1,2) t rans -d iax ia l interact ion but i t i s simpler to do so for the present argument. We shal l assume that we are dealing with protons which are relaxing exclus ive ly vi a the d ipole-dipole mechanism. Hence i t i s necessary to use 2/3 of the experimentally determined non-selective relaxation rates when ca lcu lat ing p-values and we -3 -1 can make the fol lowing formulations (in units of 10 sec ). f R y - 1 P ( n s)=p g + P i n t e r _ n . n g = 847 [6.11a] | R 1 | 1 " 2 p(ns) = P g = 573 [6.11b] | R ^ P f n s ) = P g + P a a = 940 [6.11c] | R H _ 4 p ( n s ) = 2 P g = 1193 [ 6 . l i d ] f ^ - 5 P ( n s ) = P g + p a a + p 5 p 6 p = 1360 [6.11e] Thus the R e v a l u e of H-2p gives us immediately an estimate of p - 3 -1 (573 x 10 sec ) and since interproton relaxation contributions are -3 -1 mutual, the addit ional relaxation (274 x 10 sec ) experienced by H-lp can only come from the protons of the fructofuranose r i ng ; th i s i s estimated - 239 -to be 30% of the to ta l relaxat ion experienced by H-lp. Although this arithmetic i s founded on an extremely s imp l i s t i c premise i t i s interest ing to note that the above estimate of from the H-2p resonance i s in excel lent -3 -1 agreement with the value from H-4p (595 x 10 sec ). This gives us an -3 -1 average value of 584 x 10 sec for p , which can be substituted in eqs. [6.11] thereby enabling the other p-values be readi ly evaluated as ( in units of 1 0 " 3 s e c _ 1 ) : p. . • =263 i nte r - n ng P = 356 aa 5p6p Further geometrical informations can be obtained from these p-values i f the corre lat ion times for the tumbling motion of 32_ are known. Accord-ing ly , the carbon-13 R-j-values for 32_ were determined under ident ica l experimental conditions as those used for the measurement of proton -values These values are summarized in Table 6.11. Molecule 32_ would be expected to tumble an i so t rop ica l l y and evidence for th is comes from the enhanced carbon-13 Revalue observed for C-4p which bears an equator ia l ly oriented proton. This observation is consistent with the data obtained in Chapter 5 for the 1-4 l inked disaccharides. If we assume that the pr inc ipa l ro ta -t iona l axis for 32_ runs in the general d i rect ion of the C-4p-H-4p bond and i s perpendicular to a l l the ax ia l C-H bonds of galactopyranose residue, 8 -1 Woessner's r i g i d e l l i p s o i d a l model* gives D(j = 8.6 x 10 rad sec and * — For deta i l s see Chapter 5. In th i s ca lcu lat ion C-H bond lengths are assumed to be 1.10 A and the average R,-value of 4423 x 10~3sec-l for C-2p, C-3p and C-4p is used. The assumption concerning tKe posit ion of the pr inc ipa l rotat ional axis for 32 is probably overs impl i f ied because no rate enhancement was observed for C-lp which also bears an equator ia l ly oriented proton. - 240 -- 3 -1 Table 6.11 The Carbon-13 Spin-Latt ice Relaxation Rates , (10 sec ), and Chemical Sh i f t s , <5(ppm), for Compound 32 in a 0.10 M. Deuteriochloroform Solution (degassed) at 30°C. Carbon R-|(±10%) 6(±0.1)b lp 4200 91 .3 2p 4370 72.3 3p 4480 73.5 4p 4910 59.9 5p 4420 70.2 6p 6200 41 .9 I f 5880 42.7 2f 650 103.1 3f 4170 79.6 4f 3950 78.4 5f 4090 79.0 6f 7310 44.6 a Measured with a Bruker HX-360 spectrometer operating at 90.5 MHz. Referenced to internal TMS. These resonances were unequivocally assigned through se lect ive proton decoupling. - 241 -8 -1 Dj_ = 6.8 x 10 rad sec . Thus 32 tumbles somewhat an i sot rop ica l l y with D||/Dj_ = 1.26. This means that the worst possible error that can be i n t r o -1 ir duced in the measurement of interproton distances would be [(Dj|/Dj_) - l ] , i . e . , 4% i f anisotropic reor ientat ion of 32 i s not properly corrected fo r . From these values for D| j and Dj_, the corre lat ion time (T ) for the gauche interproton relaxat ion vector ( r ) and that ( f a a ) for the 1,3-diaxial relaxation vector (r ) can be estimated. The values obtained* are x = aa g x = 2.2 x 1 0 " s e c r a d - 1 , i . e . , the reor ientat ion of the interproton aa vectors appears to be i s o t r op i c . Thus, the interproton distances for the gauche (r ) and the 1,3-diaxial ( i " a a ) interact ions can be estimated according to eq. [6.1] and these values are r^ = 2.45 A and r a a = 2.66 A. Computer 4 s imulat ions** on the basis of an undistorted C-j - conformation for the galac-topyranose r ing give r = r = 2.48 A. This implies that, in so lu t ion , the g aa actual conformation for the galactopyranose r ing of 32_ i s somewhat d i storted and th i s d i s to r t ion may be attr ibuted to the f a i r l y bulky chloro substituent a x i a l l y oriented at C-4p which causes a small f l a t ten ing of the galactopy-ranose ring at th is carbon. This i s reasonable because such a d i s to r t i on would a l t e r the r -value more substant ia l l y than the r -value. Further-aa g more, the excel lent agreement between the experimentally obtained r -value with that derived from computer simulation supports the f inding that H-lp receives a substantial amount of i t s relaxation contributions from the proton substituents of the fructofuranose r ing. Although no further experimental data are ava i lab le for 32., in the next chapter data for a * It i s assumed that r g and r a a subtend angles of 60° and 90° respectively with the pr inc ipa l rotat ional axis. * * For d e t a i l s , see Appendix II. Input parameters were: bond lengths, C-H 1.10 A, C-C = 1.52 A, C-0 = 1.42 A; and a l l bond angles = 109 28 . - 242 -disaccharide der ivat ive w i l l be provided to prove conclusively that i n te r -r i ng , proton relaxation can be substant ia l . Turning now to the data for the fructofuranose r ing of 32_ the various interproton relaxat ion contributions for the three r ing protons (H-3f, H-4f and H-5f) can be evaluated in the fol lowing way. Since we need only consider nearest* neighbour in teract ions , namely, 1,2-transdiaxial interact ions (p^) and 1,3-c i sd iax ia l interact ions (P c)> we can formulate the fol lowing equa--3 -1 tions (in units of 10 sec ). | R l j l " 3 f (ns) = P T + P C = 520 [6.8a] | R lj , " 4 f(ns) = 2p t = 593 [6.8b] f R ? " 5 f (ns ) = P T + P C + P 5 F 6 F =740 [6.8c] -3 -1 From eqs. [6.8] we f ind ( in units of 10 sec ) P t = 296 P C = 224 P 5 f 6 f = 2 2 0 I f we assume that the motional cor re lat ion times for the interproton re laxa-t ion vectors of the fructofuranose r ing are equivalent to those of the galactopyranose r ing we obtain r^ = 2.74 & (the distance between e i ther H-3f and H-4f or H-4f and H-5f) and r c = 2.87 & (the distance between H-3f and H-5f). On the basis of a f l a t fructofuranose r ing computer s imulat ion** _ For s imp l i c i t y , i t i s assumed that these protons are not relaxed by the pyranose r ing protons. Recall that H-lp i s in part relaxed by protons on the furanose r ing. This i n te r - r i n g relaxation most probably comes from the methylene protons and/or methyl protons of the other substituents of the furanose r ing. Calculat ion done in the same way as for the galactopyranose r ing. - 243 -gives r^ = 2.88 & and r c = 3.63 K. This suggests that the fructofuranose r ing favours that portion of the pseudorotational cycle centred about the 3 T 4 - t w i s t conformation in which C-3f i s displaced above and C-4f equally below the reference plane defined by C-2f:0-5f:C-5f. In th is conformation the H-3f-H-5f separation would be closer than when the fructofuranose r ing i s f l a t . The above observations are consistent with the v i c ina l proton-proton coupling constants obtained for 32_ which are shown in Fig. 6.10. Fig. 6.10 Values for the v i c i na l proton-proton coupling constants for compound 32_. 94 Following the pioneering observations of Lemieux and the subsequent 95 calculat ions of Karplus i t i s a t r i v i a l matter to i n fe r from these couplings that the pyranose r ing of 32_ has the D-galacto configuration and favours the 4 C|-cha i r conf igurat ion. Thus the couplings between H-lp:H-2p and H-3p:H-4p are charac te r i s t i c of the gauche o r ienta t ion , J 4p 5p i s t y P " i c a l o f t n e P-galacto configuration and the large value of J 2 p 3 p provides unequivocal proof that H-2p and H-3p have a t rans -d iax ia l d i spos i t ion . Turning now to the fructofuranose r i ng , we note that both 96 the v i c i na l couplings are large and, although there are many reasons why one cannot make an unequivocal conformational assignment, the values appear to be consistent with the 3 T 4 ~ t w i s t conformation assigned previously, - 244 -Although the above method of extract ing ind iv idual interproton re laxa-t ion contr ibution obviously has some serious l im i t a t i on s , i t s appl icat ion to molecules for which a reasonable number of ind iv idual non-selective Revalues can be measured, offers much the best return fo r time invested. F< more accurate work, an e x p l i c i t approach such as the method of se lect ive pulse perturbation and the method of deuteration should be used. - 245 -CHAPTER 7 A PRELIMINARY EVALUATION OF THE DETERMINATION OF THE AGLYCON-SUGAR, PROTON RELAXATION CONTRIBUTIONS OF GLYCOSIDES, INCLUDING DISACCHARIDES, BY SPECI-FIC DEUTERATION 7.1 Introduction Previous studies from th is laboratory have shown that a substantial d ifference (approximately two-fold) ex ists between the s p i n - l a t t i c e re laxa-t ion rates of the anomeric protons of reducing (H-l) and nonreducing (H - l 1 ) rings of disaccharides in aqueous solut ion (see F ig. 7.1). It was suggested reducing r ing F ig. 7.1 The reducing and nonreducing rings of a disaccharide {6-0-(g-D-glucopyranosyl )-D-galactopyranose}. _ that th i s d i f f e r e n t i a l re f l ec t s the addit ional relaxat ion contributions that H - l 1 receives from the protons on the r ing of the reducing moiety. The results in Chapters 5 and 6 of th i s thesis c l ea r l y support the v a l i d i t y of th i s speculation. Thus, from the carbon-13 R-j-values of the disaccharides discussed in Chapter 5 i t can be inferred that the rate enhancements of H- l ' are not caused by anisotropic motion of these molecules, and from the proton R-j-values of those systems discussed in Chapter 6, H- l ' could well be expected to receive a substantial amount of i t s relaxat ion from protons on the reducing sugar r ing. Unequivocal confirmatory evidence w i l l now - 246 -be provided to prove the v a l i d i t y of th is e a r l i e r speculation. The approach used is e s sent ia l l y that of Chapter 4, i . e . , se lect ive deutera-t i on . The molecules chosen to i l l u s t r a t e the approach are eight methyl D-glucopyranoside derivatives and two 1,6-linked disaccharide der ivat ives. 7.2 Results and Discussion . The spectra shown in Figs. 7.2 and 7.3 i l l u s t r a t e the determination of the non-selective and s ing le - se lect i ve relaxat ion rates for the anomeric proton of methyl e-D-glucopyranoside and the resultant data, along with that of the a anomer and the two trideuteriomethyl glucosides are given in Table 7.1. The calculated relaxat ion contributions that H-l receives from the methoxyl protons (p-j ^ ) are given in Table 7.2. The fact that the ra t i o (ns)/R-j (H-l) i s 1.5 for every compound confirms f i r s t l y , that the H-l resonances a l l relax vi a the d ipole-dipole mechanism, and secondly, that the non-selective R e v a l u e s have been determined with the correct, i n i t i a l slope approximation. It i s noteworthy that the relaxat ion c on t r i -bution received from the methoxyl protons by H-l of the 3 anomer (33) is nearly twice that received by H-l of the a anomer (35). This is con-s i s tent with the ^H-I^Hln.O.e. data reported by Lemieux 9 3 b , and c l ea r l y indicates that the d i s t r i bu t i on of rotamers about the C-l-0-1 bond of a glycoside can be very dependent on the anomeric configuration. Because of the poor dispersion of the proton spectra of the methyl D-glucopyranosides in aqueous so lut ion the above deuteration experiment could only be used to i dent i f y the methoxyl relaxat ion contr ibution to the H-l resonance. However, in the case of the corresponding tetra-C)-acetates (29_,37_-39_) a l l of the proton resonances were separately resolved in deuterioacetone solut ion and hence a d i rect comparison could be made of the non-selective Revalues of a l l the protons, including H- l , of the - 247 -2 0 0 H z i 1 Fig. 7.2 100 MHz H n.m.r. spectra of methyl 3-D-glucopyranoside, showing a two-pulse non-selective inversion-recovery determination of the s p i n - l a t t i c e relaxation rates. A l l spectra were monitored as fol lows: SW = 500 Hz, AT = 4 sec, Pl = 134 usee, P2 = 67 ysec, PD = 10 sec, NT = 8, SE = 1.5 sec, and Al = 1. The time interval (sec) between the 180° and 90° pulses are indicated to the r ight of the respective spectra. - 248 -M (oo) 3.0 2.0 0.8 0.1 2 0 0 H z Fig. 7.3 100 MHz 'H n.m.r. spectra of methyl B-D-glucopyranoside, show-ing the s ing le - se lect i ve determination -of the s p i n - l a t t i c e relaxat ion rate of H-l using a two-pulse inversion-recovery sequence. A l l spectra were monitored as for those in F ig. 7.2. except for PD = 15 sec. The duration of the se lect ive 180° pulse was 38 msec. The time interva l (sec) between the 180° and 90° pulses are indicated to the r ight of each spectrum. - 249 -Table 7.1 Spin-Latt ice Relaxation Rates 9 (x 10~ 3 sec _ 1 , ±5%) for the Anomeric Protons of Methyl D-Glucopyranosides D. R^ns) RH"Vl) 1 R 1(ns)/R! | ," 1(H-1) Methyl 3-D-glucopyranoside = (33) 640 430 1.49 Trideuteriomethyl B-D-glucopyranoside (34)~ 420 280 1.50 Methyl a-D-glucopyranoside = (35) 330 220 1.50 Trideuteriomethyl a-D-glucopyranoside (36)~ 210 140 1.50 Measured using the three-pulse, inversion-recovery sequence" with a Varian XL-100(15) spectrometer f i t t e d with a Varian 620L (16K) computer and a Line Tape unit (model C0600); the Revalues were calculated from semilog p lo t s , using a least-squares f i t , computer program. b 0.10 M solutions in DgO (99.7%)at 35°C. Table 7.2 Calculated Values for the Relaxation Contributions (x 10" sec ) to the Anomeric Proton (H-l) from the Methyl Protons (p-, C H ) Compound From R ^ n s ) 9 From R^- 1 (H- l ) b Average Value ( p l 3 C H 3 ) a v ( p l aCH 3 ) av 33 153 160 157 1.85 35 84 85 85 a P 1CH3 b P 1CH3 0.6959{R 1 H" 1(ns,0CH 3) • 1.0672{R^ _ 1(H-l,0CH 3) - R 1(ns,0CD 3)} - R n(H-l,0CD 3)} - 250 -prot io - and deuterio-methyl glycosides. As i t happened, only the H-l and H-5 resonances evidenced any detectable relaxation contr ibution from the methoxyl group and these values are summarized in Table 7.3. Although a l l the proton resonances for compounds 29_ and 37_-39_ appear to be t i gh t l y spin-coupled (see F ig. 7.4) i t i s s t i l l reasonable to make a qua l i t a t i ve comparison of the i r R e v a l u e s . For example, i t i s c lear that for both the a and 3 anomer (29 and 37_) H-l receives an equal relaxat ion contr ibution from the methoxyl protons. Furthermore, in the case of the a anomer i t i s evident that the methoxyl protons provide a s i gn i f i can t amount of relaxat ion to H-5, thereby implying that the methyl group can become quite close to H-5. These observations are consistent with the data of Section 6.3 in Chapter 6. The next important point concerns the d i s t r i bu t i on of rotamers about the C-l-0-1 bond of these glycosides. The or ientat ion of the methyl group for the a anomer appears to be more influenced by the solvent medium than is that of the 3 anomer. The preferred rotamer about the C-l-0-1 bond for both anomers in organic solvents (e.g. deuterioacetone and deuterioben-zene) appears to be the one which i s s t ab i l i z ed by the so-ca l led exo-anomeric e f f e c t * (see Section 6.3 of Chapter 6). Hence, under these circumstances the anomeric protons of the a and 3 anomers receive equivalent relaxat ion con-t r ibut ions from the methoxyl protons. However in aqueous solvent the s i tuat ion i s d i f fe rent . From the observation that the anomeric proton of the 3 anomer i s receiving nearly twice as much relaxat ion contr ibut ion from the methoxyl protons as that received by the anomeric proton of the a anomer, i t can be inferred that the methyl group of the a anomer has more rotat ional freedom about the C-l-0-1 bond than the methyl group of the a anomer. In an aqueous medium, th i s i s consistent with an e a r l i e r suggestion — . See page 251. - 251 -3 3 T Table 7 3 Non-Selective Spin-Latt ice Relaxation Rates (10 sec , ±10%) for the Protons of Methyl Tetra-0-tr ideuterioacetyl- iO-gluco-pyranosides b. Compound H-l H-2 H-3 H-4 H-5 H-6 H-6' 0CH3 29 c 270 230 150 170 360 670 650 380 37 160 220 150 180 290 680 670 -38 340 160 200 170 480 690 650 360 39 230 160 190 180 460 680 630 -Measured using the three-pulse, inversion-recovery sequence with a Varian XL-100 (15) spectrometer f i t t e d with a Varian 620L (16K) computer and a Line Tape unit (model C0600); the R-j-values were calculated from semilog p lo t s , using a least-squares f i t , computer program. b Samples were prepared as 0.1 M so lut ion in deuterioacetone (degassed) and measurements were made at 35°C. 0 The proton n.m.r. of this compound in deuteriobenzene was shown e a r l i e r in F ig. 6.4a. H6.H-6' H-4 H-5 OR'" R" 0 - OR'" H-2 H-3 OR'" 29 R' 37 R' 38 R' 39 R" H, H, OCH3, 0CD 3 , R" R" R" R" OCH3, 0CD 3 , H, H, R"1 R"1  R.. i R'" = 0C0CD 3 = 0C0CD 3 = OCOCD3 = 0C0CD„ - 252 -100 H z i 1 Fig. 7.4 The 100 MHz proton n.m.r. spectra of trideuteriomethyl t e t r a -O-trideuterioacetyl-B-D-glucopyranoside (39) showing that although indiv idual proton resonances are s u f f i c i e n t l y well resolved, they are s t i l l t i g h t l y spin coupled. - 253 -* 97 93a The anomeric and exo-anomeric effects are two d i f fe rent terms for the same general phenomenon. The anomeric e f fect relates to the pre-ference for the axia l or ientat ion of the aglycon of glycopyranosides, as i l l u s t r a t e d by the conformational preferences of structures III and IV over structures I and II for 2-methoxytetrahydropyran whereas the exo-anomeric e f fect concerns the preference for the aglyconic carbon (the methyl group carbon) to be in near syn-c l ina l or ientat ion to both the r ing oxygen and the anomeric hydrogen; i . e . , preferences for the conformations II and IV over conformations I and I I I, respectively (the arrow next to an o rb i ta l indicates that i t i s ant i -per ip lanar to a C-0 bond). Compare also Figs. 6.6 and 6.7 in Chapter 6. For further deta i l s see ref s . 93a-d. - 254 -that the a anomer does not p re fe ren t i a l l y maintain i t s exo-anomeric-effect-s t ab i l i z ed rotamer whereas the 3 anomer does. Further experimental data concerning the re l a t i ve populations of each of the possible rotamers about the C-l-0-1 bonds and the i r r e l a t i ve relaxation contributions to H-l would be required before the present relaxat ion data can be cast into a more quant itat ive form. Unfortunately the synthetic d i f f i c u l t i e s associated with the preparation of su i tab le model compounds were beyond the scope of th i s study and th i s point was not pursued further. Nevertheless, encouraged by the above experiments, i t was decided to extend th i s se lect ive deuteration approach to a disaccharide and for reasons of synthetic convenience, 6-0-(3-D-glucopyranosyl )-fJ-galactopyranose (18) * and 6-0-(g-D_-glucopyranosyl )-D_-galactopyranose-6,6-d^ (]_9_) were synthesized. The non-selective Revalues for the anomeric protons of these two der ivat ives are summarized in Table 7.4. Several sets of intercomparisons can be made. At the nonreducing centre, the pronounced (ca. two-fold) d i f f e r e n t i a l between 26 the R-j-values for H-la and H-l3 i s typ ica l of pyranose der ivat ives and re f lec t s the greater re laxat ion contributions which the ax ia l proton at C-l 26 receives from H-3a and H-5a as compared with i t s equatorial counterpart . More relevant in the present context is the enhanced relaxat ion of the non-reducing anomeric proton (H - l 1 ) when compared with i t s counterpart at the reducing centre (H- l ) . Before continuing the discussion on the R e v a l u e s of H-T i t should be noted that i t s resonance i s degenerate, corresponding to the a and g anomer at the anomeric centre of the reducing residue. Fortunately, since the tumbling motions of the a and B anomers are very s im i l a r (see Table 5.3 of Chapter 5), and H-T i s simply too far from H-l to receive any relaxat ion The carbon-13 n.m.r. of these disaccharides were studied in Chapter 5. - 255 -Table 7.4 Non-Selective Spin-Latt ice Relaxation Rates 9 (10" sec" , ±5%) for the Anomeric Protons of Disaccharides ]_8 and 1_9.D H-l (reducing residue) H- l1 (nonreducing residue) Compound H-la Ratio H " 1 B H-1B/H-1 Ratio H " V B H - l 1 B/H-l 3 18 450 1060 2.36 1820 1.72 j_9 450 950 2.11 1150 1.21 a See footnote ' a ' of Table 7.3. b 0.1 M solutions in 100% D20 at 35°C. - 256 -contr ibution from i t , th i s does not introduce any substantial systematic error into the R-j-value of H - l ' . It follows then, that the obvious source of the enhanced relaxation of H - l 1 are the protons on the reducing r ing and confirmation that the protons on C-6 const itute a substantial proportion of that relaxation contr ibut ion comes from the R-j-values of H - l ' 3 in the 6,6-dideuterio der iva-t i v e . Simple calculat ions fol lowing the procedure outl ined e a r l i e r (see Chapter 4) indicate that the p-value between H- l ' 3 and C-6 protons is -3 -1 470 x 10 sec , which i s 26% of the to ta l relaxat ion of H - l ' 3 . Further quant itat ive information cannot be extracted at th i s stage because i t would require a deta i led knowledge of the rotamer d i s t r ibut ions about both the C- l 1 -0 -6 and the C-6-0-6 bonds. Such information i s not currently ava i lab le . Of course i t s t i l l remains that the observed R-j-value for H-13 of the -3 -1 dideuterio der ivat ive i s 110 x 10 sec (^ 10%) faster than that of the prot io der ivat ive and reasons for th i s must be sought. One p o s s i b i l i t y i s that the remaining enhancement i s due to the relaxat ion contributions emanating from the other remaining protons of the galactopyranose r i n g ; obviously th i s could be checked experimentally by further deuteration experiments. The a l ternat ive explanation i s that the disaccharide molecule as a whole i s tumbling an i sot rop ica l l y and hence that the the corre lat ion times of the protons of the reducing r ing are d i f fe rent from those of the nonreducing r ing . This may be a p o s s i b i l i t y but i t appears to be un l ike ly because we know from studies of the carbon-13 R e v a l u e s of 1_8 (see Table 5.3 of Chapter 5) that the two sugar rings have very s im i l a r tumbling motions and anisotropic motion, even i f present, was not detected. - 257 -7.3 Conclusion The potential of proton s p i n - l a t t i c e relaxat ion rates as a measure of the s t e r i c interact ion between the protons of a sugar and those of an aglycon i s c l ea r l y demonstrated here. For glycosides and oligosaccharides the magni-tudes of interproton relaxat ion contributions can be conveniently evaluated by spec i f i c deuteration. It seems reasonable to suggest that a systematic study of other glycosides would be worthwhile - e.g., intercomparisons between glycosides of D-glucopyranose and D-mannopyranose might be expected to reveal the e f f e c t , i f any, of the C-2 hydroxyl group on the glycoside or ientat ion. In l i k e fashion, intercomparisons between a series of spec i -f i c a l l y deuterated disaccharides should provide rather unique information concerning the re l a t i ve spat ia l d i s t r i bu t i on of the two r ings. The extension of th is to study the complete geometry of oligosaccharides i s obvious. It i s however c lear that whi l s t the data for oligosaccharides might be i n t e r -pretable on the basis of a r i g i d geometry, th i s i s cer ta in ly not possible for the simple glycosides, for which detai led models of the rotameric i n te r -conversion rates and populations are required; such studies would appear to merit immediate consideration. - 258 -CHAPTER 8 SUMMARY As a preface to th i s Summary i t seems appropriate to give a b r i e f chrono-log ica l account of the development of the work described in th i s thes is . Pr ior 2 1 1 to September 1974 i t was well known that H-{ H}n.0.e. experiment could pro-vide valuable information concerning interproton distances and hence solut ion 98 geometry. It was further known that proton Revalues exhibited a number of interest ing qua l i ta t i ve geometrical dependences and there was cause to believe that these might be placed on a quantitat ive basis. This development was chosen as the pr inc ipal thrust for th i s study. During 1975-76 instrumentation for performing se lect ive pulse re laxa-t ion experiments ( ta i lo red exc i tat ion and audiomodulation became avai lable at the Univers ity of B r i t i s h Columbia (U.B.C.) and the appl icat ion of these forms the basis fo r Chapter 3. With se lect i ve relaxat ion data on hand i t became necessary to develop the relevant theory for these experiments. 34 38 This proved to be a lengthy task. As i t happened other laboratories ' also became interested in d ipolar relaxat ion theory; although that theory did not address the spec i f i c problem of homonuclear se lect i ve pulse exper i -ments, several of the concepts could be adapted to the present work and th i s was most he lp fu l . S im i l a r l y , the use of deuteration as a method for evaluating interproton p-values was developed simultaneously to th i s work, 31 32 by Akasaka et a l . and E l l i s and co-workers . As a resu l t of the studies described in th i s thesis i t i s now r e a l i s t i c to suggest that determination of proton Revalues can provide an accurate measure of solut ion geometry for r i g i d molecules which have well dispersed proton n.m.r. spectra, and for which the interproton distances do not span - 259 -an excessive range. This dynamic range depends c r i t i c a l l y on the experimen-ta l error in proton R-j-value measurements - the ultimate source of accuracy or error. For example, a ±5% error in proton R-|-values l im i t s the range of rat ios of interproton distances to 1.0-1.6 (approximately) i f these distances M L are to be measured within ±10% (see also Tables 4.7 and 4.8, Chapter 4). In 1975, the instruments at U.B.C. gave data accurate to ±5% provided that substantial e f fo r t s were made (see Chapter 3). In contrast the data obtained on a d i r e c t , s ingle-run basis in 1978 using an instrument equipped with a superconducting magnet had the same error or perhaps less (see Chapter 4). It seems not unreasonable then to predict that the e f fec t i ve accuracy of proton R-j-values can only increase in the future. This w i l l increase both the accuracy with which interproton distances are evaluated, and the dynamic range of d i s -tances which can be measured with acceptable accuracy; at the same time the increased spectral dispersion associated with high Zeeman f i e l d s w i l l decrease both second order ef fects in the spin systems and w i l l further reduce o f f -resonance effects accompanying se lect ive pulse experiments. For r i g i d molecules without an excessive dynamic range problem and which are tumbling in the extreme narrowing region, the complete experimental pro-tocol fo r the method can be summarized as fo l lows: 1. Measure'and define the i n i t i a l slope R^-values; 2. Quantitat ively determine the extent to which each proton i s being relaxed via the dipole-dipole mechanism (1.5 r a t i o ) ; 3. Measure the magnitudes of a l l the i nd i v i dua l , pairwise interproton relaxat ion contributions (p-values), using se lect ive pulse, spec i f i c deutera-t ion or some form of " regress ional " analysis of the non-selective Revalues (e.g. see Chapter 6, Section 6.4)*; * p-values can also be determined v ia n.O.e. measurements, see ref. 2. - 260 -4. Independently determine whether or not the molecule i s tumbling i s o t r op i c a l l y ; 5. Use the rat ios of the p-values to calculate the rat ios of a l l the corresponding interproton distances - th i s can be converted to absolute distances; and 6. Check the geometry of the molecule obtained in 5 against some other method. In Chapters 6 and 7 preliminary studies of the effects of large i n te r -proton separation, anisotropic motion, internal molecular motion (e.g. CH^) and i n te r - r i ng relaxat ion on the determination of p-values were made. It i s c lear that further studies on these ef fects are required before they can be better understood. F i n a l l y , although proton R-j-values through the i r r" dependence can provide a f a c i l e means for determining molecular geometry in so lu t ion , the same dependence also l im i t s the range of internuclear distances that can be measured with an acceptably level of accuracy. Nevertheless, in general only proton -values can y i e l d information regarding the geometry of -9 molecules (symmetrical and unsymmetrical) dissolved in a nonviscous (10 < -12 T < 10 ) medium. Exceptions to th i s general izat ion are molecules possess-ing high symmetry which can be studied p a r t i a l l y oriented in l i q u i d c r y s t a l l i n e solvents. - 261 -CHAPTER 9 EXPERIMENTAL 9.1 N.M.R. Measurements A detailed descr ipt ion of the experimental procedure used to obtain a l l the n.m.r. spectra described in Chapter 3 w i l l now be given; the same procedure was used for a l l n.m.r. measurements reported in the other chapters. A l l proton n.m.r. measurements for compound J_ were made with the (Varian) XL-100 (15) instrument at U.B.C. operating at a probe temperature of 35°C. The spectrometer was contro l led by a Varian 620L (16K) computer. A Line Tape unit (model C0600) allowed for the sequential storage (vide  in f ra ) of up to 18 separate spectra, each containing a maximum of 8K data points. The "conventional" non-selective (or "hard") pulse relaxat ion exper i -ments were based on an otherwise standard Varian program (994100-DX2) which 99 had been modified by R. Burton at U.B.C. to provide the necessary m t e r -21 face with the Line Tape unit . Options for both the two-pulse and three-28 pulse inversion-recovery sequences are ava i lab le. Extensive experience over the past four years indicates that more accurate relaxat ion rates are obtained when the fol lowing acqui s i t ion sequence i s used: For the two-pulse method, {PD-180°-t 1-90 o-AT-PD-180 o-t 2-90°-AT-PD ... t^} where i i s the tota l number of " l i t t l e t " values required for each experiment, AT is the acqui s i t ion time (the period during which the free induction decay, f . i . d . , s ignal i s acquired), PD i s the pulse delay set such that AT + PD > 5T-,, and n i s the to ta l number of transients - 262 -(acquis i t ion) required*. This approach has the merit that long term d r i f t s in resolut ion tend to be averaged across the ent i re set of measurements and a further randomization can be obtained by the order selected for the pulse interva ls ( t -va lues) ; but th i s l a t t e r point i s less important. A tota l of i = 18 f . i . d . ' s can be stored on each magnetic tape, with at least two of these corresponding to t = 5T-| so that a measure for the equi l ibr ium magne-t i z a t i on i n tens i t i e s can be obtained. For proton measurements, the lowest number of transients which give spectra with the least phase d i s tort ions i s n = 4. The set of spectra previously shown in Fig. 3.2 i l l u s t r a t e a t y p i -c a l , non-selective relaxat ion experiment using a two-pulse sequence. For the three-pulse experiments, a s imi la r sequence is used, {PD-180 0-t 1-90J-AT-PD-90^AT...t i) ; the f . i . d . ' s resu l t ing from the 90° pulses are added and the f . i . d . ' s from the 90° pulses are subtracted in the d i g i t a l computer, which results in a spectrum af ter Fourier transformation in which the i n tens i t i e s of the t rans i t i on l ines provide a measure for the quantity M (°°)-M(t). It was claimed that th i s pulse sequence can help to minimize the effects of d r i f t s in instrument resolut ion and spectrometer gain over long accumulation times. The relaxat ion data obtained for compound 1 show that there i s no real advantage in using the three-pulse sequence over the two-pulse sequence. On the contrary, the two-pulse sequence is found to-be more useful in that the motions of the nuclear magnetization for any spin can be more readi ly followed in the p a r t i a l l y relaxed spectra. Furthermore i t takes about twice longer to acquire re laxa-t ion data using the three-pulse than the two-pulse sequence. The "conventional audiomodulation" se lect ive (or " s o f t " ) pulse re laxa-t ion experiments used the same computer software with the minor change that * 100 This method of data acqu i s i t ion was i n i t i a l l y used by Mayne et a l . - 263 -the se lect ive perturbation pulses were now obtained from the Varian Gyrocode decoupler, using the standard gating ins t ruct ion and the gate provided with the instrument. The frequency bandwidth in Hz of such weak se lect ive pulses i s approximately given by l/i^gg, where i s the duration of the selec-t i ve 180° pulse in sec. It was found that for a sat i s factory inversion of a complete proton mu l t i p l e t , an " e f f e c t i v e " bandwidth of V2T^gQ Hz i s generally required. Note that the bandwidth at ha l f -he ight, Lv1 , i s given by Y B I I 2 ^ ^ISO-Equation [9.1] was used as the basis for the choice of values of I ^ Q in the se lect ive pulse experiments. Thus, the duration of 20 msec for the pertur-bation pulse, which corresponds to an e f fec t i ve frequency bandwidth of 25Hz, was chosen as being a good compromise between the bandwidth required to invert a mul t ip let resonance, without generating excessive off-resonance f i e l d s at neighbouring resonances. Observe that for 1_the widest separation between any two t rans i t i on l ines within a mult ip let is that for the H-2 resonance; th is being approximately 20 Hz, and a se lect ive pulse must be strong enough to invert a l l the t rans i t i on l ines within th i s mul t ip let with equal in tens i ty . The attenuator of the Gyrocode decoupler was set in the usual way to provide the required 180° pulse. For the s ing le - se lect i ve pulse experiments the Gyrocode frequency was set at the midpoint of the chosen mul t ip le t . For the double-selective inversion experiments the gyrocode frequency was set prec ise ly at the midpoint between the two resonances of interest and an aud io -osc i l l a to r (Wavetek, model 113), set to provide a sine wave (one vo l t peak-to-peak) of frequency equal to one-half the chemical s h i f t separation between the two resonances, was connected to the external modulation input (J1043) of the Gyrocode decoupler. - 264 -The spectra given in Fig. 3.3 are typ ica l of a s ing le - se lect i ve inversion-recovery experiment and those in F ig. 3.4 of a double-selective inversion experiment. The " t a i l o red exc i t a t i on " experiments used es sent ia l l y the same appara-29 tus as that described by H i l l and Tomlinson . The computer so f t - and hard-ware for the ta i l o red exc i tat ion experiments were i n s t a l l ed into the U.B.C. XL-100 (15) instrument by H.D.W. H i l l * as a g i f t to th i s laboratory. A l l of the experiments discussed in Chapter 3 were performed in both the conventional and ta i l o red exc i tat ion modes. The l a t t e r i s substant ia l l y the more convenient procedure for a l l experiments, and i t i s appropriate to observe that th i s convenience factor is l i k e l y to be even more marked fo r studies of more complex spin systems. That consideration apart, the pr inc ipa l difference between the two sets of procedures appears to be asso-ciated with the phase-alternation sequence which is incorporated into the ta i l o red exc i tat ion software. This eliminated the occasional phase and intens i ty anomalies which were found in some of the conventional spectra; a typ ica l example i s shown in F ig. 9.1. It i s relevant to comment that the occasional occurrence of these anomalies did not appear to s i g n i f i c an t l y detract from the accuracy of the conventional data (vide i n f r a ) , and a pulse-alternat ing sequence i s now avai lable from Varian for use with conventional experiments. The R-|-values were calculated from the experimental data using the procedures given below. Following an ent i re relaxat ion experiment the p a r t i a l l y relaxed spectra were obtained by Fourier transformation of the previously stored f . i . d . ' s and were separately plotted in the usual way, and the peak heights obtained from the teletype output. The sum of the _ Varian Associates, 611 Hansen Way, Palo A l t o , Ca l i f o rn i a 94303. - 265 -H-l H-3 Fig. 9.1 Comparison of spectra obtained vi_a the audiomodulation and ta i l o red exc i ta t ion methods. In A the Gyrocode decoupler was set to i r r a d -iate the H-2 resonance at 58825 Hz with an attenuation of 106 dB, and the resultant 180° pulse had a duration of 20 msec. The spec-trum was sampled using the conditions of F ig. 3.2 with t = 1.0 sec. The spectrum in B was obtained v ia the t a i l o red exc i ta t ion program using a transmitter of f set of 44801 Hz, "exc i ta t ion funct ion" = 289.1050.0; "random phase" = 0; "exc i ta t ion sca l i ng " = 1250; again iiic 180° pulse duration was 20 msec and t = 1.0 sec. - 266 -heights of a l l the components of each separate spin mult ip let were then obtained, i . e . , the quantity M(t^). These values were then used together with the t.- values as the input data for a computer program written by R. Burton at U.B.C. which calculates the best, least-squares st ra ight l i ne by f i t t i n g the theoret ical function to the data by minimizing the root-mean-square difference between the logarithm of the function and the logarv thm of the observed i n t en s i t i e s . Thus, Ex i Ey i Ex.y. - — - — R = -TJ " [9.2a] 1 2 ( zx , ) 2 Z x i n — Ey. Ex. A ^ " R ^ [9.2b] [9.2c] y. = *n[MH-M(t n . ) ] [9.2d] and where exp(A) gives a measure of 2M(0). The R^-values so obtained are necessari ly negative in sign because these relaxat ion l ines always possess a negative slope; and i t i s obvious that the absolute values be taken. It i s relevant to note that the r a t i o 2M(0)/M(°°) be as close to two as poss ib le; because a value of two indicates that the desired pulses (180°,90°) have been correct ly set. For a l l the relaxat ion studies reported here, th i s r a t i o was found to be > 1.9. As th i s program was wr itten for the Varian 620L (16K) computer, i t has a useful feature in that i t provides in tabular form from the te letype, the deviation of each experimental datum point from the best s t ra ight l i n e . Any data points which are c l ea r l y in substantial error can then be eliminated with x.j = t.j - 267 -and the slope recalculated. Fortunately such points seldom occur. This program also calculates the percentage standard errors in the derived R e -values according to 1 x 100% [9.3a] AR 0 Ed 2 AR? = 5—5- [9.3b] 1 (n-2)s ef d. = y. - A - R ] X i [9.3c] EX. e. = — 1 - x. [9.3d] l n i When the standard errors fo r the R-j-values were substant ia l ly large (E > 10%) the relaxat ion measurements were repeated. For most of the proton relaxat ion rates reported here, the standard errors are less than 2.5%. The measurements of carbon-13 R^-values for compound 1_ were made with a standard Varian CFT-20 (16K) spectrometer, operating at a probe tempera-ture of 35°C and using the standard acquis i t ion software without e i ther cassette or f loppy-disk device. The p a r t i a l l y relaxed carbon-13 n.m.r. spectra were obtained with the usual two-pulse inversion-recovery sequence, i . e . , (PD-180°-t i -90°-AT) n , (PD-180°-t i-90°-AT) n. The relaxat ion rates were calculated with the same program used for the proton data (vide i n f r a ) . 13 1 The C-{ H) n.O.e. measurements for compound ]_ were also measured with the CFT-20 instrument according to the gated-decoupling in s t ruct ions * of the spectrometer. The procedure used for the C-{ y i gated n.O.e. measurements i s e s sent ia l l y that described by Freeman et a l . ° - 268 -A l l subsequent TOO MHz proton and 20 MHz carbon-13 n.m.r. spectra were obtained in th i s laboratory by the author according to the methods described above, unless otherwise mentioned. Datailed experimental para-meters are noted in Figure captions and Table footnotes given in the text. The calculat ions of relaxat ion rate parameters were also s im i l a r l y performed (eqs. [9.2]). In some instances, carbon-13 resonances were assigned unequivocally by se lect ive proton decoupling. These experiments were performed on the CFT-20 instrument with a minor change; the decoupling frequency was pro-vided by a Hewlett-Packard frequency synthesizer (model 5105A), which i s driven by a "master o s c i l l a t o r " (Hewlett-Packard, model 5110B) locked to the one MHz master o s c i l l a t o r output of the CFT-20 spectrometer (J532). The 13 1 chemical s h i f t ( in Hz) of the proton resonance, whose one-bond C- H sca lar coupling i s to be i r r ad i a ted , i s entered through the synthesizer keyboard, while the necessary decoupling power i s contro l led by an attenua-tor connected between the frequency synthesizer and a Boonton Power Ampl i f ie r (Type 230A). The spectra were then sampled in the usual way. Further 23 deta i l s of th i s procedure have already been described elsewhere . The 400 and 360 MHz proton n.m.r. spectra were measured respect ively by W.E. Hu l l * and W. Schittenhelm** according to instruct ions provided by the author. The 400 MHz spectra were obtained with a Bruker WP-400 spec-trometer while those at 360 MHz were obtained with a Bruker HX-360 i n s t ru -ment both operating in the pulse Fourier transform mode. P a r t i a l l y relaxed spectra were obtained with the usual two-pulse inversion-recovery sequence. The se lect ive perturbation pulses for the 400 MHz spectra were obtained from the decoupler by the conventional method described e a r l i e r . * Bruker Analytishe Messtechnik, GMBH Bruker-Spectrospin AG 7512 Rheinsteten 1/Karlsruche Zurich Fallenden W. Germany Switzerland - 269 -The 67.89 and 90.5 MHz carbon-13 n.m.r. spectra were obtained by K. Bock* and W. Schittenhelm, respect ive ly, using a Bruker HFX-270 and a Bruker HX-360 instrument, for the author. The 61.42 MHz deuterium n.m.r. spectra were measured by W.E. Hull for the author. Although most of the relaxat ion parameters were obtained from eqs. [9.2], those of 360 MHz proton, 67.89 and 90.5 MHz carbon-13 were calculated with a d i f fe rent procedure, which is the fo l lowing. The experimental data points were f i t t e d i t e r a t i v e l y by a nonlinear least-squares method to e i ther eq. [9.4a] or eq. [9.4b] depending whether M(t.) = M(0)[l-2exp(-t i/T 1)] [9.4a] M(t-) = M(0){l-2[l-exp(-W/T 1 )]}exp(-t i /T 1 ) [9.4b] the M(t-j)'s were obtained under the condition AT + PD > 5T-|, or <5T-j, respec-t i v e l y , in the pulse sequence (180°-t i-90°-AT-PD) n. In eq. [9.4b], W = AT + PD, and i t can be seen that when AT + PD > 5T^, eq. [9.4b] s imp l i f i e s to eq. [9.4a]. In using eq. [9.4b], i t i s relevant to note that AT + PD should be set greater than one T-|-value for better accuracy 8^, and i t i s more suited for carbon-13 -value measurements, where a large number of acquis i t ions (n) i s often used, than for proton Revalue measurements where only a few acquis i t ions are usually needed. The computer programs for these nonlinear least-squares ca lcu lat ions were also wr itten by R. Burton, and were based on the Marquardt algorithm as described by B e v i n g t o n ^ . The method e s sent ia l l y finds the best curve that f i t s a set of experimental data points {M(t n-),t.} and calculates the two intercepts , M(0) and * The Technical University of Denmark, Department of Organic Chemistry, 2800 Lyngby, Denmark. - 270 -t T M i l {M ( t n i l l l ) } = 0 C9.5] 1 Jin2 ^ , , v unul1 Thus, the equi l ibr ium magnetization i n ten s i t i e s need not be known. Although these nonlinear procedures of extract ing relaxat ion parameters have the advantage of saving experimental time, they are less suited for i n i t i a l slope calculat ions because for data points close to the i n i t i a l slope eqs. [9.4] are considerably more sens i t ive to any missetting of the pulse angles than eqs. [9.2]. Thus eqs. [9.2] were used in most cases, and only in cases where saving of experimental time become c r i t i c a l were eq. [9.4a] or [9.4b] used. 9.2 Error Analysis In general, the overal l percentage experimental error for a set of measured -values i s taken to be twice the largest percentage standard error found in the set. The errors in the derived quant i t ie s , e.g., p..-values and r. . -va lues, are then calculated according to the general * expression of eq. [9.6] 2 ,3f»2 2 , ,3f,2 2 , , ,3f ,2 2 r q ,-, a = a l + a 2 + ••• + {m]n a n C 9 - 6 ] where a i s the error in the derived quantity f which i s a function of the measurables m^, m,,, mn with errors a-j, a^, a n respect ively. This approach was found to be adequate fo r studies in which R^-values were determined only once provided the standard errors are low (< 5%). The errors in the proton Revalues given in Chapter 3 were estimated S t r i c t l y , a , a r a n are standard errors , and m 1, m 2 > . . . . mn are mean values. - 271 -d i f f e ren t l y . Since several measurements were made for each of the proton Reva lues, i t was possible to calculate the standard deviations (s) for these values (eq. [9.7]). The standard s = [ I s (m i - -±fV [9.7] errors were then obtained from eq. [9.8], e = 4 [9.8] n^ n here being the number of measurements. The standard errors were then substituted into eq. [9.6] and the standard errors fo r the derived quanti-t i e s ca lcu lated. Where time and patience permit the l a t t e r method i s ce r ta in l y the more sat i s factory approach for the estimation of experimental errors in derived quant i t ies . 9.3 N.M.R. Sample Preparations For a l l proton relaxat ion measurements, the required amount of the compound was dissolved in the appropriate deuterated solvent, f i l t e r e d into a 5 mm n.m.r. tube f i t t e d with a BIO ground-glass j o i n t , degassed by s ix freeze-pump-thaw cycles, and then sealed under vacuum. Water-soluble samples were l yoph i l i zed and dissolved in e i ther 99.7% or 100% D^O, while the other samples were prepared in deuterated acetone, benzene or chloroform. The proton chemical sh i f t s for compounds 1_ (Chapter 3) and 27_ (Chapter 6) were made with solutions s im i l a r to those used for relaxation studies, containing TMS, but not degassed. The deuterium-induced proton chemical sh i f t s reported in Chapter 4 were made on the same samples used for relaxation studies, referenced to CgD^H set at 7.17 ppm downfield from TMS, for a l l the samples, compounds 2_ to 5_. - 272 -A l l 20 MHz carbon-13 n.m.r. were made in 10 mm tubes. Where sample i s p l e n t i f u l , a 1.0 M solut ion in 2.0 ml was used, otherwise the volume i s reduced to 1.0 ml ( s t i l l 1.0 M) with the other 1.0 ml space f i l l e d with a vortex plug. Due to low s e n s i t i v i t y of the CFT-20 instrument, carbon-13 relaxat ion measurements at 20 MHz were not attempted for sample concentra-tions less than 0.5 M. The higher f i e l d carbon-13 measurements were made on samples used previously for proton relaxat ion studies, i . e . 0.1 M so lu-tions in 5 mm tubes. Samples for carbon-13 measurements were generally not degassed since a l l the carbon-13 R-j-values studied here were less than 10 sec^ 3 ; the v a l i d i t y of th i s pract ice was confirmed by the 100% 1 3C-{^H} n.O.e. observed in a l l instances where n.O.e. was measured. Water-soluble samples such as those studied in Chapter 5 were not l yoph i l i zed for carbon-13 relaxat ion studies. The samples for deuterium relaxat ion studies were dissolved in protonated 83 solvents, not degassed , and measurements were made in 10 mm tubes. 9.4 Sources of Materials Materials fo r the studies described herein were e i ther obtained commer-c i a l l y , or g i f t s from others, or synthesized in th i s laboratory. Commerical materials were: deuterated and protonated solvents, c e l l o -biose, gentiobiose, lactose, maltose, melibiose, l-methoxy-2,4-dinitrobenzene and tetramethylsi lane (TMS). The commercial sources were: A l d r i c h , Eastman Kodak, Matheson Coleman and B e l l , Merck Sharp and Dohme, No re l l , and Pfanstiehl The fol lowing compounds were g i f t s from others: methyl a-D-galactopy-ranoside and methyl 3-D-galactopyranoside (K. Bock), methyl g-D-lactoside (E.J. Re i s t ) , methyl B-D-cellobioside and 6-0-(e-D-glucopyranosyl)-D-galactose (J.M. Berry), 4,6-0-benzylidene-2-deoxy-a-D-ribo-hexopyranoside (L. Evelyn), and tetrachloro-tetramesyl galacto-sucrose (L. Hough). - 273 -Commercial materials and compounds from others were used without further pu r i f i c a t i on . The fol lowing compounds were synthesized: 1,2,3,4,7,7-Hexachloro-6-exo-0-benzoyl-bicyclo [2.2.1] hept-2-ene A sample of 1,2,3,4,7,7-hexachloro-6-exo-0-hydroxyl-bicyclo [2.2.1] hept-2-ene prepared by the D ie l s -A lder condensation of v inyl acetate with the corresponding hexachlorobicycloheptadiene, followed by de-0_-acetylation was avai lable from another s t u d y ^ ' 1 0 2 . jo a so lut ion of 3.0 g of th i s alcohol in 25 ml of anhydrous pyridine was added, dropwise, 1.5g (1.2 ml) benzoyl ch lor ide, and the reaction mixture was s t i r r ed at room temperature for two hours. The pyridinium hydrochloride s a l t was f i l t e r e d off and 75 ml of ether was added to the f i l t r a t e . The ethereal solut ion was then washed with water (3 x 20 ml), 5% sodium bicarbonate so lut ion (20 ml) , water (20 ml) and dried over anhydrous magnesium sulphate. Having removed the mag-nesium sulphate by f i l t r a t i o n and the ether by evaporation, the crude pro-duct was r ec r y s t a l l i z ed from 95% ethanol. The dried pure colourless crysta l s (3.2 g, i . e . 80% y i e l d ) had m.p. 90-91°C ( l i t . v a l u e 1 0 3 91°C). Arabinopyranose Derivatives 2 to 5_ The four arabi nopyranose derivat ives 2_ to 5_ were synthesized by Dr. J.D. Stevens* who also made the neutron d i f f r a c t i o n studies on one of these der ivat ives . Detailedexperimental procedure used by Dr. Stevens for these syntheses are given below. Optical rotations were determined using a Bendix-NPL Automatic Polarimeter, Model 143. Melting points were determined using a Reichert hot stage microscope. G . l . c . analyses were carr ied out at 190°C using a 2.2 m glass column packed with 3% diethyleneglycol adipate ( S tab i l i zed , Analabs, SLP-026) on Chromosorb W-HP (80/100); under these condit ions, Department of Organic Chemistry, Univers ity of New South Wales, P.O. Box 1, Kensington, NSW 2033, Aus t ra l i a . - 274 -B-D-arabinopyranose tetraacetate had a retention time of 13.4 min and the other arabinose tetraacetates gave r i se to two peaks, at 18.4 and 20.7 min. 1,2,3,4-Tetra-Q-trideuterioacetyl-g-D-arabinopyranose (2.) To a magnetically s t i r r ed mixture of anhydrous pyridine (1 ml) and acet ic anhydride-dg (Merck, Sharp and Dohme, Canada) (1 ml) cooled in an ice-water bath was added 250 mg of Il-arabinose. After the mixture had been s t i r r ed for 10 hr at 0°C i t was allowed to warm to room temperature overnight. The reaction mixture was evaporated and a solut ion of the residue in aqueous ethanol was seeded with B-D_-arabinopyranose tetraacetate. The c r y s t a l l i n e product was co l l ec ted , washed with aqueous ethanol, and vacuum dr ied; y i e l d 96 mg, m.p. 99-100°C, g . l . c . retention time, 13.4 min. 1,2,3,4-Tetra-p_-trideuterioacetyl-5-deuterio-g-L-arabinopyranose (3_) To a solut ion of ethyl g-D-galactofuranos ide 1 0 4 (3.12 g) in water (25 ml) was added a so lut ion of sodium metaperiodate (3.42 g) in water (25 ml), 5 ml of water being used to complete the transfer. The reaction mixture was cooled for 2 min, then l e f t at 25°C. Thin-layer chromatography ( s i l i c a ge l , ethanol:ethyl acetate, 1:9) showed the absence of s ta r t ing material a f te r 10 min. A f te r 40 min, 15 ml of Amberlite IR-120(H +) res in was s t i r r ed into the reaction mixture for 15 min after which i t was passed through a bed of 5 ml of Amberlite IR-120(H + ). The ac id i c eluate was treated s im i l a r l y with Amberlite IRA-400 (HC0~) to give a neutral so lut ion. Sodium borodeuteride (0.5 g) was added to the neutral ized solut ion at 0°C. Thin-layer chromatography showed the absence of s tar t ing material a f te r 15 min. A f ter the reduction so lut ion had stood at room temperature overnight, excess borodeuteride was destroyed by the addition of acetone, and the Amberlite IR-120(H +) res in was added to remove sodium ions. To the f i l t e r e d solut ion was added 1 ml of cone, hydrochloric acid and the mix-ture was kept at 100°C f o r 3 hr a f t e r which i t was deionized using 20 ml - 275 -of Amerlite IRA-400 (HC0~). The residue l e f t on evaporation of the deionized solut ion was dissolved in abs. ethanol, benzene was added and the mixture was evaporated. After repeating th i s procedure, methanol was evaporated from the residue three times. A solut ion of the product in 15 ml of 95% ethanol plus 1 ml of water gave crysta l s of 5-deuterio-B-L-arabinopyranose which were co l lected and washed with 95% ethanol; y i e l d , 1.589 g, m.p. 154-158°C. The f i l t r a t e was evaporated and the residue dissolved in 4 ml 20 of 95% ethanol to give 201 mg of c r y s ta l s ; tota l y i e l d , 79%. [ a ] D +154.5° (1.5 min) -> 103.5° (50 min, constant; c, 1.01 in water). Acetylat ion of 350 mg of 5-deuterio-B-L-arabinopyranose using 2.5 ml pyridine and 2.0 ml acet ic anhydride-dg at 0°C gave a syrupy mixture of 105 acetates a f te r the usual work-up. These products were treated with acet ic anhydride-dg (1 ml) and a small piece of ZnC^ at 100°C for 1 hr. After the usual work-up, the l i q u i d acetates were thinned with two drops of 95% ethanol, seeded, then refr igerated for three days, during which time crysta l s formed. Af ter the mixture had been thinned with ethanol-water (1:1), the crysta l s were co l lected and washed with aqueous ethanol; y i e l d , 246 mg. Recry s ta l l i za t ion of th i s product from aqueous ethanol gave 3_, m.p. 99-100°C, g . l . c . retention time, 13.4 min. 1,2,3,4-Tetra-O-trideuterioacetyl-5,5-dideuterio-B-L-arabinopyranose (4_,5_) Ethyl B-D-galactofuranoside (4.16 g) was oxidized using sodium metaperiodate (4.49 g) as above, except that deionization was c a r r i e d out by adding a mixture of Amberlite IR-120(H +) (25 ml) and Amberlite IRA-400 (HCO^) (25 ml) to the reaction mixture. Reduced Adams Catalyst was prepared by adding dropwise a solut ion of sodium borohydride (300 mg) in water (3 ml) to a swirled suspension of Adams Pt0 2 cata lyst (0.5 g) in water (4 ml). Af ter a l l of the - 276 -borohydride so lut ion had been added, the l i q u i d was decanted from the heavy black Pt which was then washed with water by decantation un t i l the 1 iquid was neutra l . The Pt cata lyst was added to the aldehyde so lut ion and oxygen was bubbled through the mixture v ia a s intered glass d i s c , the solut ion being maintained at 50°G. Potassium carbonate solut ion was added to the oxida-t ion mixture in order to keep the pH % 8. Af ter 3 hr, no aldehyde could be detected by t . l . c . ( s i l i c a ge l , ethanol:ethyl acetate, 1:9). The tota l amount of ^CC^ consumed was 1.26 g. The residue l e f t a f te r evapora-t ion and f i n a l l y freeze-drying of the f i l t e r e d oxidation mixture was refluxed in 50 ml of dry methanol to which had been added 2.4 ml of acetyl ch lor ide. After 1 hr, the reaction mixture was cooled, f i l t e r e d , treated with 25 ml of methanol-washed Amberlite IRA-400 (HC0~), then evaporated to approx. 25 ml. To th i s g lycos id ic ester solut ion was added in portions a s lur ry of 0.5 g of sodium borodeuteride in 2 ml of 0.1 M sodium methoxide in methanol. A f ter the reduction mixture had stood for 1 hr at room temperature, t . l . c . showed that ester was s t i l l present. A further 300 mg of sodium boro-deuteride was added and the mixture l e f t overnight at room temperature. The reduction mixture was worked-up as before and the furanoside was hydro-lyzed using 40 ml of 0.05 M hydrochloric acid at 100°C for 1.5 hr. The residue l e f t on evaporation of the deionized hydrolysis mixture was dissolved in water (1 ml) and th i s so lut ion was d i lu ted with ethanol. C ry s ta l l i ne 8-L-arabinose-5-d 2 was co l lected and washed with 95% ethanol. Y i e l d , 1.340 g, m.p. 157-160°C. A further 360 mg was obtained from the f i l t r a t e ; to ta l y i e l d , 56%. The preparation of $-L-arabinopyranose-5-d 2 described above follows e s sent ia l l y the procedure u s e d 1 0 7 for the preparation of 5,5-dideuterio xylose compounds. 277 To a s t i r r ed mixture of dry pyridine (4 ml) and acet ic anhydride-dg at 6°C was added 0.800 g of e-L-arabinose-S-d^. A f ter the mixture had been s t i r r ed at 6°C for 40 hr i t was kept at 20°C for 20 hr. After a chloroform solut ion of the residue l e f t on evaporation of acety lat ion mixture had been washed successively with 1.5 M sulphuric acid and saturated sodium bicarbonate so lut ion, i t was f i l t e r e d through a short bed of s i l i c i c acid and evaporated. A solut ion of the residue in ethanol was evaporated and the l i q u i d acetates were thinned with a few drops of ethanol, seeded with _3 and refr igerated for two days. The c r y s t a l l i n e product was co l lected and washed with 50% ethanol, y i e l d 310 mg. Recrystal 1 ization of the crude pro-duct from aqueous alcohol gave (3), m.p. 101-102°C, g . l . c . retention time, 13.4 min. Lac t i t o l (20) This sugar was prepared by reducing lactose with sodium borohydride according to a procedure described in the l i t e r a t u r e . To a so lut ion of lactose (2.0 g) in water (40 ml) was added a solut ion of sodium borohydride (0.3 g) in water (20 ml). The reaction mixture which became s l i g h t l y a l ka l i ne to litmus paper was l e f t overnight at room temperature (^ 20°C). The mixture was then a c i d i f i ed with acet ic acid to destroy the excess sodium borohydride. The sodium ions were removed by passing the aqueous so lut ion through a bed of Amberlite IR-120 (H ) res in . The ac id ic eluate was treated s im i l a r l y with Amberlite CG-400 (HC0~) to give a neutral so lu t ion , which a f te r freeze-drying gave a white s o l i d (1.5 g) that was used without further pu r i f i ca t i on for the carbon-13 n.m.r. experiments. Ma l t i t o l ( 2 0 This sugar was prepared from maltose in the same way as l a c t i t o l from lactose. - 278 -Methyl 2,3,4,6-tetra-0_-acetyl-ct-D-gl ucopyranoside-2,3,4,6,6'-dg (23) and the corresponding g anomer (24), and methyl 2,3,4,6-tetra-0-tr ideuterioacetyl-a-D-glucopyranoside-2,3,4,6,6 ' -d5 (30) and the corresponding g anomer (31). These four compounds were synthesized by R. Ezzy under the author's d i r e c t i on ; fo r deta i l s see ref s . 109 and 110. 1-Tri deuterio methoxy-2,4-dini trobenzene (27) This compound was prepared according to a method given in the l i t e r -a t u r e 1 1 1 . Triethylamine (15 drops) was added to a solut ion of l - f l uo ro - 2 , 4-dinitrobenzene (3.0 g) (Eastman) in tetradeuteriomethanol (1.5 ml). The solut ion was refluxed on a steam-bath for four hours, which when cooled the product separated. Excess d i l u t e hydrochloric acid solut ion was added and the s o l i d co l l ec ted , washed with sodium bicarbonate so lut ion, and rec r y s t a l l i z ed from methanol; y i e l d 2.3 g (71%), m.p. 86-87°C ( l i t . v a l ue 1 1 1 fo r l-methoxy-2,4-dinitrobenzene was 87°C). Methyl a - and g-D-glucopyranoside (35,33), trideuteriomethyl a - and g-D-qlcopyranoside (36_,34), methyl 2 ,3 ,4 ,6 - te t ra -0 - t r ideuter ioacety l - a - and g-D-glucopyranoside (29,38), trideuteriomethyl 2 ,3 ,4 ,6 - te t ra -0 - t r ideuter ioacety l - a - and g-D -glucopyranoside (37,39). These eight compounds were prepared by D.W. Welder under the j o i n t supervision of Dr. J.M. Berry and the author. For deta i l s see ref. 112 6-0- (g-D-Glucopyranosyl )-D-gal actose-6,6' -d2 (19.) This disaccharide was synthesized in col laborat ion with Dr. J.M. Berry according to the scheme shown in Flow Sheet 1. For experimental deta i l s see ref. 113. - 279 -Flow Sheet 1. Synthesis of 6-0-(g-D-glucopyranosyl)-D-galactopyranose-6,6 ' -d 2 . - 280 -The 1:2,3:4-di-0-isopropy1idene-a-D-galactopyranose-6,6'-d 2 was prepared as depicted in Flow sheet 2. 1:2, 3:4-Di-0-isopropylidene-a-D-galactopyranose (10.0 g, from Koch-Light) was oxidized to the corresponding acid (6.0 g, dried) using basic permanganate solut ion according to a l i t e r a t u r e p rocedure 1 1 4 . The acid (1.5 g) was then reduced by l i th ium aluminium deuteride in anhydrous tetrahydrofuran (THF) to the product 115 (1.2 g, r e d i s t i l l e d syrup) using the method of Brown et a l . Flow Sheet 2. Synthesis of 1:2,3:4-di-0-isopropylidene-a-D_-galactopyranose-6,6 '-d~. - 281 -REFERENCES 1. F.A.L. Anet and J.R. Bourn, J . Am. Chem. S o c , 87, 5250 (1965). 2. J.H. Noggle and R.E. Schirmer, "The Nuclear Overhauser Ef fect : Chemical App l i ca t i on " , Academic Press, New York, 1971. 3. R.E. Richards and J.W. White, Chem. Soc. Faraday Discuss., 34, 96 (1962). 4. R.A. Bell and J.K. 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Welder, B.Sc Thesis, Univers ity of B r i t i s h Columbia, 1976. 113. J.M. Berry, Ph.D. Thesis, Univers ity of B r i t i s h Columbia, 1974. 114. H. Ohle and G. Berend, Ber., 58, 2577 (1925). 115. H.C. Brown, P.M. Weissman, and N.M. Yoon, J . Am. Chem. S o c , 88, 1458 (1966). - 287 -APPENDIX I TWO-PULSE INVERSION-RECOVERY SEQUENCE FOR DETERMINATION OF R,-VALUES A diagrammatic representation of the rotating reference frame model of a s p i n - l a t t i c e relaxation measurement using a two-pulse invers ion-recovery sequence i s shown in F ig. 1.1. F ig. 1.1 In A the.magnetization of the nuclei i s at thermal equi l ibr ium with the l a t t i c e . In B th is magnetization has been inverted through 180° by the appl icat ion of a 180° pulse; the nuclei are no longer in thermal equ i l ib r ium, and s p i n - l a t t i c e relaxat ion causes the magnetization to revert back along the z-axis towards i t s equi l ibr ium pos i t ion. A f ter a known delay time, t sec, the residual magnetization C i s assayed by the appl icat ion of a 90° pulse which t ips the magnetization up into the xy plane D. BD i s the Zeeman f i e l d . - 288 -APPENDIX II PROGRAM "NEWCART" This computer program, wr itten in FORTRAN, i s a modified*version of the program "CART" provided by Dr. C.E. Holloway of York Univers i ty, Ontario. The program calculates the posit ions of atoms in the pr inc ipa l Cartesian coordinate system given an arb i t rary s tar t ing coordinate system. The output data include interatomic distances, the centre of mass, the moments of i ne r t i a and any relevant transformation matrices. Also, given the appro-pr iate atom numbers of any C-H vectors, the program calculates the d i rect ion cosines in the pr inc ipa l Cartesian coordinate system. These d i rect ion cosines can be used in conjunction with Woessner's formulations (see Chapter 5) for the ca lcu lat ion of rotat ional d i f fus ion constants. The added features in th i s program are: 1. The ca lcu lat ion i s extended to 96 atoms instead of 50. 2. The simulated structure of the molecule can be v i sua l l y displayed with any "o r ientat ion " at the ADAGE terminal of the U.B.C. Computing Centre. 3. The simulated structure can be p lotted. The second and th i rd features provide a rapid check for the correctness of the input data. A l i s t of input parameters i s given in Table I I . l . As an example, the input data for the simulation of the structure of methyl e-D-galactopyranoside (9_) i s given below. Assistance in modif ication was provided by R. Burton. - 289 -Table I I . l Parameter L i s i tng for Program NEWCART Parameter Comment  NOAT tota l number of atoms NO "atom number" - atoms numbered consecutively NA "number" of atom A ( i . e . atom 1) NB "number" of atom B which together with NA defines the pos i t ive x axis NC atom C which together with atoms A and B define the xy plane such that the pos it ive half plane is on the same side of the x axis as atom C R bond length NO-NA (A) TE bond angle NO-NA-NB - for tetrahedral angles TE = 0 PH dihedral angle between the plane NC-NB-NA and the plane NO-NA-NB - fo r a r ight handed coordinate system observe the configuration from the d i rect ion of atom C along- the bond NB-NA or NA-NB depending on whether NC i s bonded to NB or NA - rotate about NB-NA or NA-NB to move atom C into the plane NO-NA-NB -anti-clockwise rotations are defined as pos i t ive WT atomic mass of atom NO N3 number of vectors fo r which d i rect ion cosines are to be calculated I "atom number" of one atom of the vector (e.g. carbon) J "atom number" of second atom of the vector (e.g. hydrogen) - 290 -9 11 17 (= NOAT) NO NA NB NC R TE PH WT 1 6 5 4 1.52 0.0 60.0 12.0 2 1 6 5 1.42 0.0 -60.0 16.0 3 2 1 6 1.52 0.0 60.0 12.0 4 3 2 1 1.52 0.0 -60.0 12.0 5 4 3 2 1.52 0.0 60.0 12.0 6 5 4 3 1.52 0.0 -60.0 12.0 7 3 2 1 1.10 0.0 60.0 1.0 8 3 2 1 1 .52 0.0 180.0 32.0 9 4 3 2 1.10 0.0 180.0 1.0 10 4 3 2 1 .42 0.0 -60.0 18.0 11 5 4 3 1.10 0.0 60.0 1.0 12 5 4 3 1.42 0.0 180.0 18.0 13 6 5 4 1.10 0.0 -60.0 1.0 14 6 5 4 1.42 0.0 180.0 18.0 15 1 2 3 1.10 0.0 -60.0 1.0 16 1 2 3 1.38 0.0 180.0 16.0 17 16 1 2 1.79 0.0 . 60.0 15.0 5 = (= N3) 1 15 (= I J) 3 7 4 9 5 11 6 13 - 2 9 1 -D I M E N S I O N C O R ( 1 9 0 , 3 ) , W ( 1 0 0 ) , X ( 1 5 0 , 3 ) , V 3 A ( 3 ) , V C A ( 3 ) ,R J A ( 3 ) D I M E N S I O N T R A N S ( 3 , 3 ) , P R C ( 3 ) , 1CAR ( 1 0 0 , 3) , D N E R ( 3 , 3 ) ,CM ( 3 ) , TP. (3 , 3 ) , E T ( 1 0 0 ) , NR ( 3 0 0 ) ,NCO ( 3 0 0 ) , 2 D A T ( 1 5 0 ) ,0 ( 5 0 ) , S S ( 3 ) R E A L D A T A ( 1 0 0 , 4 ) T N T E G E R * 4 I DATA ( 1 0 0 , 4 ) , D I S P ( 2 0 0 1 ) L O G I C A L * 1 P L O T / - F A L S E . / L O G I C A L EQI7C C D A T A I S R E A D I N T O T H E A B O V E TWO A R R A Y S . COMMON C O R , X , C A E , N R , N C O , D A T COMMON D C V E R S I O N O F C A R T WITH 9 6 A T O M S MAX I N S T E A D O F 5 0 . C O N = . 1 7 U 5 3 E - 0 1 J O K E = 0 9 5 F O R M A T ( 1 X , 1 0 0 ( « * ' ) ) W R I T E ( 7 , 5 0 ) 5 0 F 0 R M A T ( 1 X , » P R O G R A M C A S T ( 1 0 0 A T O M S M A X . ) ' ) R E A D ( 4 , 6 6 ) N O A T 6 6 FORM A T (I 2) DO 9 8 7 6 1 = 1 , N O A T R E A D ( 4 , 1 0 ) ( I D A T A ( I , J ) , J = 1 , 4 ) , ( D A T A ( I , J ) , J = 1 , 4 ) 9 8 7 6 C O N T I N U E 3 3 3 C A L L G D A T A ( I D A T A , D A T A , 1 , N O , N A , N B , N C , R , T E , P H , W T ) 1 0 F O R M A T ( 4 1 2 , F 5 . 3 , T 6 . 2 , F 7 . 2 , F 7 . 3 ) W R I T E ( 7 , 19) N O , N A , N B , N C , R , T E , P H , WT W (NO) =WT C O E ( N O , 1 ) = 0 . 0 COR ( N O , 2 ) = 0 . 0 C O R (NO, 3) = 0 . 0 1 1 0 C A L L G D A T A ( I D A T A , D A T A , 2 , N O , N A , N 3 , N C , K , T E , P H , W T ) W R I T E ( 7 , 19) N O , N A , N B , N C , R , T E , P H , W T 1 9 FORM A T ( 2 H , 4 I 4 , 4 F 1 2 . 6 ) V (NO) =WT C O P (NO , 1) =R C O R ( N O , 2) = 0 . 0 COR ( N O , 3 ) = 0 . 0 1 1 6 C A L L G D A T A ( I D A T A , D A T A , 3 , N O , N A , N B , N C , R , T E , P H , WT) W R I T E ( 7 , 1 9 ) N O , N A , N B , N C , R , T E , P H , * T W ( N O ) = W T I F ( T E ) 1 2 0 , 1 1 8 , 1 2 0 1 1 8 C S = - 0 . 3 3 3 3 3 SS=0.94281 G O T O 121 120 C S = C O S ( C O N * T E ) S S = S I N ( C O N * T E ) 121 I F ( N A - 1 ) 128, 122, 128 122 C O R ( N O , 1) = C O R ( N A , 1) *R*CS G O T O 129 128 COR ( N O , 1) = C O R ( N A , 1 ) - R * C S 129 C O R ( N O , 2 ) = R * S S C O R ( N O , 3 ) = 0 . 0 I F ( N O A T - 3 ) 9 9 9 9 , 1 6 1 , 1 3 0 1 3 0 DO 1 6 0 1 = 4 , N O A T C A L L G D A T A ( I D A T A , D A T A , I , N O , N A , N B , N C , R , T E , P H , W T ) W R I T E ( 7 , 19) N O , N A , N B , N C , R , T E , P H , W T W (NO) =WT I F ( T E ) 1 3 3 , 1 3 2 , 1 3 3 132 C S = - 0 . 3 3 3 3 3 SS=0.94281 GO T O 135 - 292 -1 3 3 C S = C O S ( C O N + T E ) S S = S I N ( C O N * T E ) 1 3 5 D S Q = 0 DO 1 3 8 M = 1 , 3 VBA (M ) = COR ( N B , M ) -COR ( N A , M ) V C A ( M ) = C O R ( N C , M ) - C O R ( N A , M) 1 3 8 DSQ = D S Q * V B A (M) * * 2 R A B = S 0 R T ( D S Q ) S C A L E = 0 . 0 DO 1 4 2 M = 1 , 3 T R A N S ( M , 1 ) = V B A ( M ) / R A B 1 1 2 S C A L E = S C A L E + T 3 A N S ( M , 1 ) * V C A ( M ) D S Q = 0 . 0 DO 1 4 6 M = 1 , 3 R J A ( M ) = V C A ( M ) - S C A L E * T R A N S ( M , 1 ) 1 4 6 D S Q = D S Q + R J A (M) * * 2 R A J = S Q E T ( D S Q ) DO 1 4 8 8 = 1 , 3 1 4 8 T R A N S ( M , 2 ) = P J A (rt) / R A J T E A N S ( 1 , 3 ) = T R A N S ( 2 , 1 ) * T R A N S ( 3 , 2 ) - T R A N 3 ( 3 , 1 ) * T S A NS ( 2 , 2 ) T R A N S ( 2 , 3 ) = T R A N S ( 3 , 1 ) * T R A N S ( 1 , 2 ) - T K A H S ( 1 , 1 ) * T R A N S ( 3 , 2 ) T R A N S ( 3 , 3) =TR A NS ( 1 , 1 ) * T R A N S ( 2 , 2 ) - T R A N S ( 2 , 1) * T R A N S ( 1 , 2 ) P R C ( 1 ) = R * C S P R C ( 2 ) = P * S S * C O S ( C O N + P H ) P R C ( 3 ) = R * S S * S I N ( C O N * ? H ) DO 1 6 0 fl=1,3 COR ( N O , M ) = C O R ( N A , M ) DO 1 6 0 K = 1 , 3 1 6 0 COP. ( N O , M ) =COR ( N O , M ) • T R A N S ( M , K) * P E C (K) W R I T E ( 7 , 9 5 ) 1 6 1 W R I T E ( 7 , 6 0 ) 6 0 F O R M A T ( 1 X , » ATOM N O . X Y Z M A S S * ) DO 1 6 4 I = 1 , N O A T 1 6 4 W R I T E ( 7 , 6 2 ) I , ( C O R ( I , r t ) , M = 1 , 3 ) ,W ( I ) 6 2 F O R M A T ( 4 X , 1 3 , 3 X , 3 ( F 6 . 2 , 6 X ) , F 7 . 3 ) W R I T E ( 7 , 9 5 ) 1 2 3 0 W R I T E ( 7 , 6 8 ) 6 8 F O R M A T ( 1 X , ' A T O M D I S T A N C E C H E C K ' ) DO 1 2 3 6 I = 1 , N O A T DO 1 2 3 4 J = 1 , N O A T D S Q = 0 . 0 DO 1 2 3 3 H = 1 , 3 B E ( r t ) = C O R ( J , M ) - C O R ( I , r t ) 1 2 3 3 D S Q = D S Q + R R ( r t ) * R R (M ) 1 2 3 4 D ( J ) = S Q R T ( D S Q ) 1 2 3 6 W R I T E ( 7 , 6 9 ) I , (D ( J ) , J = 1 , N O A T ) 6 9 F O R M A T ( 5 H 0 A T O M , I 3 / ( 7 F 1 0 . 6 ) ) 1 6 8 W T = 0 . 0 DO 1 7 0 I = 1 , N O A T 1 7 0 W T = W T + W ( I ) D O 1 8 0 8 = 1 , 3 C W ( M ) = 0 . 0 DO 1 7 9 I = 1 , N O A T 1 7 9 C M ( M ) = C H ( r t ) - W ( I ) *COR ( I , rt) 1 8 0 CM ( M ) = C M ( M ) / W T DO 1 8 5 I = 1 , N O A T R T ( I ) = 0 . 0 D O 1 8 5 rt=1,3 X ( I , M ) = C O R ( I , r t ) +CM (M) 1 8 5 R T ( I ) = R T ( I ) • ( X ( I , M ) ) **2 - 2 9 3 -DO 1 9 0 1 = 1 , 3 DO 1 9 0 J = 1 , 3 D N E R ( I , J ) = 0 . 0 DO 1 9 0 K = 1 , N O A T I F ( I - J ) 1 8 9 , 1 8 7 , 1 8 9 1 8 7 D N E R ( I , J ) = D N E R ( I , J ) * K ( K ) * ( S T ( K ) - X ( K ,1) * X ( K , I ) ) GO TO 1 9 0 1 8 9 D N E R ( I , J ) = D N E R ( I , J ) - W ( K ) * X ( K , I ) * X ( K , J ) 1 9 0 C O N T I N U E W R I T E ( 7 , 9 5 ) W R I T E ( 7 , 8 0 ) V T , ( CM (M) , M = 1 , 3 ) 8 0 F O R M A T ( 1 X , • I N E R T I A T E N S O R * , 8 X , « M A S S = • , F 8 . 3 , 1 5 X , • C - M . = • , 3 F 7 . 3 ) DO 1 9 2 1 = 1 , 3 1 9 2 W F I T E ( 7 , 3 2 ) (DNER ( I , J ) , J = 1 , 3 ) 8 2 F O R M A T ( 1 X , 3 F 1 2 . 6 ) N E R = 0 N = 3 I E G E N = 0 C A L L H D I A G ( D N E H , N , I E G E N , T R , N R B ) W R I T E ( 7 , 9 5 ) 2 0 0 W R I T E ( 7 , 8 4 ) ( D N E R ( I , 1 ) ,1 = 1 , 3 ) 8 4 F O R M A T ( 1 X , • P R I N C I P A L M O M E N T S ' , 3 F 1 2 . 6 , ' A N D T R A N S F O R M A T I O N S * ) 2 0 1 DO 2 0 2 1 = 1 , 3 2 0 2 W R I T E ( 7 , 8 2 ) ( T R ( I , J ) , J = 1 , 3 ) DO 2 1 0 I = 1 , N O A T D C 2 1 0 J = 1 , 3 C A R ( I , J ) = 0 . 0 DO 2 1 0 K = 1 , 3 2 1 0 C A R ( I , J ) = C A F ( I , J ) +TR ( K , J ) * X ( I , K ) W R I T E ( 7 , 9 5 ) W R I T E ( 7 , 8 6 ) 8 6 F 0 R M A T ( 1 X , ' P R I N C I P A L C A R T E S I A N C O O R D I N A T E S ' ) W R I T E ( 7 , 6 0 ) DO 2 1 5 I = 1 , N O A T 2 1 5 W R I T E ( 7 , 6 2 ) I , ( C A R ( I , M) , M = 1 , 3 ) , V ( I ) WFITE ( 7 , 9 5 ) W R I T E ( 7 , 3 2 5 ) 3 2 5 F O R M A T ( 1 X , ' C A L C U L A T E D D I R E C T I O N C O S I N E S F O R G I V E N V E C T O R S ' ) R F A D ( 4 , 3 2 3 ) N 3 3 2 3 F O R M A T ( I 2 ) DO 5 6 6 N 2 = 1 , N 3 R E A D ( 4 , 3 2 2 ) I , J 3 2 2 F 0 R M A T ( 2 I 2 ) X D 2 = ( C A R ( I , 1 ) - C A R ( J , 1 ) ) * * 2 Y D 2 = ( C A R ( I , 2 ) - C A R ( J , 2 ) ) * * 2 Z D 2 = ( C A R ( 1 , 3 ) - C A B ( J , 3 ) ) * * 2 S 0 M 3 = X D 2 * Y D 2 * Z D 2 D E N O M = S Q R T ( S 0 M 3 ) C S X = ( C A P ( I , 1 ) - C A R ( J , 1 ) ) / D E N O M C S I = ( C A R ( I , 2 ) - C A R ( J , 2 ) ) / D E N O M C S Z = ( C A R ( I , 3 ) - C A R ( J , 3 ) ) / D E N O M W R I T E ( 7 , 3 2 4 ) N 2 , I , J , C S X , C S Y , C S Z 3 2 4 F O R M AT ( 1 X , 3 ( 1 3 , 2 X ) , 3 ( F 6 . 3 , 5 X ) ) 5 6 6 C O N T I N U E WRITE ( 7 , 9 5 ) C F I N D E X T R E M E S O F D I S P L A Y D A T A X M A X = C A R ( 1 , 1 ) X M I N = X M A X Y M A X = C A R ( 1 , 2 ) Y M I N = Y M A X - 294 -ZMAX=CAR (1,3) ZMIN=ZMAX DO 222 1=1,NOAT T=C AR (1,1) IF(XMAX.LT.T) XMAX=T IF(XMIN.GT.T) XMIN=T T=CAR (1,2) IF(YMIN.GT.T) YMIN=T IF(YMAX.LT.T) YMAX=T T=C AR (1,3) IF(ZMIN.GT.T) ZflIN=T IF(ZMAX.LT.T) ZMAX=T 222 CONTINUE RANG E=XM A X-XMIN T=YKAX-YMIN IF(T.GT.RAN GE) RA NGE = T T=ZMAX-ZMIN IF (T.GT. RANGE) RANGE=T IF(RANGE.LE.0.0) STOP 444 SCALE=11.5/RANGE XADJ = 0.5*(XMAX-XMIN) *SCALE YADJ=0.5* (YMAX-YKIN) *SCALE ZADJ=0. 5* (ZMAX-ZMIN) * SCALE C SET UP DATA FDR AGT DISPLAY. C USE BONDS DESCRIBED IN INPUT TO CAFT. C AND THOSE ADDED BY C AND X. 255 DO 223 1=1,NOAT C C DO START OF BOND. (PEN UP) J=IDATA(I,1) ZP= (CAR(J,3)-ZMIN) *SCALE-ZADJ CALL AGTCVT (DISP (4 *I-3) , 0. 0, ZP, 0, 0) XP= (CAR ( J , 1) -XMIN) *SCALE-XADJ YP= (CAR (J,2)-YMIN) *SCALE-YADJ CALL AGTC7T(DISP (4*1-2) ,XP,YP,0,0) C C DO END OF BOND (PEN DOWN) J=IDATA(1,2) ZF= (CAR ( J , 3) -ZMIN) *SCALE-Z\DJ CALL AGTCVT (DISP (4*1-1) ,0.0,ZP,0,0) XP= (CAR(J,1)-XMIN)*SCALE-XADJ YP= (CAR (J,2)-YMIN) *SCALE-YADJ CALL AGTCVT(DISP(4*1) rXP,YP,1,0) 223 CONTINUE NWORD=4*NOAT C C C MODIFY/DISPLAY? 9191 WRITE(6,9001) 9001 FORM AT(• A=A DD BOND,D=DISPLAY,Q=QDIT,P=PLOT,X=AXES,C=CHANGE*) READ(5,9002) LOG 9002 FORMAT (A 1) IF(EQUC(LOG,'Q')) GO TO 9999 IF(EQUC(LOG,•A')) GO TO 9850 IF(EQUC(LOG,•P 1)) GO TO 9900 IF ( E Q n C(LOG, ,D«)) GO TO 9990 IF(EQUC(LOG, ,C»)) GO TO 9950 IF (EQUC(LOG,»X»)) GO TO 9975 GO TO 9191 C - 295 -C C IF A ADD A 30ND TO BE DISPLAYED. 9850 WRITE(6,9851) 9851 FORMAT(* ADD A BOND FROM ATOM #, TO ATOM #») NOAT=NOAT*1 READ (5,9852) I, J 9856 IF(I.LT.NOAT) GO TO 9855 1=1/10 GO TO 9856 9855 IF(J.LT.NOAT) GO TO 9857 J=J/10 GO TO 9855 9857 IDATA (NOAT, 1) =1 I DATA (NO AT , 2) =J 9852 FORM AT (213) GO TO 255 C C C IF C CHANGE A LINE OF DATA AND RECALCOLATE. 9950 WRITE(6,9951) 9951 FORK AT (• WHICH LINE DO YOU WANT TO CHANGE?') READ(5,9953) I 9953 FORM AT (I 2) WRITE (6, 9952) (IDATA ( I , J) ,J=1,4) , (DATA ( I , J) ,J=1,4) 9952 FORM AT (3 H , 4F1 2. 6) READ (5, 19) (IDATA ( I , J) , J=1 ,4) , (DATA ( I , J) , J= 1 , 4) REWIND 4 READ (4,66) NOAT DO 9954 J=1,NOAT 9954 READ(4,66) K GO TO 333 C C C IF D DISPLAY ON ADAGE 9990 CALL AGTDSP(DISP,NWORD,2001, 1, 1) GO TO 9191 C C C IF P PLOT (MAX SIZE 10"). 9900 CALL AGPLOT(10.0,2000) WKITE(6,9901) 9901 FORM AT (* PLOT HAS BEEN WRITTEN, REMEMBER PLOT:Q') PLOT=-TRUE. GO TO 9191 C C C IF Q 9999 IF(.NOT.PLOT)STOP WRITE(6, 9998) 9998 FORM AT( 1 ***** REMEMBEB *****«,/,«$RUN PLOT:Q PAR= BLANK*) CALL PLOTND STOP C C C IF X DRAW AXES 9975 WRITE(6,9976) 9976 FORM AT(* AXES DRAWN*) C DESCRIBE ENDS OF AXES H=NOAT*1 CAR (N, 1) =XHIN - 296 -CAE (N,2) =Y»IN CAR (N,3) = ZMIN IDATA (N, 1) =N0AT+1 IDATA (N, 2) =N0AT+2 N = N*1 CAR (N, 1) = XMAX CAR (N,2) = YMIN CAP. (N,3) =ZHIN IDATA (N , 1) = NOAT* 1 IDATA (N, 2) =NOAT+3 N = N+1 CAR (N, 1) = XMIN CAR (N ,2) = YMAX CAR (N, 3) =ZM IN IDATA (N, 1) =NOAT+1 IDATA (N, 2) =NOAT«-4 N = N + 1 CAR (N, 1) = XMIN CAR (N,2) = YMIN CAR (N,3) = ZMAX IDATA (N, 1)=NOAT+1 IDATA (N , 2) = NO AT + 2 NOAT = NOAT«-4 GO TO 255 END C C C SUBROUTINE RDIAG ( I I , N, IEGEN, U, NR) DIMENSION H (3,3) ,U (3, 3) ,X (3) , IQ (3) IF(IEG5N) 15, 10,15 10 DO 14 1=1, N DO 14 J=1,N IF(I-J)12,11 ,12 11 U(I,J)=1.0 GO TO 14 12 U(T,J)=0.0 14 CONTINUE 15 NE=0 IF(N-1) 1000, 1000, 17 17 NMI1=N-1 DO 30 I=1,NMI1 X (I) =0. 0 IPL1=I+1 DO 30 J=IPL1,N IF (X (I) - ABS (H(I, J) )) 20,20,30 20 X (I) =ABS (H(I,J) ) IQ(I)=J 30 CONTINUE RAP=.745058E-08 HDTEST=1 . 0E38 40 DO 70 I=1,NMI1 IF (I- 1) 60,60,45 45 IF (XMAX-X (I)) 60,70,70 60 XMAX = X(I) IPIV=I JPIV=IQ(I) 70 CONTINUE IF (XM AX) 1000, 1000,80 80 IF(HDTEST) 90,90,85 - 297 -85 IF(XMAX-HDTEST) 90,90, 1U8 90 HDIHIN=ADS (H (1, 1) ) DO 110 1 = 2,N IF(HDIMIN-ABS (H (1,1) ) ) 110,110,100 100 HDIMIN=ABS (H ( I , I) ) 110 CONTINUE HDTEST=HDIMIN*RAP IF (HDTEST-XHAX) 148,10 00, 1000 148 NE=NR+1 XDIF=H(IPIV,IPIV) - H(JPIV,JPIV) XO= SIGN (2.0 ,XDIF) *H (IPIV, JPIV) XS=XDIF**2 + 4.0*H (IPIV, JPIV) **2 150 TANG = XO/(ABS (XDIF) *SQRT(XS) ) COSINE=1.0/SQRT (1. 0 + TANG**2) SINE=TANG*COSINE HII=U (IPIV,IPIV) H (IPIV, IPIV) =COSINE**2* (HII•TANG* (2-0*H (IPIV, JPIV) +TANG*H(JPIV,J 1V)) ) a (JPIV, JPIV) =C0SINS**2* (H (JPIV, JPIV) -TANG* (2.0 *H (IPIV, JPIV) -TANG1 111)) H(IPIV,JPIV) =0.0 I F (H (IPIV,IPIV)-H (JPIV, JPIV) ) 15 2, 153, 153 152 HTEMP = H (IPIV,IPIV) H (IPIV,IPIV) = H (JPIV, JPIV) H (JPIV, JPIV) =HTEMP HTF!1P=SIGN {1.0,-SINE) *COSINE COSINE=ABS(SINE) SIN E=HTEMP 153 CONTINUE DO 350 I=1,NMI1 IF (I-IPIV) 2 10,35 0,200 210 IF (IQ (I)-IPIV) 230, 240, 230 200 IF(I-JPIV)210,350,210 230 I F (IQ (I)-JPIV) 350, 240, 350 240 K=IQ(I) 250 HTEMP=H (I,K) H(I,K) =0.0 IPL1 = I*-1 X (I) =0.0 DO 320 J=IPL1,N I F (X ( I ) - ABS (H (I, J) ) ) 30 0,30 0,320 300 X (I) = ABS ( H ( I , J) ) I Q d ) =J 320 CONTINUE H (I , K) =HTEMP 350 CONTINUE X(IPIV)=0.0 X (JPIV)=0.0 DO 5 30 I = 1,N IF(I-IPIV)370,530,420 370 HTEMP=H(I,IPIV) H (I,IPIV)=COSINE*HTESP+SINE*H(I,JPIV) I F (X (I)-ABS (H ( I , IPIV)) ) 380,3 90,390 380 X (I)=AES (H(I,IPIV) ) IQ(I)=IPIV 390 Ii ( I , JPIV) =-SINE*liTENP*COSINE*H ( I , JPIV) I F (X (I)-ABS (H ( I , JPIV) )) 400,5 30, 530 400 X (I) =ABS (H ( I , JPIV) ) IQ(I)=JPIV GO TO 530 - 298 -420 IF (I-JPIV)430,530,480 430 HTEMP=H(IPIV,I) H (IPIV, I)=COSINE*HTEMP*SINE*H(I,JPIV) IF (X (IPIV) - ABS(H(IPIV,I)))4 40,450,450 440 X (IPIV) = ABS (H (IPIV,I) ) IQ(IPIV)=I 4 50 H (I,.IPIV) =-SINE*HTEMP+COSINE*H (I, JPIV) IF (X (I) - ABS (H (I , JPIV) ) ) 4 00,5 30, 530 480 HTEMP=H(IPIV,I) H (IPIV,I)=COSINS*HTEMP*SINE*H(JPIV,I) IF (X (IPIV) - ABS (H (IPIV,I) ) ) 490,50 0,500 490 X (IPIV) = ABS (B (IPIV,I) ) IQ(IPIV) =1 500 H (JPIV,I) =-SINE*HTEMP+COSINE*H (JPIV,I) IF (X (JPIV) - ABS (H (JPIV,I) ) ) 510 ,5 30,530 510 X (JPIV) = ABS (H (JPIV,I) ) IQ(JPIV) =1 530 CONTINUE IF(IEGEN) 40,540, 40 540 DO 550 1=1,N HTEHP=n (I,IPIV) U ( I , IPIV) =COSINE*HTEMP«-SINE*U (I , JPIV) 550 U ( I , JPIV) =-SINF.*HTE*Pt-COSINE*a ( I , JPIV) GO TO 4 0 1000 RETURN END C GDATA GETS DATA FROM DATA IDATA. SUBROUTINE GDATA (IDATA,DATA,I,NO,NA,NB,NC,X,XX,XXX,XXXX) INTEGER*4 IDATA(100,4) REAL DATA(100,4) NO=IDATA (I, 1) NA=IDATA (1,2) NB= ID AT A (I, 3) NC=I DATA (1,4) X=DATA (1,1) XX= DATA(1,2) XXX= DATA (I,3) XXXX=DATA (1,4) RETURN END PUBLICATIONS K.F. Wong and S. Ng, "Hydrogen Bonding and Geminal Proton Coupling", J . Magn. Resonance, 1_3, 239-242 (1974). K.F. Wong, T.S. Pang and S. Ng, "Correlat ion Between Hydrogen-bond Sh i f t in Nuclear Magnetic Resonance Spectra and Change in Enthalpy", J.C.S. Chem. Comm., 55-56 (1974). K.F. Wong and S. Ng, "Nuclear Magneti Resonance Study of the Hydrogen Bonding of Chloroform with A l i phat i c Tert iary Amines and Ethers", J.C.S. Faraday II, 71_, 622-630 (1975). K.F. Wong, T.S. Pang and S. Ng, "Measurement by NMR Spectrometry of Hydrogen Bonding to Bases Having More Than One Equivalent Electron Donor S i t e " , Chem. Phys. Letters , 30, 309-313 (1975). K.F. Wong and S. Ng, "On the Use of the Modified Benesi-Hildebrand Equation to Process NMR Hydrogen Bonding Data", Spectrochim. Acta, 32A, 455-456 (1976). L.D. H a l l , K.F. Wong and W. Schittenhelm, "High Resolution Nuclear Magnetic Resonance Spectroscopy: A Probe of the Structure and Solution Conformation of Sucrochemicals", in "Sucrochemistry", J.H. Hickson, Ed., American Chemical Society, 1977, pp. 22-39. J.M. Berry, L.D. H a l l , D.W. Welder and K.F. Wong, "A Quantitative Measurement of the Aglycon-sugar, Proton-relaxation contr ibution of Glycosides, including Disaccharides", Carbohydr. Res., 54, C22-C24 (1977). J.M. Berry, L.D. Hall and K.F. Wong, "Concerning the Tumbling Motion of Disac-charides in Aqueous So lu t ion " , Carbohydr. Res., 56_, C16-C20 (1977). J.M. Berry, L.D. H a l l , D.G. Welder and K.F. Wong, "Proton Spin-Latt ice Relaxa-t i on : A New, Quantitative (?) Measure of Aglycon-Sugar Interact ions " , W.A. Szarek and D. Horton, Eds., American Chemical Society, 1979, pp. 30-49. L.D. H a l l , H.D.W. H i l l and K.F. Wong, "Quantitative Determination of Interproton Distances for Diamagnetic Molecules i n Solution v ia the Measurement of Selective Proton Spin-Latt ice Relaxation Rates", J . Am. Chem. S o c , submitted. L.D. H a l l , W.E. H u l l , J.D. Stevens and K.F. Wong, "Non-Selective Proton Spin-Lat t i ce Relaxation Rates Measured at 400 MHz: A Quantitative Determination of the Geometry of Diamagnetic Molecules in So lut ion " , J . Am. Chem. S o c , submitted. 

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