Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Applications of new pulse NMR techniques in chemistry : two-dimensional NMR spectroscopy Sukumar, Subramaniam 1981

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1981_A1 S85.pdf [ 8.95MB ]
Metadata
JSON: 831-1.0060722.json
JSON-LD: 831-1.0060722-ld.json
RDF/XML (Pretty): 831-1.0060722-rdf.xml
RDF/JSON: 831-1.0060722-rdf.json
Turtle: 831-1.0060722-turtle.txt
N-Triples: 831-1.0060722-rdf-ntriples.txt
Original Record: 831-1.0060722-source.json
Full Text
831-1.0060722-fulltext.txt
Citation
831-1.0060722.ris

Full Text

APPLICATIONS OF NEW PULSE NMR TECHNIQUES IN CHEMISTRY: TWO-DIMENSIONAL NMR SPECTROSCOPY B.Sc. (Hons.), University of Ceylon, Colombo, Sri-Lanka, 1975 M.Sc, Dalhousie University, Halifax, Canada, 1977 THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF THE FACULTY OF GRADUATE STUDIES (Department of Chemistry) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA February, 1981 (T) Subramaniam Sukumar, 1981 by SUBRAMANIAM/SUKUMAR DOCTOR OF PHILOSOPHY in In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department o r by h i s o r her r e p r e s e n t a t i v e s . I t i s understood t h a t c o p y i n g or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a llowed without my w r i t t e n p e r m i s s i o n . Department of CHEMISTRY  The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date ,19th, February, 1981. ABSTRACT The potential of three recently developed techniques, proton 2D J-. 13 1 • C- H chemical s h i f t correlation- and proton zero-quantum tra n s i t i o n (ZQT)-spectroscopy, for resolving and assigning complex proton spectra has been evaluated. The main part of this work describes the features of proton 2D J spectroscopy and related experiments and includes discussions on the optimum methods for displaying the spectra and e f f i c i e n t methods for the processing of data. It i s shown that phase-sensitive cross-sections offer a convenient and p r a c t i c a l method for these purposes. Proton 2D J spectra can also provide e f f e c t i v e l y the equivalent of broad band homonuclear and hetero-nuclear decoupling, thus distinguishing between these different scalar couplings. Assignment techniques based on 2D NMR spectroscopy have many advantages over conventional assignment techniques such as double resonance. Thus, the 13 1 combination of proton 2D J spectroscopy and C- H s h i f t correlation spectroscopy is a powerful tool for studying complex molecules. A preliminary study is described, i n which ZQT (2D) spectroscopy is used to assign the proton spectrum of a model compound. A new method (spin-echo absorption spectroscopy) for obtaining high-resolution absorption mode proton spectra from b i o l o g i c a l samples i s demonstrated, using some model systems, including a preliminary study on red-blood c e l l s . This approach can be incorporated into a new concept, "integrated NMR experiments". Most of the discussions i n this thesis are aimed towards practicing chemists who are interested in the analysis of complex organic molecules and in the e f f i c i e n t methods for performing 2D NMR experiments. - i v -TABLE OF CONTENTS Page CHAPTER I - INTRODUCTION 1 1.1 Background 2 1.2 Pulsed Fourier transform NMR spectroscopy 4 1.3 The concept of two-dimensional spectroscopy 14 1.4 Organisation of th i s thesis 16 References 18 CHAPTER II - Spin-echo Fourier transform spectroscopy 19 2.1 History 20 2.2 Spin-echo pulse sequence 22 2.3 The e f f e c t of radiofrequency pulses on a spin system 24 2.4 Spin-echo absorption spectroscopy 29 2.5 Applications of SEAS i n chemistry 34 2.6 Applications of SEAS i n biology 45 References 55 CHAPTER III - Two-dimensional Fourier transform NMR spectroscopy 57 3.1.1 Introduction 58 3.1.2 Pulse sequence and data a c q u i s i t i o n 59 3.1.3 Data processing 61 3.2 Applications 72 3.2.1 General analysis 72 3.2.2 The phase twist e f f e c t i n 2D spectra 77 3.2.3 Problems associated with the magnitude or power mode 80 spectra 3.2.4 The dynamic range problem i n NMR spectroscopy 82 - v -Page 3.2.5 The overlap or hidden resonance problem i n NMR 83 spectroscopy - the use of t i l t e d 2D J spectra 3.2.6 Strong coupling e f f e c t s i n 2D J spectra 91 3.3 Miscellaneous topics related to 2D J spectroscopy 97 3.3.1 Elimination of dynamic range e f f e c t s i n 2D J spectroscopy 97 3.3.2 Phase-sensitive t i l t routine 103 3.3.3 Lineshape c h a r a c t e r i s t i c s i n phase-sensitive t i l t e d 110 2D J spectra 3.3.4 Generalised a c q u i s i t i o n of spin-echo data - integrated 122 NMR experiments References 127 CHAPTER IV - Spectral assignment techniques in NMR 130 4.1 Introduction 131 4.2.1 l^C-^H chemical s h i f t c o r r e l a t i o n spectroscopy 132 4.2.2 The experiment 133 4.2.3 Experimental r e s u l t s 137 4.3 Broad band heteronuclear and homonuclear decoupling v i a 145 2D J spectroscopy References 155 CHAPTER V - High res o l u t i o n zero quantum t r a n s i t i o n (2D) spectroscopy 157 5.1 Introduction 158 5.2 Creation and observation of ZQT's in pulse NMR 159 5.3 Spectral analysis 165 5.3.1 Generalization 165 5.3.2 AB system 166 - v i -Page 5.3.3 ABC system 167 5.3.4 ABCD system 170 5.4 Applications of ZQT i n chemistry 176 References 185 CHAPTER VI - Summary and Discussion 187 References .197 CHAPTER VII - Experimental section 198 7.1 The spectrometer 199 7.2 Chemicals used 200 7.3 Red blood c e l l s , sample preparation 201 7.4 2D J spectroscopy 202 7.5 ^ H s h i f t c o r r e l a t i o n spectroscopy 204 7.6 Zero-quantum t r a n s i t i o n (2D) spectroscopy 205 References 208 APPENDICES 209 Basic computer programs 209 Abbreviations 216 Nomenclature 218 - v i i -LIST OF TABLES Chapter IV A.l Carbon-13 and proton NMR spectral data of a,8 cellobiose 4.2 Carbon-13 and proton NMR spectral data of 5,epi-sisomycin Chapter V 5.1 The energy l e v e l representation and the possible n-QT frequencies for an AB spin \ system 5.2 a\2 a n c * 023 elements of the density matrix of an AB system following the n-QT (2D) spectroscopy pulse sequence 5.3 The energy levels and the ZQT frequencies for an ABC system 5.4 (A) The energy levels for an ABCD system. (B) The ZQT frequencies for an ABCD case 5.5 Energy levels and basic (symmetry) functions corresponding to an A B 3 system 5.6 The ZQT18 and their energies for an A B 3 case 5.7 The conventional and ZQT spectra data for compound 6 Page 137 142 159 163 168 170 173 174 177 - v i i i -LIST OF FIGURES Page Chapter I 1.1 Resolution of a magnetization vector into i t s components along the x, y and z coordinates 1.2 The magnetization vector model and the energy l e v e l representation of a spin % system 1.3 T1IR and T2CP experimental spectra Chapter II 2.1 Carr-Purcell (method A) pulse sequence 2.2 Effect of pulses on an AX system during the C-P pulse sequence 2.3 J modulation i n SEFT spectroscopy 2.4 Comparison of the magnetization i n t e n s i t i e s of a large and small molecule i n SEFT experiment 2.5 270 MHz proton spectrum of BSA 2.6 SEAS data from a mixture of ct, 8-D-xylose, a-cyclodextrin and dextran T-10 2.7 SEAS data from a mixture of B-methylxylopyranoside and dextran T-10 2.8 SEFT data from a mixture of a,8-D-xylose, a-cyclodextrin and dextran T-10 2.9 SEAS and SEFT data of lysozyme 2.10 SEAS data to i l l u s t r a t e the effect of l y s i s on an NMR spectrum of RBC 2.11 SEAS data on RBC-glucose systems Chapter I I I 3.1 The 2D J pulse sequence 3.2 Phase modulation of SEFT spectra 3.3 The second FT of the t r i p l e t signals of die t h y l malonate 15 23 25 30 35 36 39 41 43 44 48 49 60 62 65 - i x -3.4 The second FT of the quartet signals of diethyl malonate 3.5 A contour plot of a 2D J spectrum 3.6 Diagrammatic representation of the various display modes in 2D J spectroscopy 3.8 A comparison between the normal and p a r t i a l 2D J spectra of 6, 3.9 A comparison of the ID and 2D NMR spectral data to i l l u s t r a t e effect of strong coupling and resolution of overlapping multiplets by 2D J spectroscopy 3.10 The t i l t operation, to i l l u s t r a t e i t s advantages i n 2D J spectroscopy 3.11 The 270 MHz proton spectrum of uridine (8), and a comparison of ID and 2D J spectral data 3.12 The resolution of a "hidden resonance" by the use of the t i l t routine i n a sample of a,8-D-xylose in D£0 3.13 A p a r t i a l 270 MHz proton spectrum of a,8 cellobiose (9) i n D2O, and the corresponding 45° skew projection 3.14 A t i l t e d proton 2D J spectrum of cellobiose at 270 MHz 3.15 A comparison of the normal and proton-decoupled proton spectrum of 10, to i l l u s t r a t e the effect of strong coupling i n 2D J spectroscopy 3.16 An experimental and simulated 2D J spectra of the 6P and 6P1 protons of 10 to i l l u s t r a t e the effect of strong coupling i n 2D J spectroscopy 3.17 The comparison of the simulated and experimental projections of the strongly coupled 6P and 6P' protons Page 66 68 70 3.7 The 2D J spectrum of an a-methyl glucoside (6) 73 74 76 85 86 88 89 90 93 94 95 3.18 Diagram to i l l u s t r a t e the use of solvent nulled (T1IR) 2D J 99 spectroscopy 3.19 Diagram to i l l u s t r a t e the advantages of solvent nulled 2D J spectroscopy on the p a r t i a l J spectra of uridine (8) i n D2O 100 3.20 The resolution of the H-4 and H-5e multiplets of 4 i n a 102 mixture containing dextran T-10, by SEAS and D2D J spectroscopy - x -117 119 120 Page 3.21 A diagram to i l l u s t r a t e the t i l t operation, using the 106 quartet of diethyl malonate 3.22 Resolution enhancement of a doublet by the use of phase- 108 sensitive t i l t routine 3.23 The "phase-twist" effect i n 2D spectroscopy m 3.24 A simulated, phase-sensitive, t i l t e d 2D J spectrum to show 114 the lineshape characteristics 3.25 An experimental 2D J plot of a singlet to show the lineshape 116 characteristics and the " t i - n o i s e " 3.26 A comparison of simulated, conventional and phase-sensitive t i l t e d spectra 3.27 Experimental and simulated sub-spectra, to show the interference from an intense neighbouring signal 3.28 The comparison of the multiplets of furoic acid from a normal, and p a r t i a l J spectra, the l a t t e r being displayed i n the magnitude, power and phase-sensitive mode 3.29 The comparison of the skew projections (integral and maximal) 122 of furoic acid obtained from magnitude, power and phase-sensitive 2D J spectra 3.30 The whole acquired data matrix of an integrated NMR 124 experiment and the d i v i s i o n of the signals for the various indi v i d u a l experiments Chapter IV 4.1 The pulse sequence used to measure the ^Cj- *H s h i f t 133 correlation spectra and the o r i g i n a l pulse sequence of Maudley and Ernst 4.2 The normal carbon-13 spectrum of 5,epi-sisomycin and the 139 traces corresponding to the proton spectrum obtained from the *-*C- s h i f t correlation spectrum 4.3 Proton 2D J data of 5,epi-sisomycin i n D2O at 400 MHz 140 4.4 The 1 3 C r *H s h i f t correlation 2D spectrum of the 141 h i g h - f i e l d region 4.5 Broad band homo- and heteronuclear decoupling by 2D J 146 spectroscopy: compound 13 - x i -Page 4.6 Broad band homo- and heteronuclear decoupling by 2D J 148 spectroscopy: compound 14 4.7 Broad band homo- and heteronuclear decoupling by 2D J 149 spectroscopy: compound 15 4.8 Broad band homo- and heteronuclear decoupling by 2D J spectroscopy: compound 16 4.9 45° projection and the f\ projection of a 2D J spectrum to show the limitations in absolute mode displays Chapter V 5.1 The basic pulse sequence for the creation and detection of n-quantum transition spectra 5.2 Energy level representation for an AB2 spin h system 5.3 The 270 MHz proton spectrum of 6 in CDD6 5.4 Traces indicating the cancellation of higher order transitions, by using suitable phase shifted pulse sequences for the selective detection of ZQT spectra 5.5 ZQT spectra of the H-l, H-2, H-3 and H-6" protons in 6,, measured at 270 MHz 151 152 161 167 176 178 181 - x i i -LIST OF COMPOUNDS 1. a,8-xylose 2. a,cyclodextrin 3. dextran T-10 4. 8-methyl xylopyranoside 5. ot,B-glucose 6. trideuteriomethy1 2,3,4,6-tetra-0-trideuterioacetyl-a-D-glucopyranoside 7. 2,3,4-tri-0-acetyl-6-deoxy-a-D-glucopyranosyl 3,4,di-0-acetyl-l,6-dideoxy-B-D-frue to furanos ide 8 . uridine 9 . a,8 cellobiose 10. 1',4,6,6'-tetrachloro -1',4,6,6'-tetradeoxy-galacto-sucrose tetramesylate 11. furoic acid 12. 5,epi-sisomycin 13. 1,2,3,4,7,7-hexachloro-6-exo-fluoro-bicyclo[2.2.1] hept-2-ene 14. 3,4,6-tri-0-acetyl-2-deoxy-2-fluoro-8-D-glucopyranosyl fluoride 15. 4,4-d ideute rio-2-oxo-2-phenoxy-5-pheny1-1,3,2-dioxaphosphorinane 16. diphenyl-1,1,1-trifluoro-isopropyl-phosphate - diethyl malonate - x i i i -ACKNOWLEDGEMENTS It i s a pleasure to thank Drs. G. Pouzard and G.A. Morris for many helpful discussions, on various aspects of NMR spectrscopy. The work on ZQT spectroscopy and on red blood c e l l work was done i n collaboration with Dr. G. Pouzard and Mr. R. Snoek respectively, to both of whom I am greatly indebted. The experience and knowledge of Ms. T. Markus, H. Chow and J . Sallos of the Electronics group at the U.B.C. Chemistry department who helped to construct and maintain the spectrometer used i n most part of this work i s greatly appreciated. My thanks also reach out to the many friends who have contributed to the completion of this thesis, either d i r e c t l y or i n d i r e c t l y , and made by stay i n Vancouver so memorable. F i n a l l y , I wish to thank my director, Professor L.D. H a l l , for providing an excellent opportunity and encouragement to work i n a new area of science, which made the current work so interesting and worthwhile. - 1 -CHAPTER I INTRODUCTION - 2 -1.1 Background Since the o r i g i n a l work of Bloch et a l . (1-3) and of Purcell e_t a l . (4) in 1946, nuclear magnetic resonance (NMR) spectroscopy has developed and d i v e r s i f i e d into widely d i f f e r i n g f i e l d s including physics, chemistry, biology and medicine. Chemists (and some biochemists) generally have been involved i n studies of the structural and chemical properties of molecules using high resolution (5,6) and more recently s o l i d state NMR techniques, whereas NMR imaging (7) and "t o p i c a l magnetic resonance" (TMR) (8) are some of the latest techniques to become available for c e l l b i o l o g i s t s , physiologists and physicians. The rapid progress of NMR spectroscopy i n these many different areas can be attributed mainly to the development of multipulse Fourier transform NMR techniques, of magnets which operate at very high ("super-conducting") magnetic f i e l d s , and of advances i n (mini-)computer technology and the associated data storage systems. As a r e s u l t , i t is now possible to perform routinely rather sophisticated NMR experiments which include both hardware and software operations automated under computer control. In addition to these c a p a b i l i t i e s the advent of new experimental concepts, such as two-dimensional (2D) NMR spectroscopy (9,10) has provided the chemist, for example, with methods for studying structures of a molecular complexity, which only a few years ago would have been regarded as essentially impossible.^ The f i r s t commercial high resolution NMR spectra were available around 1956, and prior to 1966 most spectra were obtained i n the continuous wave (CW) mode. Much of the early developments and research involved multiple resonance studies of protons and understanding connectivity relationships between the energy levels of spin systems (11). This proved to be a valuable tool for *Some t y p i c a l examples are considered i n Chapters I I I and IV 3 -assigning spectra but the major limitations i n those days were the r e l a t i v e l y low s e n s i t i v i t y (signal to noise ratio) of NMR spectroscopy and the compli-cations a r i s i n g from overlapping signals i n proton NMR spectra. Presently, the commercial a v a i l a b i l i t y of superconducting magnets which operate at f i e l d s equivalent to a resonance frequency of up to 600 MHz for protons have considerably eased both problem of signal overlap and s e n s i t i v i t y . The development by Cooley and Tukey (12) in 1965 of a fast Fourier transform algorithm, ideal for use with a minicomputer, and the subsequent introduction of pulsed Fourier transform (FT) technique into NMR spectrosocpy by Ernst and Anderson (13) i n 1966 has had a substantial impact i n chemistry, p a r t i c u l a r l y i n organic chemistry. Besides f a c i l i t a t i n g numerous proton NMR experiments, the increased efficiency of this method has opened many new avenues of research, including studies of low sensitive nuclei such as carbon-13, and of multipulse FTNMR spectroscopy. The measurement of high resolution NMR spectra using the continuous wave (CW) or "slow-passage" method involves the slow variation of either the frequency or f i e l d such that the resonance absorption of radiofrequency (RF) energy by each group of equivalent nuclei is measured i n d i v i d u a l l y , to y i e l d the NMR spectrum. In contrast, in the basic pulsed Fourier transform technique a strong radiofrequency pulse is applied such that i t excites a l l nuclei simultaneously. The response, or the free induction decay (FID) si g n a l , which i s measured as a function of time, contains a l l the (resonant) frequency information of the nuclei influenced by the pulse, and can be viewed i n frequency space after Fourier transformation. The resulting spectrum is i d e n t i c a l to that obtained by the CW method and represents a plot of signal i n t e n s i t y versus frequency. - 4 -In view of the importance of the pulsed FT technique, both to NMR spectroscopy i n general and to the work of this thesis i n p a r t i c u l a r , a b r i e f d i s c u s s i o n of this method i s given i n the next section. This w i l l f a m i l i a r i z e the reader with the basic concepts and nomenclature used i n pulsed FTNMR spectroscopy, which are often referred to i n subsequent chapters in the context of spin-echo and 2D Fourier transform spectroscopy. As w i l l be seen there are two d i f f e r e n t models (the c l a s s i c a l magnetization vector model and the quantum mechanical description) which are commonly used to explain FTNMR experiments; these w i l l be b r i e f l y reviewed i n the next section, mainly from an experimental chemist's point of view, without indulging into mathematical d e t a i l s . 1.2 Pulsed Fourier transform NMR spectroscopy Pulsed Fourier transform NMR spectroscopy involves study of the responses from s u i t a b l e magnetic n u c l e i to pulses of radiofrequency energy. The c l a s s i c a l magnetization vector model provides a simple and convenient picture for understanding some of the basic features of these experiments. In this model, the e f f e c t of RF pulses on an ensemble of nuclear "spins" which have been subjected to a s t a t i c magnetic magetic f i e l d (B Q) are described i n terms of the behaviour of a macroscopic or net magnetization vector M. At equilibrium this can be represented as a vector precessing at a c h a r a c t e r i s t i c (Larmor) frequency and aligned along the d i r e c t i o n of the f i e l d B q ( F i g . 1 . 1 ) . At equilibrium the x and y components of the magnetization w i l l be e f f e c t i v e l y zero due to precession of M about z, but the z component w i l l be f i n i t e since i t s magnitude does not vary with time. - 5 -Figure 1.1: The magnetization of a set of equivalent nuclei in a magnetic f i e l d B n are represented by a (macroscopic) vector M which precesses about z at i t s characteristic Larmor frequency. At any instant, M can be represented by i t s components i n the x, y and z directions, indicated by Mx, M.y and M z respectively. - 6 -It is generally more convenient to v i s u a l i z e the behaviour of individual sets of equivalent nuclei i n multipulse NMR experiments i n terms of their individual magnetization components i n a "rotating reference frame". In this model, the x and y coordinates represented i n F i g . 1.1 are assumed to be rotating about the z axis at the transmitter frequency of the spectrometer and in the same sense as the nuclear precession. The new coordinates are now defined as x 1, y' and z', and in this reference frame the applied RF f i e l d (usually along the x' direction) appears to be fixed. The effect of an RF pulse on a spin system at equilibrium i s to rotate ( " f l i p " ) the t o t a l magnetization vector from i t s position along z' through an angle a' (= 2Tia), about the dir e c t i o n of the pulse as shown i n Figure 1.2A. The f l i p angle a' is given by a' = V B 1 t a (radians) [1.1] where y = gyromagnetic r a t i o (rad. s ^gauss ^ ) ; = magnetic induction of the RF pulse (gauss); t a = pulse duration. Given that both y and B^ are held constant, and that the NMR receiver system i s designed to detect the component of magnetization along the y axis, i t follows that the amplitude of the detected signal is a function of the duration of the RF pulse, varying in a sinusoidal fashion. Thus, a = 90° corresponds to the f l i p of Mz, onto the +y' di r e c t i o n and corresponds to the maximum observable signal; i n contrast, a = 270° leaves Mz, along the -y' axis and produces a minimum (negative) signal. Zero values correspond to the i n i t i a l state (a = 0° or 360°) and the "inverted" state (a = 180°), when the magnetization l i e s along the longitudinal axis (Fig. 1.2A). Although this c l a s s i c a l vector model i n the rotating reference frame usually suffices for a quali t a t i v e understanding of many pulsed NMR (a) (b) (c) Equilibrium 9 0 ° pulse 1 8 0 ° pulse Magnetization Figure 1.2: (A) The magnetization vector model in the rotating reference frame and (B) the energy le v e l representation, to i l l u s t r a t e the effect of 90° and 180° pulse on a spin 1/2 system AP represents the spin population difference between the two levels. ¥ ~ Y/2TT - 8 -experiments from an application chemist's point of view, i t i s inadequate for a more detailed understanding of, for example, spectral analysis or time dependent phenomena, for which purposes the quantum mechanical model i s used. In this l a t t e r model, each magnetic nucleus i s considered to be associated with discrete energy levels. For example, a spin h nucleus (such as or 13 C) i n a magnetic f i e l d is represented by two energy l e v e l s , which correspond e f f e c t i v e l y to the direc t i o n of the nuclear moment being oriented " p a r a l l e l " or " a n t i - p a r a l l e l " to the magnetic f i e l d ; these are generally referred to as the ct- and 8-states respectively (Fig. 1.2B). The energies of these states are given by E = -1 yhmB0 [1.2] 2TT where h = Planck's constant (erg. s) and m = +^5, corresponding to the a- and 8-states respectively. The energy difference between the levels i s therefore, A E = 1 YhB n [1.3] 2TT In accordance with Planck's law, absor tion (or resonance) is established by providing the system an RF energy equal to, A E = hv Q [1.4] = 1 YhB n 2TT hence, v 0 = J _ Y B Q 2TT [1.6] Equation [1.6] refers to the resonance condition and corresponds to the resonance frequency or Larmor precession frequency. For an ensemble of equivalent n u c l e i , the "spins" are d i s t r i b u t e d between the energy le v e l s according to Boltzmann's law; the spin population r a t i o between the lower ( n ^ and upper (n u> l e v e l i s given by 1 n^ _ exp 2 A E 1 + 2AE [1.7] kT kT k = Boltzmann's constant (erg deg.~l) The maximum observable magnetization or NMR signal i n t e n s i t y w i l l be proportional to the excess spin population 2AP i n Figure 1.2B. Two equivalent, but rather simple models were presented above; the c l a s s i c a l vector model is associated with the e f f e c t of magnetizations i n the rotat i n g reference frame and the simple quantum mechanical model i s associated with spins, and t h e i r d i s t r i b u t i o n or t r a n s i t i o n s within the energy l e v e l s . The various features involved i n pulsed NMR are now explained i n terms of both these models. A 90° pulse equalizes the spin population between two lev e l s ("saturation") corresponding to an optimum absorption of energy and hence a maximum si g n a l i n t e n s i t y . A 180° pulse, on the other hand, reverses the equilibrium Boltzmann d i s t r i b u t i o n (a transformation which i s referred to as going to a negative spin-temperature); i n the rota t i n g frame, a 90° pulse represents a transfer of the t o t a l magnetization onto the y' plane, hence corresponds to a maximum s i g n a l ; i n contrast, the 180° pulse transfers the Mz, magnetization onto the -z' d i r e c t i o n and therefore does not induce an NMR signal i n the receiver c o i l ( c f . Figs. 1.2A and B). Ex c i t a t i o n causes a non-equilibrium state by a l t e r i n g the Boltzmann d i s t r i -bution from which the spins can return to t h e i r equilibrium value by ex-changing energy with t h e i r surroundings (the l a t t i c e ) v i a f i r s t - o r d e r process *2AE i s usually much smaller than kT at ordinary temperatures of s p i n - l a t t i c e relaxation, characterised by the s p i n - l a t t i c e relaxation time, (=1/R^, where refers to the relaxation rate). In the vector model the s p i n - l a t t i c e relaxation process is depicted as the return to equilibrium of the longitudinal component of the magnetization; hence i t i s often referred to as longitudinal relaxation. In contrast, another relaxation process which involves the exchange of energy between two opposite spin states with no loss of t o t a l energy of the system is referred to as spin-spin relaxation. In the vector model this can be visualized as a loss of phase coherence of the individual components of the transverse magnetization; hence i t is referred to as transverse relaxation. Spin-spin relaxation time (T^ = 1/^) determines the l i n e widths of the resonances i n an NMR spectrum whereas s p i n - l a t t i c e relaxation governs t h e i r 1 i n t e n s i t i e s . So far the phenomena of excitation and relaxation were considered using two simplified models. Unlike most other forms of spectroscopy ( i n which resonance or absorption of energy is studied as a function of frequency), the observed NMR signal is a time evolution signal which for the current purposes 2 i s discussed i n terms of the vector model. A transverse magnetization component caused by excitation of the nuclei can be represented i n the rotating frame as precessing at a frequency v 0 , which is the frequency difference (offset frequency) with respect to that of the transmitter or " c a r r i e r " (see sec. 2.1). The receiver c o i l of the spectrometer is designed to U f t e r excitation (by a 90° pulse), a s u f f i c i e n t relaxation delay ( ca. 5Tj) must be allowed for the system to return to thermal equilibrium, prior to repeating a pulse sequence. ^The quantum mechanical model using the density matrix approach w i l l be given i n Ch. V. measure the induced voltage arising from this transverse magnetization. In single phase detection (SPD) spectrometers the y' component of the magnetization (M^,) is detected following a pulse which is applied along the x' d i r e c t i o n . I t is also possible to detect M , and M , simultaneously by x y quadrature phase detection (QPD) which has several merits, including an improvement i n s e n s i t i v i t y by a factor of ca. 1.4 over the SPD method. The amplitudes of the signals detected along the x' and y' directions, M .(t) and M .(t), show characteristics of cosine and sine functions y' x' respectively.^ The behaviour of the y' component, which i s usually observed 2 i n "conventional" (SPD) NMR experiments, can be expressed as, M y,(t) = M q sin(cx) cos(2irv ot) exp(-tR 2) [1.8] where, M q represents a>unit amplitude and the sin ot term describes the effect of f l i p angle on the signal magnitude. The exponential term i n the above equation indicates a "damping" of the NMR signal with time due to transverse relaxation. In practice the detected signal is f i r s t d i g i t i z e d so that i t can be stored, and subsequently processed in a computer. The conditions for data acquisition are determined by the sampling theorem which states that the highest frequency from the transmitter ( i n SPD) that can be correctly represented i n a spectrum w i l l be half the sampling rate, or Nyquist frequency. A l l frequency components outside the spectral width (SW) w i l l be ^The FID signal i n QPD can be regarded as a complex time s i g n a l . In this case i t is possible to distinguish between positive and negative frequencies with respect to the transmitter. ^The signal that i s measured i n a spectrometer i s compared (subtracted) with the reference frequency from the transmitter, hence the frequency term i n equation 1.8 i s represented by v Q (=vt-y), where v t = RF c a r r i e r frequency. - 12 -"folded back" into the spectrum. Since noise i s also folded back, to the detriment of the overall signal to noise r a t i o , i t i s common practice to use suitable analog f i l t e r s (to remove the unwanted frequencies) to improve the s e n s i t i v i t y . The relationships between the various acquisition parameters are given by the following expressions SW = 1 [1.9] 2(SR) DR = _1 = 2(SW) = 1 [1.10] AT BS (BS)(DW) where SR = sampling rate (points s * ) ; AT = acquisition (sampling) time ( s ) ; SW = spectral width (Hz); BS = block size or number of sampling points; DW = dwell time (s); DR = d i g i t a l resolution. For a given spectrometer, the bandwidth of the power spectrum of the RF pulse w i l l be inversely proportional to the pulse width (say, t^^o). I t is generally desirable to have the maximum excitation bandwidth and hence to use as short a sampling pulse as possible; commonly 90° pulses of 5-50 us are used. However selective pulses capable of exciting a single multiplet can be generated by using a lower transmitter power and longer pulse duration (ca. 10-100 ms). One of the advantages of using QPD is that the transmitter can be placed i n the centre of the spectrum thus e f f e c t i v e l y halving the RF power requirements as compared to SPD i n which the transmitter i s placed at one end of the spectrum. The d i g i t i z e d time domain signal i s usually subjected to a mathematical treatment referred to as " d i g i t a l f i l t e r i n g " ; t his i s intended either to improve the resolution or the signal to noise r a t i o of the f i n a l spectrum, both of which are interdependent (14). - 13 -Fourier transformation of the time domain signal (eq. [1.8]) yields a complex, frequency domain spectrum (10), S ( v ) = Mp^sina - iM02TTAvT^sina [1.11] 1+(2TTAVT2)2 1+(2TTAVT2)2 = a - d where A v = v - v o « The re a l (a) and imaginary (d) parts correspond to the Lorentzian-absorption and -dispersion mode signals respectively. In practice, however, instrumental factors such as receiver "dead time"* and analog f i l t e r s introduce an additional phase term i n the time-domain signal (eq. [1.8]), hence the resulting frequency-domain spectrum contains a mixture of absorption and dispersion terms. These are easily separated (phase corrected) by user-interactive data manipulation routines to y i e l d the desired absorption mode peaks i n the f i n a l spectrum. The effect of pulse width or f l i p angle on the magnetization vectors was discussed e a r l i e r with the aid of equation [1.1] and Figure 1.2. I t i s also possible to change the phase (<j>) of the RF pulses and thereby to change the sense of rotation of the magnetization; for example, a 90° pulse applied along the -y* direction (<j> = 90°) would f l i p the equilibrium magnetization about -y' onto the x d i r e c t i o n . The p o s s i b i l i t y of using the variables a and <J>, together with the durations (T) between a series of pulses to manipulate nuclear spins i n a wide variety of ways has led to a new area of research, commonly referred to as "multipulse NMR spectroscopy". For many chemists some of the p r a c t i c a l l y useful experiments of this class are high resolution s o l i d state and 2D NMR spectroscopy. With the aid of (mini-)computers, pulse programmers and appropriate hardware devices i t i s now possible to "custom design" new NMR experiments by introducing these variables (<j> , ot and T) in a ^A delay (=DW) prior to sampling, i n order to minimize interference from the RF pulse. multiple sequence. Such experiments can provide interesting molecular information, for example, regarding chemical structure and conformation, exchange phenomena and motional properties, etc. Recently the novel concept of double Fourier transformation has been introduced to NMR spectroscopy; as we s h a l l see this results i n an NMR spectrum which i s displayed i n two frequency dimensions and provides an elegant method for resolving and assigning complex spectra. 1.3 The concept of two-dimensional spectroscopy The two-pulse inversion recovery sequence T1IR i s one of the well known multipulse sequences used for the measurement of s p i n - l a t t i c e relaxation rates (R^). This sequence may be represented as {180° - T - 90° - Acquisition} where T i s a variable delay; 180° and 90° refer to the f l i p angle of the two pulses. The signals acquired for various delays T, may be presented, after Fourier transformation i n a two-dimensional display as shown i n Figure 1.3, which represents the exponential recovery back to thermal equilibrium of the magnetization vectors (or spins), which have been inverted by the 180° pulse, as a function of time T. These exponential rate constants are a direct measure of the respective R^-values of the signals. Let us now consider another two pulse sequence, the Carr-Purcell pulse sequence (T2CP; (15)), which i s used for the measurement of spin-spin relaxation rates ( R 2 ) , represented by, { 90° - T - 180° - T - Acquisition) As before, the observed magnetization (corresponding to a single trace i n Fig. 1.3) i s a function of two time variables (a " f i x e d " variable T and a running - 15 -Figure 1.3: Spectra obtained from the s p i n - l a t t i c e , inversion recovery (T1IR) pulse sequence and the Carr-Purcell method for T2 measurement (T2CP). The T1IR spectra show the negative (inverted) signals returning to their equilibrium values as a result of s p i n - l a t t i c e relaxation. The T2CP spectra represent the exponential decay of the signal amplitude (which i s more c l e a r l y indicated by the unmodulated central peak) together with the phase modulation of the outer lines of the t r i p l e t as a function of T. - 16 -variable from 0 to AT). However, i n contrast to the T1IR experiment i n which the signals show a simple exponential recovery from a negative to a positive signal, the spectra obtained from the T2CP experiment show, i n addition to their exponential decay due to spin-spin relaxation, a phase modulation of the signals as a function of T. This modulation frequency i s related to the spin-spin coupling constant and a detailed discussion follows i n the next chapter. It i s also possible to design experiments such that the observed signals are amplitude and/or phase modulated with time ( t ^ ) , at some correlated frequencies. I f these data arrays are subjected to a second Fourier transformation, with respect to t ^ , this reveals the frequency components corresponding to the amplitude or phase modulations i n a second dimension. The resulting signal matrix is referred to as a two-dimensional spectrum, and is equivalent to a conventional spectrum "resolved" i n two frequency domains. More detailed discussions of the various aspects of these experiments w i l l be presented in the following chapters. 1.4 Organisation of this thesis The discussion i n this thesis, for most part, are directed towards the application of proton NMR as an a n a l y t i c a l tool i n chemistry.* Chapter I I of this thesis is concerned with the FT equivalent of the basic spin-echo experiment of Carr-Purcell (method A), and with a simple modification of the data processing routine (spin-echo absorption spectroscopy) which has several useful applications i n chemistry and biology. The description of the effect l-The general discussions of the various multipulsed experiments apply only to weakly coupled systems. of pulses on the spin system i s also applicable to 2D J resolved NMR experiments which constitutes the p r i n c i p a l emphasis of Chapters I I I and IV although other 2D techniques are also included. Chapter V describes i n d e t a i l the application of a zero quantum transition (ZQT), two-dimensional NMR experiment i n chemistry; as w i l l be seen, neither the vector model nor the simple quantum mechanical description introduced e a r l i e r are s u f f i c i e n t to explain a l l the features of the ZQT experiment, and the density matrix approach (16) i s introduced i n that chapter. The reader w i l l note that most of the chemical systems used in this thesis to i l l u s t r a t e the potential of the various experiments involve carbohydrates. The proton NMR spectra of these molecules are generally rather complicated mainly due to the presence of anomeric mixtures i n aqueous solution and the extreme overlap of the resonances. Such spectra pose a serious challenge for chemists attempting to study these systems by conventional techniques. I t i s also worthwhile noting at this juncture that the f i r s t demonstration that NMR parameters exhibit chemically useful stereospecific dependencies was made on carbohydrates by Lemieux et^ a_l. (17,18) in 1958. In a more contemporary context, the numerous, important roles of carbohydrates i n areas ranging from chemistry to biology and medicine, provide a compelling need for the exploration of new sources of structural information. - 18 -References (Chapter I) 1. Bloch, F., Hansen, W.W., Packard, M. Phys. Rev. (1946) 69, 127. 2. Bloch, F. Phys. Rev. (1946) 70, 460. 3. Bloch, F., Hansen, W.W., Packard, M. Phys. Rev. (1946) 70, 474. 4. P u r c e l l , E.M., Torrey, H.C., Pound, R.V. Phys. Rev. (1946) 69, 37. 5. Shaw, D. "Fourier Transform NMR Spectroscopy", E l s e v i e r : Amsterdam, 1976. 6. Martin, M.L., Martin, G.J., Delpuech, J . J . " P r a c t i c a l NMR Spectroscopy:, Heyden: London, 1980. 7. "Nuclear magnetic resonance of intact b i o l o g i c a l systems". P h i l . Trans.  R. Soc. Lond. B (1980) 289, 379, and references therein. 8. Gordon, R.E., Hanley, P.E., Shaw, D., Gadian, D.G., Radda, G.K., Styles, P., Chan, L. Nature (1980), to be published. 9. Aue, W.P., Bartholdi, E., Ernst, R.R. J . Chem. Phys. (1976) 64, 2229. 10. Freeman, R., Morris, G.A. Bui. Magn. Reson. (1980) 1_, 5. 11. Hoffman, R.A., Forsen, S. "Progress i n NMR Spectroscopy:, Ems ley, J.W., Feeney, J . , S u t c l i f f , L.H. Eds.; Pergamon Press: Oxford, 1966; Vol. 1, Chapter 2. 12. Cooley, J.W., Tukey, J.W. Math. Comput. (1965) 19, 297. 13. Ernst, R.R., Anderson, W.A. Rev. S c i . Instrum. (1966) 271, 93. 14. Ernst, R.R. "Advances i n Magnetic Resonance", Waugh, J.S., Ed.; Academic Press: New York, 1966; Vol. 2, Chapter 2. 15. Carr, H.Y., P u r c e l l , E.M. Phys. Rev. (1954) 94, 630. 16. S l i c h t e r , C P . " P r i n c i p l e s of Magnetic Resonance", 2nd ed., Springer-Verlag: B e r l i n , 1978. 17. Lemieux, R.U., K u l l n i g , R.K., Moir, R.Y. J . Am. Chem. Soc. (1958) 80, 223. 18. Lemieux, R.U., K u l l n i g , R.K., Bernstein, H.J., Schneider, W.G. J . Am. Chem. Soc. (1958) 80, 6098. - 19 -CHAPTER II SPIN-ECHO FOURIER TRANSFORM SPECTROSCOPY - 20 -2.1 History Hahn and Maxwell (1,2) i n 1950 were the f i r s t to demonstrate that the decay of the NMR signal i n the transverse plane, due to instrumental e f f e c t s such as inhomogeneity of the magnetic f i e l d , can be reversed by the a p p l i c a t i o n two 90° pulses to the spin system. The rejuvenation (refocussing) of the NMR signal a f t e r a time T (which was equal to the spacing between the two pulses) was refered to as spin-echo formation. Two p r a c t i c a l l y u s eful pulse sequences were l a t e r published by Carr and P u r c e l l (3) i n 1954, which were i n i t i a l l y used to measure spin-spin relaxation rates (R^-values) and t r a n s l a t i o n a l d i f f u s i o n c o e f f i c i e n t s using the time domain NMR s i g n a l s . The basic C a r r - P u r c e l l (C-P) pulse sequence d i f f e r s from that of Hahn i n that the second pulse i s a 180° pulse. The p o t e n t i a l of the C-P experiment i n chemical studies was not r e a l i z e d u n t i l the FT technique was introduced to NMR spectroscopy (4). In 1970, Allerhand and Cochran (5) published a Fourier transformed spectrum from a C-P pulse sequence, and the method was appropriately referred to as spin-echo Fourier transform (SEFT) spectroscopy. As a r e s u l t i t became possible to study the behaviour of the time domain signals i n a spin-echo experiment i n frequency space; obviously this makes the experiment suitable for the study of m u l t i - l i n e spectra. It became apparent that for studies using multipulse sequences, imperfections i n pulse f l i p angles could lead to cumulative errors and r e s u l t i n undesirable consequences p a r t i c u l a r l y for quantitative experiments (6). The various phase-shifted pulse sequences suggested by Meiboom et a_l. (6) and by Freeman £t a_l. (7) represent important examples of how some pulse imperfections can be corrected by including appropriate phase-shifts i n a multipulse sequence. - 21 -One of the remaining l i m i t a t i o n s to the general a p p l i c a t i o n of the spin-echo pulse sequence i n high r e s o l u t i o n proton NMR spectroscopy to, for example, spin-spin relaxation time measurements or chemical exchange studies, is the phase modulation of the signals which arises as a r e s u l t of homonuclear spin-spin coupling. Various methods have been suggested to overcome t h i s problem and to obtain the desired high res o l u t i o n absorption spectra, but these have generally been r e s t r i c t e d i n the range of molecules or spectra (7-11) to which they can be applied and as a r e s u l t spin-echo techniques have not been widely applied to "chemical" systems. Its p o t e n t i a l i n biology was r e a l i z e d by Campbell et al,. (12) who demonstrated that the sharp signals of a biomolecule associated with the slowly relaxing n u c l e i could be s e l e c t i v e l y studied by suppressing the broad (r a p i d l y relaxing) peaks by SEFT spectroscopy. Later the same p r i n c i p l e was used to study small molecules which are involved i n the d i f f e r e n t metabolic pathways i n l i v e red blood c e l l s (13). Even though the SEFT spectra obtained s u f f e r the phase and i n t e n s i t y problem mentioned e a r l i e r , i t provided a convenient method to "see" within the broad envelope which i s c h a r a c t e r i s t i c of the NMR spectra of most macromolecules. Bax et_ a l . (11) have suggested a method, based on a Fourier transformation of the whole-echo s i g n a l , which eliminates the phase problem i n spin-echo experiments. In i t s o r i g i n a l form the above technique appears to be suitable only for molecules with long spin-spin relaxation rates and narrow spectral widths. However, a convenient procedure i s described in this thesis whereby spin-echo absorption spectroscopy (SEAS) can be used for studying complex systems. The p o t e n t i a l use of this method, i s discussed i n Sections 2.5 and 2.6. - I I -I.l The spin-echo pulse sequence The basic Carr-Purcell (method A) pulse sequence includes a 90° and a 180° pulse separated by a delay T, followed by signal a c q u i s i t i o n which usually commences a f t e r an equal delay T. The behaviour of the NMR signal (echo-formation) i s i l l u s t r a t e d i n Figure 2.1. Fourier transformation of the (second) half-echo-signal w i l l produce a frequency spectrum i n which the phases of the peaks are modulated as a function of time T (due to spin-spin coupling when pulses are applied n o n - s e l e c t i v e l y ) . The decay of the magnitude of the peak with time (2T) w i l l be due to the combined ef f e c t s of spin-spin relaxation and d i f f u s i o n of the spins i n the sample during the delay 2T. The Car r - P u r c e l l method B minimizes d i f f u s i o n e f f e c t s by using a ser i e s of 180° pulses a f t e r an i n i t i a l 90° e x c i t a t i o n pulse; this is represented by (90° - (T - 180° -T) - Acquisition} n In t h i s case study T is kept s u f f i c i e n t l y short so that the molecules i n the samples do not d i f f u s e appreciably during that period.^ However pulse imperfections ( i n c o r r e c t f l i p angles) i n the above sequence w i l l have cumulative e f f e c t s , which may be compensated by using the Meiboom-Gill modification of the C a r r - P u r c e l l sequence, given by (6), {90°y - (T - 180° - T - 180° - T) - Acquisition} n The 90° pulse i s phase s h i f t e d by <|>= 90°, ( i . e . the RF pulse i s applied along the y' axis) as a r e s u l t the imperfections i n the refocussing pulse are ^The i n t e n s i t y of the transverse magnetization component along y' at time t is given by, M y.(t) = M Q{exp (-t/T 2) + (-Y 2G 2Dt 3/12n 2) } G = f i e l d gradient along z (gauss cm -*); D = d i f f u s i o n c o e f i c i e n t . n w i l l be equal to one i n the C-P method A pulse sequence. The term on the r i g h t indicates the decay of magnetization due to d i f f u s i o n of molecules i n a magnetic f i e l d gradient. Note the t 3 dependency. 90° pulse 180° pulse spin-echo - ^ 0 1 W N " ~ > * * W * ^ ^ -*-Defocussing Refocussing interval T D interval 7"R Evolution period tj N> OJ Detection period t 2 Fieure 2 . 1 : The Carr Purcell (method A) pulse sequence and the i l l u s t r a t i o n of the spin-echo formation of the NMR s i g n a l . T p ^ R ^ t ! . The two detection periods represent the signal a c q u i s i t i o n for whole-echo (SEAS) and half-echo Fourier transformation. - 24 -corrected on every even numbered echo. In another related procedure suggested by Freeman and Wittekoek (7), the phase of the refocussing pulse is alternated by 180° ( i . e . the pulse i s applied along the ^x' d i r e c t i o n s ) . In most of those parts of t h i s thesis involving SEAS and 2D J experiments, the Carr-P u r c e l l method A with phase al t e r n a t i o n procedure of Freeman e_t a_l. (7) was used. It w i l l be noted l a t e r that use of such phase s h i f t e d pulse sequences i s c r i t i c a l , p a r t i c u l a r l y i n SEAS. The next section provides an introduction to the e f f e c t s of RF pulses, on a spin system. This can be e a s i l y v i s u a l i z e d considering the magnetization vector model i n a r o t a t i n g reference frame to provide an understanding of the many features of spin-echo spectroscopy such as phase and amplitude modulation and refocussing e f f e c t s . Since the same basic spin-echo pulse sequence is also used i n 2D J and related experiments, this discussion also provides a basis for a q u a l i t a t i v e understanding of the p r i n c i p l e s of those experiments which w i l l be discussed in l a t e r chapters. 2.3 The e f f e c t of radio frequency pulses on a spin system Using the nomenclature of the rotating reference frame model, the RF pulse of a conventional, single pulse NMR experiment creates a net magnetization in the x'-y' plane. This i s i l l u s t r a t e d i n Figure 2.2 a-b where a 90° pulse applied i n the x' d i r e c t i o n , generates a transverse magnetization component by f l i p p i n g the z' component onto the y' d i r e c t i o n . When this excited system i s allowed to "evolve" the magnetization vectors corresponding to each set of equivalent spins precess with t h e i r own c h a r a c t e r i s t i c frequencies which, i n the r o t a t i n g frame, i s seen as precession of each vector at an o f f s e t frequency ( v Q ) with respect to the transmitter. (g) (h) (b) (C) (d) (0>A*W) (0)A-7TJ') (e) / (OJA-W) ( f ) Equilibrium Magnetization 90° pulse time^O Free precession 180° pulse TD - i /2t , Figure 2.2: The behaviour of the A magnetization of an AX system i n the r o t a t i n g frame during the C-P pulse sequence. The sequence (a-f) represents the e f f e c t of a non-selective 180° pulse which re s u l t s in an accumulation of a phase angle 2<|>. Application of a s e l e c t i v e 180° pulse to the A spins does not r e s u l t in a phase modulation of the A components as a function of t \ (a-d, g, h ) . The f i e l d inhomogeneity e f f e c t s are represented by the " d i f f u s i o n " of the magnetization vectors which are refocussed at t j (the r e l a t i v e v e l o c i t i e s of the "isochromats" are indicated by the inner arrows). The chemical s h i f t component w i l l always l i e along the +y d i r e c t i o n at t^ (f and h) and are therefore "refocussed". and J' r e f e r r e s p e c t i v e l y to the angular v e l o c i t y ((DA=offset with respect to the transmitter) i n the r o t a t i n g frame, and the coupling constant in radians. The magnitude of the transverse magnetization decays exponentially with time due to spin-spin interactions i n the medium, which i s characterised by i t s spin-spin relaxation rate (R 2 = 1/T 2). In p r a c t i s e , inhomogeneities i n the s t a t i c magnetic f i e l d B q also contribute to the decrease of the transverse s i g n a l . This f i e l d inhomogeneity causes d i f f e r e n t regions of the sample to experience s l i g h t l y d i f f e r i n g l o c a l f i e l d s , thereby causing the n u c l e i i n those d i f f e r e n t regions to precess at s l i g h t l y d i f f e r e n t frequencies. This r e s u l t s i n a loss of phase coherence (dephasing e f f e c t ) of the magnetization "isochromats", which leads to a rapid damping of the transverse s i g n a l . For most p r a c t i c a l purposes the composite decay rate i s assumed to be exponential, with a time constant T 2*, which i s related to the r e s u l t i n g s p e c t r a l l i n e width at half-height given by, Av jj = 1_ = R£* (Hz) [2.1] T2*7T Tl The l i n e widths observed i n a conventional high r e s o l u t i o n NMR experiment are usually governed by instrumental e f f e c t s (R^), and the r e l a t i o n s h i p to the " n a t u r a l " spin-spin relaxation rate can be represented by, R2 = V " R2 [ 2 ' 2 ] As a r e s u l t l i n e width measurements, do not therefore, provide a convenient method for spin-spin relaxation time measurements i n most cases. However T 2 measurements can be made v i a the experiments based on C-P pulse sequence described e a r l i e r . The consequences of the spin-echo pulse sequence on a spin system can be e a s i l y v i s u a l i z e d i n terms of c l a s s i c a l magnetization vectors i n the rotating reference frame (7). Figure 1.2 i l l u s t r a t e s the e f f e c t of pulses on the A doublet of an AX spin system. At equilibrium, the t o t a l magnetization vector corresponding to the A spins l i e s along the z 1 d i r e c t i o n ; the i n i t i a l 90 u pulse transforms this magnetization onto the transverse plane, along y' as shown i n Figure 2.2 a-b. During the delay the magnetization of the A spins evolves and s p l i t s into two components, symmetrically disposed about the chemical s h i f t component, and correspond to the two A t r a n s i t i o n s in a frequency spectrum. The phase angle between them w i l l be proportional to the spin-spin coupling constant and the delay T. Inhomogeneities in the B o~magnetic f i e l d , cause the magnetization "isochromats" to lose phase coherence; t h i s is represented in Figure 2.2c as, each component " d i f f u s i n g " or "fanning-out" i n the transverse plane; the r e l a t i v e angular v e l o c i t i e s are represented by the inner arrows i n d i c a t i n g the " f a s t " and "slow" moving components. In conventional pulsed NMR the r e s u l t i n g magnetization is detected over a period (usually >3 T 2 * ) equal to the sampling time, p r i o r to Fourier transformation. The rapid decay of the magnetization due to the instrumental factors ( s t a t i c f i e l d inhomogeneity) or R* e f f e c t can be reversed or "refocussed" by applying a 180° pulse to the spin system. However, the ultimate r e s u l t of this pulse on a spin system depends on the nature of the refocussing pulse; for example, the l a t t e r could be a non-selective pulse in a homonuclear system or a pulse applied s e l e c t i v e l y to only the A n u c l e i as in a heteronuclear case. A s e l e c t i v e pulse applied along the x' d i r e c t i o n to the A spins w i l l have two e f f e c t s on the R magnetization isochromats - a) i t f l i p s each vector into i t s mirror image p o s i t i o n about the x' axis as shown in Figure 2.2d; t h i s causes the r e l a t i v e l y fast and slow components (which had developed as a r e s u l t of both inhomogeneity e f f e c t s and free precession) to be - 28 -placed i n t r a i l i n g and leading positions respectively i n r e l a t i o n to the d i r e c t i o n of precession ( F i g . 2.2d,g). As a r e s u l t , during the delay T R, the magnetization isochromats of the two A vectors converge thus eliminating the e f f e c t s due to magnetic f i e l d inhomogeneities at time t^ = T^+T^ ( F i g . 2.2h). At that same instant, the two components corresponding to the J. , scalar spin-spin coupling would have also refocussed and l i e along the -y' d i r e c t i o n . Hence i n this experiment, the e f f e c t s of magnetic f i e l d inhomogeneity, coupling constants and chemical s h i f t s are a l l simultaneously refocussed or eliminated at the "echo-maxima".^ In contrast, i f the 180° pulse i s non-selective and i s applied to both A and X spins, i t s e f f e c t i n addition to that indicated i n Figure 2.2d, w i l l be to invert a l l spin states thereby "exchanging the i d e n t i t y " of the two A components as indicated i n Figure 2.2e (c_f. F i g . 2.2g). As a r e s u l t these two components continue to diverge during time T and accumulate a t o t a l phase angle of 2$ between them at time Tn+T ( F i g . 2.2f); note however that the e f f e c t s of chemical s h i f t and the magnetic f i e l d inhomogeneity are, as before, refocussed at this time. For a general case of a m u l t i p l e t , weakly coupled to X equivalent n u c l e i , the phase angle of each A component is given by, <f> = + hnVL^JT radians [2.3] where i s the t o t a l z spin component of the X spins and T the delay time between the pulses. Fourier transformation of the half-echo signa l w i l l show the phase modulation of each frequency component according to equation [2.3] Its magnitude i s given by the echo maxima which decays exponentially with a time 1Th is phenomenon can be used to d i s t i n g u i s h homonuclear and heteronuclear spin-spin coupling i n 2D J experiments (see Chapter IV). - 29 -constant T j . These features are shown i n Figure 2.3 for the t r i p l e t and quartet resonances (J = 7.1 Hz) of d i e t h y l malonate, ((CH 3CH 2C0 2) 2CH 2) i n CDCl^ s o l u t i o n . * This c y c l i c v a r i a t i o n of the phases of each component as a function of T i s also referred to as J-modulation, and i t has been one of the serious l i m i t a t i o n s to the a p p l i c a t i o n of the SEFT technique to chemical systems, eg. for T 2 measurements and related experiments i n high r e s o l u t i o n proton NMR spectroscopy. Although methods have been suggested to circumvent the problem of J-modulation i n simple spin systems (8,9), for example, by 2 choosing T values equal to an integer of 1/J, by absolute value c a l c u l a t i o n s or by s e l e c t i v e e x c i t a t i o n methods (7), these are however not generally applicable to t y p i c a l (complex) organic molecules. 2.4 Spin-echo absorption spectroscopy Recently Bax et a_l. (11) have shown using the Carr-Purcell-Meiboom-Gill sequence that proton spin-spin relaxation rates can be obtained by Fourier transformation of the whole-echo, rather than the half-echo s i g n a l generally 3 used in SEFT applications . The authors showed that a symmetric whole-echo ^Note that the i n d i v i d u a l components of a mu l t i p l e t may have d i f f e r e n t spin-spin relaxation time. 2The acquired (half-echo) signal along the y d i r e c t i o n is given by S(t„) « cos(uH-cp)t [2.4] 2 y r, c-, S ( t 2 ) y <* cos(u>t)cos(4>t) - sin(ut)sin((J)t) l ^ . J J Substituting n/J = T, (n=0,1 ,2 , . . . ) i n equations [2.3] and [2.5] y i e l d s , a f t e r Fourier transformation, an absorption mode s i g n a l . In the case of a groups of protons coupled to many non-equivalent n u c l e i these equations become more complex. ^Although the o r i g i n a l SEFT spectrum (5) was obtained by acquiring a symmetric whole-echo signal and f o l d i n g i t about the centre of the echo, the r e s u l t i n g spectrum ( a f t e r cosine FT), would be expected to show an amplitude modulation as a function of T. - 30 -Figure 2.3: J modulation i n (Carr-Purcell) SEFT spectroscopy. The traces corresponding to t ^ O are equivalent to an A2X3 spectrum obtained i n conventional FT spectroscopy, and show no phase or i n t e n s i t y anomalies. The i n d i v i d u a l peaks obtained by the half-echo FT show J modulation with an exponential decay due to spin-spin re l a x a t i o n , as a function of time, t\. Note that the ce n t r a l component of the t r i p l e t (M=0) shows no phase modulation. - 31 -signal when Fourier transformed and subjected to further data manipulation steps yielded for the sine and cosine transforms, pure absorption signals, whose amplitudes were respectively sine and cosine modulated as a function of T. In effect the dispersive components of a signal were eliminated from the resulting spectrum so that the magnitude spectrum in this case displays only pure absorption peaks. The major conditions for the Bax experiment are that: a) the echo-signal should be symmetric with respect to the acquisition time t 2 (ie. = 2T), b) relaxation (T^) during the acquisition period should be negligible, and, c) the signal at the beginning and the end of acquisition should be minimal (to avoid truncation effects). It w i l l be recalled that the di g i t a l resolution of the real part of the spectrum for example, is related to the acquisition time and spectral width, given by equation [1 .10] , DR = _1 = 2.(SW) AT BS In order to obtain a suitable spectral resolution i t may be necessary to acquire the NMR signal over a long period 2T, equal to the acquisition time. Although signals with long spin-spin relaxation times (1^) can be acquired over a suitably long period, without significant loss of the echo-signal during acquisition, those with short value w i l l lead to echo-signals which w i l l be asymmetric. It is apparent from the above discussion that the most suitable chemical systems for study by the above, spin-echo absorption mode spectroscopy are molecules with relatively small spectral widths and long spin-spin relaxatioi times (T^), conditions which are generally found for only rather small, simple molecules. Conversely, the above experiment appears to have serious l i m i t a t i o n s which prevents i t s use for studying larger molecules with wider s p e c t r a l widths, and r e l a t i v e l y short transverse relaxation times. Fortunately, as w i l l be demonstrated these l i m i t a t i o n s can e a s i l y be overcome ( i n many cases) by using a very general pulse sequence and data processing routine ( c f . Refs. 10 and 14); these can be e a s i l y performed with the standard software programs available with modern NMR spectrometers. The pulse sequence for the SEAS experiment is given by, (90° - T - 180° - Acquisition} +x n where +x refers to the phase a l t e r n a t i o n of the refocussing pulse by 180°. The signal is acquired on a suitable block size and z e r o - f i l l e d i f necessary to provide the d i g i t a l r e s o l u t i o n needed i n the f i n a l spectrum. In order to obtain a pure absorption mode frequency spectrum, the "echo-signal" should be completely symmetric* Also, the echo-signal at the beginning and end of the a c q u i s i t i o n should, i d e a l l y , be zero to minimize truncation e f f e c t s i n the Fourier transformed spectrum. The above condition is usually achieved i n practice by applying the 180° refocussing pulse a f t e r the o r i g i n a l l y induced FID signal has decayed to a miminum; th i s is i l l u s t r a t e d i n Figure 2.1. S p i n - l a t t i c e r elaxation during the delay T^ causes a l o n g i t u d i n a l component of magnetization to develop, which also experiences the refocussing pulse; however, deviations i n the f l i p angle from 180° w i l l create a re s i d u a l transverse magnetization, and give r i s e to a f i n i t e signal at the beginning of the data a c q u i s i t i o n . The asymmetry caused by this r e sidual signal may be eliminated by the use of suitable phase s h i f t e d pulse sequences. l i t should be noted that only the "echo-signal" needs to be symmetric for SEAS, and not the acquired whole-echo s i g n a l . - 33 -For example, a l t e r n a t i o n of the phase of the re focussing pulse by 180° f l i p s the l o n g i t u d i n a l magnetization i n opposite d i r e c t i o n s , which causes c a n c e l l a t i o n of the r e s i d u a l magnetization on alternate scans, while the desired transverse components contribute additive to the spin-echo s i g n a l . In the present work, p a r t i c u l a r l y when dealing with systems having a wide dynamic range of signals, i t was not possible to completely eliminate the residual s i g n a l by the above procedure. It is also possible to minimize the unwanted signal at the beginning of the a c q u i s i t i o n by suitable d i g i t a l f i l t r a t i o n , or by " l e f t - s h i f t i n g " the acquired s i g n a l by a few data points. It was assumed i n the o r i g i n a l paper by Bax et a_l. (11) that the echo-si g n a l decays mainly due to instrumental e f f e c t s (T 2*) and that spin-spin relaxation during a c q u i s i t i o n can be neglected. Such assumptions are probably not v a l i d for the type of molecules chosen i n this study; the e f f e c t of this on the acquired signal would be to make i t asymmetric as a r e s u l t of exponential damping due to re l a x a t i o n . It was found that this s l i g h t asymmetry can often be ignored, or else a symmetric echo may be generated by suit a b l e d i g i t a l f i l t r a t i o n (11). The above discussions dealt with the conditions for obtaining spin-echo absorption mode spectra, and how a whole-echo signal can be generated for a t y p i c a l organic system. Fourier transformation of this s i g n a l , followed by magnitude c a l c u l a t i o n y i e l d s an absorption mode spectrum s i m i l a r to that obtained i n conventional high r e s o l u t i o n spectra, and unlike half-SEFT spectra, these are independent of phase. The importance of SEFT spectroscopy is due to the p o s s i b i l i t y of s e l e c t i v e l y observing the r e l a t i v e l y slowly relaxing signals of a complex spin system. The p r i n c i p l e involved can be e a s i l y explained with the aid of Figure - 34 -2.4; t h i s represents the range of exponentially decaying signals i n the trans-verse plane of, for example, a less "mobile" macromolecule (R 2 = 100-10s) and a smaller r a p i d l y "tumbling" small molecule (R 2 = 2 - l s ) . A SEAS spectrum from such a mixture obtained with an i n i t i a l delay (T) of about 0.2s, w i l l show "some" signals from both the slowly relaxing macromolecule and the rapi d l y relaxing small molecule; however, an i n i t i a l delay of about 0.4s w i l l contain, almost e x c l u s i v e l y , the signals from the small molecule. A feature of p r a c t i c a l importance i s that i n spite of the o r i g i n a l dynamic range between the two systems, s e l e c t i v e detection of one group of signals can be achieved. This feature could have a great p o t e n t i a l i n extending the scope of NMR spectroscopy to study b i o l o g i c a l systems (15,16) and the applications of SEAS for the study of such systems is discussed i n the following sections i n three contexts: the f i r s t , using a monomer and a polymer, the second using an enzyme, to d i s t i n g u i s h the sharp components i n the spectrum and f i n a l l y to study low molecular weight metabolites i n red blood c e l l s . 2.5 Ap p l i c a t i o n of SEAS i n chemistry It i s well known that studies of biochemical samples of high molecular weight by conventional proton NMR spectral analysis are frequently impossible due to extreme broadening of l i n e s ( ca. 10 Hz) r e s u l t i n g from the short spin-spin relaxation times ( ca. 30 ms) of the signals ( F i g . 2.5). Many macromolecules ( C £ . 5,000 MW) may be considered to give r i s e to two types of signa l s ; one set of signals a r i s i n g from n u c l e i attached to the r e l a t i v e l y r i g i d backbone which contribute broad l i n e s , and the second from those attached to r e l a t i v e l y mobile parts of the molecule, which give r i s e to the sharper l i n e s i n the spectrum. Frequently the NMR spectra of biomolecules are Figure 2.4: Comparison of the magnetization i n t e n s i t i e s of a " l a r g e " and small molecule i n a SEFT experiment. The signals from the large molecule are assumed to be ten times more intense than the small molecule, with spin-spin relaxation rates ranging from R2=100 to 10 s. For short delay times (ti~0.25 s) most of the magnetization detected is from the large molecule. However at longer delays t\ ( ca. 0.5 s ) , the small molecules i n the mixture contribute s i g n i f i c a n t l y to the r e s u l t i n g spectra due to their r e l a t i v e l y slower relaxation rates (R2=2 to 1 s ) . Figure 2.5: 270 MHz IR NMR spectrum of bovine serum albumin (BSA) i n D 20. Most of the sharper components are completely hidden within the broad signals which are from protons which have'veryTast spin-spin relaxation rates. The r e s i d u a l HOD peak at 64.8 was ( p a r t i a l l y ) presaturated; the signals at 61.1 are due to impurities. - 37 -broadened to such an extent that the sharp components are hardly v i s i b l e . Since the analysis of these sharp signals could provide i n t e r e s t i n g s t r u c t u r a l and motional information many methods have been suggested to detect these l i n e s (15,16). Generally these methods are based on the d i f f e r e n t i a l r elaxation times between the broad and narrow components and include a) delayed Fourier transform (DEFT; (17)), b) convolution difference (18), c) SEFT (12) and d) s e l e c t i v e " s p i n - d i f f u s i o n " or saturation transfer (19). Convolution d i f f e r e n c e , and the related d i g i t a l f i l t e r i n g techniques (20) are based on data manipulation of a conventional FID to eliminate the broad components. The method involving s p i n - d i f f u s i o n i s performed by i r r a d i a t i n g a sample at an appropriate frequency for a given period (pre-saturation) p r i o r to s i g n a l a c q u i s i t i o n by the usual method. The broad l i n e s can be s e l e c t i v e l y suppressed (saturated) by this method leaving the narrow lin e s i n the r e s u l t i n g spectrum. I t should be r e a l i z e d that the f i n a l r e s u l t depends on the experimental conditions such as power, frequency and duration of the i r r a d i a t i n g f i e l d . SEFT experiments are convenient and above a l l provide a method to study spectra as a function of a single variable t ^ . This makes i t more convenient to compare or standardize experimental data, for example, from the l i t e r a t u r e , and also to measure spin-spin relaxation rates either for the purpose of quantitative studies or for spectral a n a l y s i s . The major l i m i t a t i o n of the SEFT and DEFT techniques, however, are the phase and i n t e n s i t y anomalies due to J-modulation as discussed e a r l i e r . The SEAS experiment o f f e r s a convenient solution to this problem by eliminating the dispersive components from a Fourier transformed spectrum. A p r a c t i c a l a p p l i c a t i o n of SEAS technique is demonstrated here using a D o0 mixture containing res p e c t i v e l y ca. 20, 10 and 5% by weight of - 38 -a ,B-D-xylose (1, MW 150), a-cyclodextrin (2, MW 972) and dextran T-10 (MW ca. 10,000, a l-*6 linked polymer of D-glucopyranose, 3). The 400 MHz 1H spectrum of the mixture i s shown i n Figure 2.6A (note the magnitudes of the signals i n the mixture i n r e l a t i o n to the xylose peaks); for reference purposes the spectrum of pure xylose i s shown i n Figure 2.6B. Fourier transformation of the whole-echo, followed by magnitude c a l c u l a t i o n y i e l d s , for d i f f e r e n t T values, the SEAS traces E, D and C i n Figure 2.6D. It can be seen from these spectra that the signals from the polysaccharide and c y c l i c hexasaccharide may be s e l e c t i v e l y eliminated from the SEAS traces due to the r e l a t i v e l y faster relaxation rates (R^) of t h e i r constituent protons as compared to those of the monosaccharide; see, for example, the re s o l u t i o n i n Figure 2.D of the H-2 and H-5g protons from within the broad peaks shown i n Figure 2.6A. This i l l u s t r a t e s the use of th i s technique for the se l e c t i v e detection of signals from the r e l a t i v e l y more mobile units or molecules when they are normally hidden beneath broader l i n e s ; i t s effectiveness i s e s s e n t i a l l y independent of the dynamic range between the signals ( c f . F i g . 2.4). It can be noticed that the signals i n Figure 2.6E are broader as compared to the other two SEAS traces; this broadening arises mainly from the dispersive contribution i n the magnitude spectra due to the asymmetry of the echo-signal. Such lineshape d i s t o r t i o n s a r i s e whenever a s i g n i f i c a n t signal i n t e n s i t y is present at the beginning of the a c q u i s i t i o n , whether i t be due to pulse ( f l i p angle) imperfections which generates a residual transverse magnetization, or to the a p p l i c a t i o n of the refocussing pulse before the i n i t i a l s i g n a l has decayed ( T 2 * relaxation) to a minimum. The former signal contribution can be minimized i n prac t i c e by suitable phase s h i f t e d pulse sequences, as discussed i n the previous section. 39 -=0.1 S =0.43 s r=0.55s H2^ MIL 2.5 8 (ppm) Figure 2.6: (A) the 400 MHz proton spectrum of a mixture of ot,8-D-xylose ( l ) , a-cyclodextrin (2) and dextran T-10 (3) i n D2O (ca. 20, 10 and 5% by weight^ respectively; NA=24, AT=5.45s; BS=16K) (B) The equivalent spectrum of 1 i n D2O (C, D, E). Spectra (NA=64) obtained by Fourier transform of the whole-echo acquired on a 16K block size in the absolute value mode with the T values indicated. Note that i n (C), a l l signals from the HOD and dextran T-10 have been suppressed, leaving some components from the a-cyclodextrin. Subscripts CD and D r e f e r to the cyclodextrin and dextran u n i t s , r e s p e c t i v e l y . - 40 -It was demonstrated by Bax et al. (13) that the whole-SEFT method can be used to measure transverse relaxation times of small molecules (1,1,2-trichloroethane). The SEAS method described here can also be used to measure spin-spin r e l a x a t i o n times of protons i n larger molecules by studying the s i g n a l i n t e n s i t y as a function of t^; this provides another NMR parameter for semi-quantitative spectral a n a l y s i s . This a p p l i c a t i o n i s i l l u s t r a t e d using a model system containing a mixture of 0.01M Dextran T-10 and 0.1M B-methylxylopyranoside (4) i n D 20. The decay of the magnitude of the m u l t i p l e t s i n the SEAS traces shown i n Figure 2.7C, D and E represents the decay of each s i g n a l of the xyloside i n the transverse plane due to spin-spin 1 r e l a x a t i o n . Although the concept of " s e l e c t i v e detection" based on transverse relaxation rates has been extended to the study of biochemical systems using the half-SEFT experiment, this has several i n t r i n s i c l i m i t a t i o n s . Figures 2.8B, C and D show the spectra obtained by Fourier transformation of the half-echo time domain signals from a mixture containing xylose, a-cyclodextrin and dextran T-10 (c_f. F i g . 2.6). In common with the r e s u l t s given by other complex systems these spectra show the expected phase and i n t e n s i t y v a r i a t i o n s , l l n order that each SEAS trace i n Figure 2.7 be d i r e c t l y comparable i t i s e s s e n t i a l that the corresponding time domain signal be " s i m i l a r " for the various delay times and be subjected to s i m i l a r d i g i t a l f i l t e r functions. This may be achieved by modifying the basic SEAS pulse sequence to {90° - T V D " 180° - T F D - 180° - Acquisition} where Tyo a n <* Tpp are r e s p e c t i v e l y variable and fixed delays (Tpj) would be the "minimum" delay before the refocussing pulse i s applied p r i o r to a c q u i s i t i o n ) . This sequence ensures that the shape of the echo-signals are s i m i l a r since the echo-maxima occur at Tpp- Corrections for pulse imperfections and d i f f u s i o n e f f e c t s can also be accommodated into the above pulse sequence by including, for example, the Carr-Purcell-Meiboom-Gill sequence, although these v a r i a t i o n s were not c a r r i e d out in the present work. - 41 -JA. rmsec j ^ J ^ x d k — 816.0 554.0 L 256.0 Figure 2.7: Conventional spectrum of a mixture of 0.01M dextran and 0.1M 8-methylxylopyranoside (4) in D 2 O (lyophilized three times in D 2 O ) . (B) Spectrum of the pure xyloside (C, D, E) SEAS traces at different delay times plotted in the absolute value mode (NA=48). (C) shows mostly the signals from the xyloside, but some residual signals from the dextran s t i l l remain; (D) and (E) show the gradual disappearance of those signals depending on their spin-spin relaxation rates. - 42 -and the r e s u l t i n g d i s t o r t i o n s . It should be cautioned that i n t e r p r e t a t i o n of the m u l t i p l e t patterns of spectra which contain such J modulations (as sug-gested i n Ref. 11) can be misleading; for example, the rather small differences between the spin-spin coupling constants ( J ^ ^e = 11.7; J,- a ^ = 10.6; J. - = 9.4; J . _ = 9.4 Hz) of the " t r i p l e t s " H-3B, H-5a, and H-2B 4,3 3,2 a are nevertheless s u f f i c i e n t for them to give completely d i f f e r i n g responses as a function of the T values. The s e l e c t i v e detection of the narrower components i n the NMR spectrum of a biomolecule is demonstrated using lysozyme (MW = ca. 14,500, 15% w/v i n B^O, pD 4.0). The l i n e widths (and also chemical s h i f t s ) of the signals corresponding to t h e i r i n d i v i d u a l amino acid constituents of enzymes (proteins) are l a r g e l y dependent on the r e l a t i v e p o s i t i o n of a unit in the macromolecule. Thus protons of the units on the more mobile side chains of the protein tend to show somewhat narrower l i n e widths when compared to those which are part of the r i g i d "backbone", or those which are s u f f i c i e n t l y embedded i n the core of the molecule as to be subjected to rapid relaxation by t h e i r neighbouring protons (dipolar i n t e r a c t i o n s , (21)). Since the a c q u i s i t i o n of the whole-echo i n SEAS i s limited by the choice of an i n i t i a l , minimum delay, for the reasons discussed e a r l i e r , t h i s experiment i s generally best suited for studying the r e l a t i v e l y slowly relaxing s i g n a l s . A comparison of SEAS and the half-SEFT method is given i n Figure 2.9; the conventional FTNMR spectrum shows the presence of broad and narrow components i n the biomolecule. Even short delay time (T=10 ms) such as that used to measure Figure 2.8B (by the half-SEFT), allows most of the r a p i d l y relaxing components to relax i n the transverse plane thereby decreasing the i n t e n s i t y due to the broader components i n the r e s u l t i n g - 43 -_ i I I 1 1—=-4.5 4.0 3.5 3.0 2.5 8 (ppm) Figure 2.8: (A) As for F i g . 2.6A. Traces (B), (C) and (D) were obtained by Fourier transformation of the half-echo from a C-P pulse sequence with the values indicated. Figure 2.9: (A) The normal 400 MHz proton spectrum (NA=64) of a 15% D2O solution of lysozyme (from Worthington Biochemicals Co.; l y o p h i l i z e d three times i n D2O) at pD 4.0. (B, C) Spectra obtained by Fourier transformation of the half-echoes and (D-F) those obtained by the whole-echo Fourier transform of signals from the C-P pulse sequence, with phase a l t e r n a t i o n of the 180° pulse (NA=200; temperature=50°C; SW=400 Hz; BS=16K). - 45 -spectrum. As a r e s u l t many of the (well dispersed) peaks that appear as broad s i n g l e t s i n a conventional spectrum, show d e f i n i t e spin-spin coupling patterns ( c f . F i g . 2.8A and 2.8B). Inevitably though, increasing the delay T, i n addition to eliminating the broad components also introduces phase anomalies due to J-modulation, which can be seen i n Figure 2.9C. These anomalies are suppressed i n the absorption-mode spin-echo spectra which are shown i n Figure 2.9D, E and F. A further advantage of SEAS i s that, because the whole-echo i s subjected to Fourier transformation the resultant spectrum i s expected to show an improvement i n s e n s i t i v i t y by a factor of about 1.4 over the half-echo method. 2.6 Applications of SEAS i n biology The previous studies i l l u s t r a t e some of the problems facing the a p p l i c a t i o n of conventional NMR to biochemical samples and some possible applications of SEAS. In order to probe the possible extension of this work to " l i v i n g " systems, some SEAS experiments involving red blood c e l l s (RBC) were undertaken. Although the proton NMR spectrum of the RBC sample were not expected to provide useful information ( F i g . 4.10A), i t was anticipated that i t should be possible to monitor the spectra of small molecules associated with them. In t h i s work, SEAS was used to study the behaviour of glucose (5) in RBC; the i n i t i a l aim of this work was to compare SEAS with the half-SEFT (12) technique. However, due to some differences between t h i s study and previous data i n the l i t e r a t u r e , i t was necessary to perform a d d i t i o n a l control experiments. The r e s u l t s summarised here allow us to make some conclusive statements on the system studied and also raises some questions on the assumptions and conclusions reached by the previous workers (22,23). - 46 -RBC are one of the simplest c e l l s , with the cytoplasm comprising of mainly haemoglobin (an iron containing protein) and the remaining protein being mainly enzyme systems for the various metabolic pathways that take place within the c e l l . * The c e l l i t s e l f i s highly active, and i s involved with various dynamic processes such as the v i t a l metabolic pathways, and controlled d i f f u s i o n of molecules or ions across the c e l l membrane. The studies of biochemical pathways have always been of i n t e r e s t to biochemists from a c l i n i c a l point of view since they provide information on p h y s i o l o g i c a l processes at the molecular l e v e l . For example, studies have been made to e s t a b l i s h c o r r e l a t i o n s between the r e l a t i v e concentration of molecules (or metabolites) i n c e l l s and d i f f e r e n t ailments using fresh RBC samples from patients (26). That spin-echo NMR techniques o f f e r a convenient, non-destructive method for studying such systems has already been claimed i n the l i t e r a t u r e (12,13) and this point is further demonstrated here using SEAS for 2 RBC-glucose systems. One of the v i t a l metabolic pathways in l i v i n g animal c e l l s i s the Embden-Meyerhoff or g l y c o l y t i c pathway (25). One of the functions of t h i s process i s the u t i l i z a t i o n of glucose ( v i a the pentose phosphate pathway) to 3 provide the energy needed i n chemical form as adenosinetriphosphate (ATP); one of the end products i s l a c t i c acid (CH^.CH(OH).CO2H). 1-For detailed structure and function of RBC the reader is referred to references 24 and 25. 2Sample preparations were ca r r i e d out by Rob Snoek i n the Pathology Department at UBC. 3The energy i s released i n c e l l s with the linkage of one of the phosphate bonds to form adenosinediphosphate and inorganic phosphate. - 47 -Small molecules within the c e l l such as glucose, l a c t i c acid, pyruvic a c i d , glycine and oxidized glutathione can d i f f u s e across the c e l l membrane, and are c o n t r o l l e d by processers c a l l e d " f a c i l l i t a t e d d i f f u s i o n pumps". The RBC were prepared* from freshly drawn venous blood and washed i n phosphate buffered s a l i n e s o l u t i o n . They were then washed i n Krebs-Ringer sol u t i o n (pH 7.2) with (Procedure B) or without (Procedure A) 10 mM glucose. The sample that was exposed to glucose was incubated i n glucose for two hours at room temperature. The samples were centrifuged and either the supernatant or the " p e l l e t " was used i n the NMR studies. The haematocrit of the p e l l e t samples were usually 85-95%. The NMR spectrum of a sample of RBC ( p e l l e t ) shows, as expected, a broad envelope a r i s i n g from the various high molecular weight substances ( F i g . 2.10A). Perhaps the only signals that could be assigned are i n the aromatic region, and arise from the h i s t i d i n e residues of the haemoglobin. SEAS can be used to reveal the signals that are normally hidden under this broad back-ground as shown by the corresponding traces i n Figures 2.10 and 2.11. Figure 2.11A shows a SEAS spectrum of a RBC ( p e l l e t ) sample, which was obtained a f t e r washing with an isotonic saline (Krebs-Ringer) solution containing 10 mM glucose (Procedure B). As expected, the trace i n Figure 2.11A shows i n addition to the normal peaks ( F i g . 2.10B) the peaks corresponding to glucose ( F i g . 2.11D) and the lactate peak at 1.286. Because most of the r i n g protons of glucose appear as overlapping m u l t i p l e t s i n the region 3 to 46, i t is more convenient to use the signals of the anomeric protons to monitor the concentration of glucose in the sample. Figure 2.11B shows a SEAS spectrum obtained from a RBC sample which was washed with Krebs-Ringer solution (without glucose) and then made up to about See Experimental Section (Ch. VII). - 48 -D Figure 2.10: (A) The normal 270 MHz spectrum of RBC p e l l e t (NA=32) with the solvent nulled by an inversion recovery sequence (THR). (B) The spectrum from SEAS, T=60 ms of a glucose depleted sample measured about 30 hours a f t e r preparation. Note the signals corresponding to the haemoglobin residues due to p a r t i a l l y s i s . (C) The SEAS spectrum (T«=60 ms) of an RBC p e l l e t , which was incubated i n glucose and p a r t i a l l y lysed. (D) The SEAS spectrum of the supernatant of a lysed RBC sample (T«=80 ms). The solvent peak in B, C and D were presaturated. The time domain signal was m u l t i p l i e d by a li n e a r function to eliminate the residual transverse magnetization and then by an exponential function. * i n d i c a t e spikes caused by the decoupler.(see experimental section) - 49 -A .tt—±S*Kj*%>< • ***** HJat B c 7C D j IL -1 0 S(ppm)8 4 Figure 2.11: Spectra from SEAS with T=70 ms. (A) RBC (haematocrit 90%) incubated for 2 hours i n 10 mM glucose, (B) RBC depleted i n glucose but with equal volume of 10 mM glucose added (haematocrit 50-60%). (C) Same as for (B) but the experiment was carried out about 10 hours l a t e r . (D) Supernatant of the RBC and glucose mixture (NA=200) showing mostly the glucose spectrum and some lactate s i g n a l s . Experimental times were approximately 1*5 to 2 hours using 1400 acqui s i t i o n s for A, B and C. a and 8 re f e r to the anomeric protons and L to the methyl s i g n a l from l a c t i c acid (see experimental section) - 50 -60% haematocrit solution by adding 10 mM glucose i n V^O containing the Krebs-Ringer buffer solution. The appearance of the l a c t a t e peak indicates that within the time course of the experiment ( = 2 h), glucose has diffused into the c e l l and has been metabolized. With time, t h i s l a c t a t e peak increases i n si z e due to the glucose metabolism by the g l y c o l y t i c pathway, and th i s e f f e c t is accompanied by a decrease i n the i n t e n s i t y of the glucose peaks i n the SEAS trace ( F i g . 2.11C). The i n i t i a l increase in the lactate resonance i s subsequently followed by a decrease i n i n t e n s i t y which i s due to the exchange of the protons i n the methyl group with the solvent deuterons (figure i s not shown). These observations are as expected and have been reported by e a r l i e r workers using the half-SEFT technique (13). However, a s t r i k i n g feature of the traces shown i n F i g . 2.11A, B and C i s the absence of the signals corresponding to haemoglobin, which were a dominant c h a r a c t e r i s t i c i n a l l the half-SEFT spectra reported i n the l i t e r a t u r e . With time, however, we did see signals corresponding to haemoglobin; the example shown i n Figure 2.10B is from a RBC sample (prepared v i a Procedure A) a f t e r about t h i r t y hours. It was also noted that the i n t e n s i t y of the haemoglobin signals in the samples containing glucose (Procedure B) was smaller than i n those that were depleted i n glucose, i n d i c a t i n g the r e l a t i v e s t a b i l i s a t i o n of RBC i n an aqueous glucose medium. Figure 2.10C shows a SEAS trace that was obtained from a solution prepared by l y s i n g the RBC p e l l e t ( v i a Procedure B) by the addition of a few drops of D 2 O . * Now the c h a r a c t e r i s t i c peaks, mostly due to the h i s t i d i n e residues iRBC are sen s i t i v e to s l i g h t changes i n the osmotic pressure ("tonicity") of the medium. A few drops of D2O decreases the t o n i c i t y , causing l y s i s (release of haemoglobin, e t c . ) . This i s seen as a bright red c o l o r a t i o n of the supernatant. For obvious reasons this is not noticeable i n the p e l l e t . - 51 -of haemoglobin, are c l e a r l y seen. In order to resolve the peaks i n the SEAS traces more c l e a r l y , the supernatant from a lysed RBC sample (depleted i n glucose) was subjected to SEAS with a delay, T = 80 ms, and with sample spinning ( c f . F i g s . 2.10C and D); note the r e s o l u t i o n of peaks "a" and "b" which are c l e a r l y v i s i b l e as a t r i p l e t and quartet r e s p e c t i v e l y . As expected SEAS can be used to obtain high res o l u t i o n spectra of small molecules from within the broad peaks of the RBC, without the complications of phase- and intensity-anomalies which are i m p l i c i t i n the half-SEFT experiment. Based on our a l b e i t limited experience so f a r , i t would seem that SEAS leads to the following information about RBC: a) The decrease i n i n t e n s i t y of the signal of the anomeric proton of the glucose i s an i n d i c a t i o n of the consumption of glucose by the g l y c o l y t i c pathway i n the RBC. b) The appearance of the lactate peak, both in the sample containing the p e l l e t ( F i g . 2.11B) and i n the supernatant l i q u i d ( F i g . 2.11D) are i n d i c a t i v e of the d i f f u s i o n of glucose into, and of lactate out of the c e l l s . Studies of the supernatant l i q u i d , rather than of the c e l l suspension ( p e l l e t ) i t s e l f , o f f e r number of advantages. In terms of the NMR experiment, the supernatant l i q u i d i s a homogeneous solution and provides spectra which can be studied by most of the conventional NMR techniques to provide high r e s o l u t i o n NMR spectra (eg. F i g s . 2.10Cand 2.11D).* In terms of the biochemistry of the system, t h i s provides a suitable method for following the k i n e t i c s of the system. However, since the RBC are undergoing dynamic changes T-The relaxation times of solutes i n the supernatant are much longer than those i n the p e l l e t ; t h i s favours the conditions for an " i d e a l " SEAS experiment (see Sec. 2.4) and also improves the s e n s i t i v i t y of the technique ( i t s h a l l be r e c a l l e d that the i n t e n s i t y of signals i n a spin-echo experiment is related to t h e i r spin-spin relaxation times as explained i n Section 2.2). both "chemically" and " p h y s i c a l l y " (eg. d i f f u s i o n of molecules across the membrane) such studies w i l l be limited i f the t o t a l data a c q u i s i t i o n time for an experiment is too long. The absence of haemoglobin peaks i n those RBC samples (eg. F i g . 2.11A) which had been fr e s h l y prepared, and the appearance of these signals i n p a r t i a l l y lysed samples, suggests strongly that i t is not possible to detect resonances from haemoglobin within the RBC. This observation and conclusion contradicts that suggested by e a r l i e r workers who have assumed that the signals detected i n (half-)SEFT experiments are from molecules within the RBC. It also seems apparent from a l l the half-SEFT spectra previously published that p a r t i a l l y s i s of c e l l s had occurred during the course of the experiment. Unfortunately, i t i s not possible to conclude from the SEAS experiments performed so far whether the signals corresponding to the smaller molecules (eg. glucose and lactate) represent molecules which are i n t e r n a l and/or external. Such small molecules can d i f f u s e across the membranes and hence may e i t h e r be present i n the i n t e r n a l cytoplasm or in the aqueous e x t r a c e l l u l a r space. Brindle et aj_. (22) have assumed that the i n t e r n a l medium i s magnetically homogeneous whereas the e x t r a c e l l u l a r space is magnetically inhomogeneous, and on that basis have concluded that the signals from molecules outside the c e l l s relax more r a p i d l y than those within the c e l l . * This conclusion was based on t h e i r observation of a constant rate of increase of e x t e r n a l l y added (0.01 ml of 0.3M) alanine peak i n t h e i r SEFT experiment, both with and without the addition of a paramagnetic reagent 2 (0.001 ml 0.025 M Dy-DTPA ). It was assumed that Dy-DPTA, which i s a large signalswere considered to decay as a function of T 3 (see the footnote on p. 19), due to the larger f i e l d gradients outside the c e l l s . ^Diethylenetriamine penta-acetic a c i d . - 53 -paramagnetic complex, does not d i f f u s e across the membrane, and would a f f e c t only the external molecules by creating large f i e l d gradients i n the extra-c e l l u l a r region. The increase i n the alanine (or lactate) peaks were then regarded as due to d i f f u s i o n of these molecules into the c e l l s . However, there seems to be a number of inconsistencies i n those studies; the addition of very small volumes of ( r e l a t i v e l y concentrated) material and i t s subsequent d i f f u s i o n or mixing i n the "heterogeneous" and viscous RBC medium should have been evaluated. In addition, the e f f e c t of l y s i s should have also been taken into consideration i n t h e i r study. These factors may well be the reason for some of the rather substantial inconsistencies i n th e i r experimental r e s u l t s as quoted; for example (22), " i t was also found that v a r i a t i o n s i n transport rate for alanine up to +_ 50% were observed i n erythrocyte from d i f f e r e n t people. This was much greater than the experimental error and larger than the 1 2 differences observed between samples prepared i n ^ 0 and ^ 0 . At present the o r i g i n of these var i a t i o n s i s not c l e a r . " It has been reported by many workers that glucose binds chemically and p h y s i c a l l y with haemoglobin and other proteins (27); although the extent of binding i s not yet c l e a r , some have suggested up to 80% of glucose may be in bound form i n RBC. I f this were so, i t would not seem unreasonable to suggest that most of the glucose may be i n bound form inside the c e l l and hence be undetectable by SEFT techniques. C e r t a i n l y the mobility of the bound glucose units would be reduced s i g n i f i c a n t l y over that of the free molecules and as a r e s u l t the spin-spin relaxation rates of the corresponding protons would be increased and hence the corresponding NMR signals would decay so r a p i d l y during the (T) delay period as to be undetected.* ^In a d i f f e r e n t series of experiments i t was observed that the signal corresponding to a carbohydrate unit which was linked to bovine serum albumin was v i r t u a l l y undetectable (at T^60 ms) and decayed almost at a s i m i l a r rate (R 2) as the BSA s i g n a l s . - 54 -In order to reach a p o s i t i v e conclusion as to whether the detected signals of small molecules i n the SEFT experiment were from inside or outside the c e l l s i t would be necessary to study molecules but with a l l d i f f u s i o n processes across the membrane frozen by the use of a s p e c i f i c "paralysing" agent. A preliminary attempt was made i n th i s study using HgCl^to i n h i b i t the "glucose d i f f u s i o n pump"; unfortunately, however, the HgCl^ changed the physical nature of the sample which was not s a t i s f a c t o r y for a comparative NMR study involving experiments. At the time of submission of this thesis we were i n v e s t i g a t i n g s u i t a b l e agents for use with RBC systems, but the substances required were not a v a i l a b l e . It i s apparent from this study, as from the other, that b i o l o g i c a l samples can, under well c o n t r o l l e d conditions, be studied by NMR techniques. However as with most other biochemical studies proper control experiments are needed to understand the e f f e c t of a foreign environment to l i v i n g systems and the associated chemical and physical changes of the sample on the NMR (SEFT) experiment. - 55 -References (Chapter II) 1. Hahn, E.L. Phys. Rev. (1950) 80, 580. 2. Hahn, E.L., Maxwel, D.E. Phys. Rev. (1952) 88, 1070. 3. Carr, H.Y., P u r c e l l , E.M. Phys. Rev. (1954) 94, 630. 4. Ernst, R.R., Anderson, W.A. Rev. S c i . Instrum. (1966) 27, 93. 5. Allerhand, A., Cochran, D.W. J . Amer. Chem. Soc. (1970) 92, 4482. 6. Meiboom, S., G i l l , D. Rev. S c i . Instrum. (1958) 29, 688. 7. Freeman, R., H i l l , H.D.W. "Dynamic Nuclear Magnetic Resonance Spectroscopy", Jackman, L.M., Cotton, F.A. Eds.; Academic Press: New York, 1975; Chapter 5. 8. Shaw, D. "Fourier Transform NMR Spectroscopy", E l s e v i e r : Amsterdam, 1976. 9. Martin, M.L., Martin, G.J., Delpuech, J . J . " P r a c t i c a l NMR Spectroscopy", Heyden: London, 1980. 10. McLaughlin, A.C., McDonald, G.G., Leigh, J.S. J . Magn. Reson. (1973) 11, 107. 11. Bax, A., Mehlkopf, A.F., Smidt, J . J . Magn. Reson. (1979) 35, 373. 12. Campbell, I.D., Dobson, CM., Williams, R.J.P., Wright, P.E. FEBS L e t t . (1975) 57, 96. 13. Brown, F.F., Campbell, I.D., Kuchel, P.W., Rabenstein, D.C. FEBS Let t . (1977) 82, 12. 14. H a l l , L.D., Sukumar, S. J . Magn. Reson. (1979) 38, 559. 15. Dwek, R.A. "Nuclear Magnetic Resonance i n Biochemistry", 2nd ed., Clarendon Press: Oxford, 1975. 16. James, T.L. "Nuclear Magnetic Resonance i n Biochemistry", Academic Press: New York, 1975. - 56 -17. S e i t e r , C.H.A., Feigenson, G.W., Chan, S.I., Hsu, M. J . Amer. Chem. Soc. (1972) 94, 2535. 18. Campbell, I.D., Dobson, CM., Williams, R.J.P., Xavier, A.V. J . Magn.  Reson. (1973) 11, 172. 19. Akasaka, K., Konrad, M., Goody, R.S. FEBS Le t t . (1978) 96, 287. 20. De Marco, A., Wuthrich, K. J . Magn. Reson. (1976) 24, 201. 21. Richarz, R., Wuthrich, K. J . Magn. Reson. (1978) 30, 147. 22. Brindle, K.M., Brown, F.F., Campbell, I.D., Grathwohl, C , Kuchel, P.W. Biochem. J . (1979) 180, 37. 23. Brown, F.F., Campbell, I.D. P h i l . Trans. R. Soc. Lond. B. (1980) 289, 395. 24. Rose, I.A., Rose, Z.B. (1969) Compr. Biochem. 17, 96. 25. Sturgenor, D.M. (ed.) "The red blood c e l l " , 2nd ed., Academic Press: New York, 1974. 26. Jones, A.J., Kuchel, P.W. C l i n i c a Chemica Acta (1980) 104, 77. 27. Nathan, S. S c i e n t i f i c American (1980) 243, 90. - 57 -CHAPTER III TWO-DIMENSIONAL FOURIER TRANSFORM SPECTROSCOPY - 58 -3.1.1 Introduction The concept of a two-dimensional Fourier transform NMR experiment was f i r s t proposed by Jeener in 1971 (1), but the importance of h i s idea was not r e a l i z e d u n t i l several years l a t e r . The f i r s t experiments related to high re s o l u t i o n NMR were published in 1975 (2,3) by Ernst's group in Switzerland, to be followed l a t e r by a detailed t h e o r e t i c a l analysis of 2D NMR spectroscopy (4) which has formed the basis for most subsequent developments in t h i s area. This concept has also been applied i n s o l i d state NMR (5,6), zeugmatography (7), and i n detection of forbidden (zero and multiple quantum) t r a n s i t i o n s (4). The work of this thesis deals mainly with proton 2D J spectroscopy, but also includes heteronuclear chemical s h i f t c o r r e l a t i o n (2D) spectroscopy and preliminary r e s u l t s from zero quantum t r a n s i t i o n (2D) spectroscopy (8,9). 2D Fourier transform NMR experiments involve the generation of a data matrix, S(t^,t2)» which represents the responses of the nuclear spins as a function of two time variables t^ and t^. Double Fourier transformation of t h i s data array with respect to these two time domains generates a two-dimensional spectrum, S ( f ^ , f 2 ) , i n which the magnetization response of the system is displayed over the orthogonal frequency axes, f^ and f2 r e s p e c t i v e l y . The f2 domain generally represents the conventional (or the observable) spectrum and the f^ domain represents some "c o r r e l a t e d " frequencies; the choice of the two frequency domains depends on the nature of 13 1 the pulse sequence used. For example, i n the C H 2D chemical s h i f t c o r r e l a t i o n experiments (10,11,12) the two dimensions represent proton and carbon resonant frequencies re s p e c t i v e l y , and i n 2D J spectroscopy (13,14) the two domains correspond to chemical s h i f t s and coupling constants respectively. Thus this technique can be used to either separate or correlate NMR frequency - 59 -components i n a v a r i e t y of rather unique ways. Such information may be obtained by multiple resonance methods (15) i n one-dimensional (ID) NMR spectroscopy, however, the v e r s a t i l i t y of the 2D technique s u b s t a n t i a l l y extends the p o t e n t i a l of NMR spectroscopy for the solution of chemical and b i o l o g i c a l problems. Most of the discussions i n the following sections pertain to proton 2D J spectroscopy, giving the advantages and l i m i t a t i o n s of the technique and including various modifications developed during the present study which make i t s uitable for general chemical a p p l i c a t i o n s . I n i t i a l l y the basic pulse sequence and the data processing procedures are explained, followed by a more p r a c t i c a l approach of the features of 2D J spectroscopy. The l a t t e r part of the chapter contains more detailed discussion of a few topics related to 2D J spectroscopy which are of p r a c t i c a l s i g n i f i c a n c e . This approach was adopted for the convenience of the reader who may not be f a m i l i a r with the concepts and nomenclature i n 2D NMR spectroscopy. It should be noted that the general discussions are s t r i c t l y applicable only to weakly coupled systems. 3.1.2 The pulse sequence and data a c q u i s i t i o n The basic pulse sequence used i n homonuclear (proton) 2D J spectroscopy is that of Carr and P u r c e l l (C-P, method A; (18)) represented by, {90° - n.T - 180° - n.T - A c q u i s i t i o n ) and i s diagramatically represented i n Figure 3.1;* the basic pulse sequence and i t s e f f e c t on the magnetization vectors was previously discussed i n Chapter II i n r e l a t i o n to the spin-echo FT experiments. In a 2D J experiment l-The "heteronuclear" analogue of this experiment, for example l^C 2D J spectroscopy i s performed by either simultaneously applying an 180° pulse to both n u c l e i ("proton-flip" (14)) or by gating the *H decoupler during one of the delay periods (13,14). 90° pulse 180° pulse spin-echo Defocussing interval n.T Refocussing interval n.T Evolution period t| Acquisition Detection period t 2 o Figure 3.1: The 2D J pulse sequence N half-echo signals are acquired for d i f f e r e n t evolution periods ( t l f which are incremented by a constant value of 2T. n=0, 1, 2 ... N-1). - 61 -a series of C-P pulse sequences are performed i n which t^ i s incremented by a constant time T so that t^ = 2nT, where n = 0, 1, 2, ... N-1. The sampling rate i n the t^ domain is equal to 1/2T corresponding to an f^ s p e c t r a l width of + SW^  = 1/4T. The number of experiments N w i l l correspond to the number of points i n f^, r e s u l t i n g i n a d i g i t a l r e s o l u t i o n of 1/2NT Hz*. The signals that are acquired, S(t^,t2)» for each t^ increment are saved for subsequent data processing routines. 3.1.3 Data processing The various data processing steps involved in 2D J spectroscopy are summarised i n Scheme 1. The acquired s i g n a l S ( t l 9 t 2 ) encodes a l l the c h a r a c t e r i s t i c s of a conventional free induction decay signal containing chemical s h i f t and coupling constant information, with each component decaying at i t s c h a r a c t e r i s t i c decay rate ( l ^ * ) . The phases of these components are, however, dependent on the e f f e c t of the 180° pulse on the magnetization vectors during the evolution period, t ^ . The " p r e - a c q u i s i t i o n " information of each component are coded into the detected s i g n a l , S(t^,t2) and are r e f l e c t e d i n the spectra S(t^,f2) shown i n Figure 3.2, which were obtained a f t e r the f i r s t Fourier transformation with respect to t2« The phase and i n t e n s i t y v a r i a t i o n s observed, as a function of time t^ are predictable as discussed i n Chapter II , and has been reviewed i n the past (19,20). The homogeneity- and chemical s h i f t - r e f o c u s s i n g e f f e c t s of the 180° refocussing pulse are not obvious from Figure 3.2, nor is the fact that the behaviour of the signals as a function of t^ i s only related to the spin-spin coupling ^In practice i t i s preferable to set the r a t i o of the d i g i t a l r e s o l u t i o n in f 2 to fj_, to an integer value to minimise d i s t o r t i o n s a r i s i n g from 2D i n t e r p o l a t i o n procedures i n subsequent data processing routines. - 62 -sR(t„y .JUL. 0 UHZ) 5 0 11, (msec) o fp(Hz) 50 Figure 3.2: Phase modulation of spin-echo spectra. The quartet and t r i p l e t resonances of d i e t h y l malonate showing the J modulation af t e r the f i r s t FT. The phase of the outer lines of the quartet is "cycled" three times (3x360°), while the phase of the inner ones changes through one cycle i n the same period. For the t r i p l e t the outer l i n e s are cycled twice; however the c e n t r a l component is unmodulated (see t e x t ) . S C H E M E 1 S(t 1 f t 2 ) - ^ S ( t | f f 2 ) S ^ ^ - S ^ f , ) * DISPLAY 45° tilt as ^magnitude or power mode - 64 -constant. However, these features can be v i s u a l i z e d by transposing the data matrix S(t^,f2) to S ( f 2 , t ^ ) , since this makes i t possible to trace the behaviour of both the r e a l and imaginary points corresponding to any chosen resonance frequency in f2» as i s shown in Figures 3.3 and 3.4.* In weakly coupled systems these t^ time domain signals contain the following c h a r a c t e r i s t i c features: a) since chemical s h i f t e f f e c t s are "refocussed" at the echo maxima ( F i g . 2.2) the "echo-interferograms" (21), S(f2»t^), do not contain chemical s h i f t frequency information, b) according to equation [2.2] the phase of each s i g n a l of an spin system i s given by = + 2:rM xJt 1 radians; [3.1] t h i s r e f l e c t s the opposite phases of the high and low frequency components of a mu l t i p l e t (cf. F i g s . 2.2 a-f, 3.3 and 3.4). Note that si n g l e t s and c e n t r a l component of a multiplet (for which M x = 0) are unmodulated. c) the time dependent ( t ^ ) phase modulation of each component which i s also referred to as J-modulation, occurs at a frequency proportional to the magnitude of the spin-spin coupling constant, d) because the s t a t i c magnetic f i e l d inhomogeneity e f f e c t s are refocussed at the echo maxima, i t follows that each "echo-interferogram" w i l l show an exponential damping with a rate constant equal to the "natural" spin-spin re l a x a t i o n rate (lU,) ( d i f f u s i o n e f f e c t s and experimental imperfections being neglected). ^The time domain s i g n a l , S ( f 2 , t i ) i s analogous to the complex time signal observed by quadrature phase detection i n conventional NMR. The major difference being that the l a t t e r is obtained as a r e s u l t of resonance (or coherence) phenomenon whereas the former i s due to e i t h e r phase or amplitude modulation (eg. "gated decoupler" method) of s i g n a l s . SR(f2,t,) s, (f2It,) f2(Hz) A FT t,(sec) -14 0 f,(Hz) —I 14 Figure 3.3: A and B represent selected r e a l and imaginary time domain signals in t j of the t r i p l e t components of d i e t h y l malonate obtained by transposing the S(tj_,f2) data matrix. A second Fourier transformation y i e l d s the corresponding traces S ( f 2 , f i ) , of the 2D J spectrum (C). The outer lines of the t r i p l e t correspond to p o s i t i v e and negative frequencies, as a r e s u l t of the sense of phase modulation, which can be seen in the upper and lower traces of B ( c f . F i g s . 3.2 and 2.2). The r i p p l e s on the unmodulated time domain s i g n a l are due to noise and a r t i f a c t s which are v i s i b l e in the Fourier transformed spectrum. The adjacent traces from a 2D plot are shown in the inset to i l l u s t r a t e the "phase-twist" e f f e c t of 2D peaks. Figure 3.4: As for Figure 3.3, but showing the components of the quartet of d i e t h y l malonate. - 67 -The implications of these features becomes more obvious i n the frequency space display, S ( f 2 , f ^ ) , which i s obtained by a second Fourier transformation of S(f2»t^) with respect to t^; Figure 3.3C and 3.4C show the relevant traces of the t r i p l e t and quartet r e s p e c t i v e l y . These traces correspond to the peaks seen i n the p a r t i a l J spectra (22) which are obtained from the f i n a l 2D J spectrum; a l l multiplets i n the f^ domain are symmetric with respect to zero frequency, and the linewidth of each peak i s determined by i t s c h a r a c t e r i s t i c spin-spin relaxation rate, I^. Although the traces i n Figures 3.3C and 3.4C correspond to resonance frequency i n f2» r e f l e c t i n g a pure absorption s i g n a l ( a f t e r applying the same phase c o r r e c t i o n ) , the complete 2D J spectrum w i l l show a complex two-dimensional lineshape which consists of a mixture of two absorption and dispersion s i g n a l s ; t h i s is referred to as the "phase-twist" and i s i l l u s t r a t e d by the inset i n Figure 3.3 (4,21). These complications are often conveniently avoided by presenting the absolute-value mode displ a y . There are many ways of displaying a 2D J spectrum i n order to extract the necessary information from i t . One method i s to plot a l l the traces i n the form of a "stacked plot"; although a e s t h e t i c a l l y pleasing, this display suffers from the p r i n c i p l e disadvantages that i t i s rather time consuming and i t is inconvenient to obtain from i t by d i r e c t measurements the NMR parameters of i n t e r e s t . A more rapid d i s p l a y routine for complex 2D spectra may be the isometric (contour) p l o t ; this provides a convenient means of representing frequencies and i n t e n s i t i e s as i l l u s t r a t e d by the plo t of the 2D spectrum of a quartet i n Figure 3.5. Perhaps the most useful and convenient displays for measuring frequencies and i n t e n s i t i e s are obtained by taking projections of selected regions of a 2D Figure 3.5: Contour diagram of the quartet resonance of d i e t h y l malonate from a 2D J spectrum plotted i n the absolute value mode. The two axes have i d e n t i c a l scales hence the multiplet l i e s along the diagonal or at 45°. As expected the " t a i l s " along f£ appear broader than those along (]•. spectrum onto various axes (23). The "summed" or " i n t e g r a l " p r o j e c t i o n i s obtained by summing each point of a 2D spectrum taken along a s p e c i f i e d d i r e c t i o n onto an axis perpendicular to i t . A "maximal" proj e c t i o n (24) corresponds to a trace representing the highest point along a p a r t i c u l a r d i r e c t i o n . A diagrammatic representation of the various display modes are shown i n Figure 3.6; the "model" 2D J spectrum i n Figure 3.6A i s shown as a contour (isometric) p l o t . It i s worthwhile noting at this juncture that each component of a weakly coupled m u l t i p l e t i n a 2D J spectrum l i e s on an axis such that, 6f2/6f^ = 1; i f both f^ and £^ a r e plotted on the same scale, as in Figure 3.5, this axis would be set along the diagonal or at 45° to the reference axis. Projection ( i n t e g r a l ) of the 2D spectrum onto the £^ axis gives the equivalent of the conventional, one-dimensional spectrum ( F i g . 3.6a) and shows a well resolved quartet and, although i t is not unambiguous, two overlapping t r i p l e t s . A p r o j e c t i o n of the 2D J spectrum onto an axis such that Sf^/Sf^ = -1, gives three " s i n g l e t s " each corresponding in i.^ v a l u e to the chemical s h i f t frequency of the resonance; t h i s a r i s e s , as explained e a r l i e r , because each multiplet in a 2D J spectrum l i e s at "45°" (25). This trace i s often referred to as 45° or "skew" projection, and corresponds to a "broad-band proton-decoupled" proton spectrum. Projection onto the f^ axis of the section ( s l i c e ) corresponding to each mu l t i p l e t from the 2D J spectrum y i e l d s a " p a r t i a l J spectrum". This i s i l l u s t r a t e d by Figure 3.6C for the quartet and Figure 3.6C for the t r i p l e t s ; the l a t t e r i n e v i t a b l y r e s u l t in the overlap of both the t r i p l e t s , centred about zero-frequency i n f ^ . Although i n a limited number of cases this projection may help to resolve overlapping - 70 -2 0 Hz f 2 (S,J) f?'(o) Figure 3.6: Diagrammatic representation of the various display modes used in proton 2D J spectroscopy including the t i l t routine. The (u n t i l t e d ) 2D J spectrum (A) when projected onto the f 2 axis y i e l d s the conventional spectrum, (a). A 45° projection gives a "proton-decoupled" proton spectrum, (b). Projection of a s l i c e of the 2D J spectrum (B) gives the p a r t i a l J spectrum (c) of the quartet. Similar projection of C, y i e l d s a trace with the t r i p l e t s superimposed (d). T i l t i n g the 2D J spectrum by ( 45°) y i e l d s a S(6,J) matrix (D); cross-sections at the respective chemical s h i f t s give the p a r t i a l J spectra of the t r i p l e t s . - 71 -m u l t i p l e t s (26), t h i s is generally not the case in p r a c t i c e , p a r t i c u l a r l y when dealing with complex molecules. Fortunately a more elegant method has been described by Nagayama et a l . (23) - the whole 2D data-array i s " t i l t e d " by an angle 6 (equivalent to 45°) about f^ = 0 using an i n t e r p o l a t i o n procedure, to y i e l d a " t i l t e d 2D J spectrum", S ^ ' ^ f ^ ) or S(J,6). As represented by Figures 3.6C-3.6D, th i s procedure allows complete separation of chemical s h i f t and coupling constants onto perpendicular axes; i t i s now possible to "pick out" from the 2D spectrum the p a r t i c u l a r trace corresponding to each m u l t i p l e t as shown i n Figure 3.6e and 3.6f. In e f f e c t t h i s amounts to taking "cross-sections" of a 2D J spectrum, S ( f ^ , f 2 ) along the dotted lines as indicated i n Figure 3.6A. This data manipulation procedure converts the 2D J experiment into an extremely powerful technique for resolving overlapping m u l t i p l e t s . At the time this thesis work was started there were two excellent papers i n the l i t e r a t u r e , one based on a t h e o r e t i c a l (4) d e s c r i p t i o n and the other giving a more p r a c t i c a l (21) approach to 2D NMR spectroscopy. Also, two preliminary communications, one using a mixture of amino acids (27) and a second, a biomolecule (28) had been published to i l l u s t r a t e the p o t e n t i a l importance of proton 2D J spectroscopy i n biochemistry. However there was l i t t l e i nsight or p r a c t i c a l d e t a i l s which would enable a p r a c t i c i n g chemist to know i n advance, or with c e r t a i n t y , the types of p r a c t i c a l d i f f i c u l t i e s which might accompany any attempt to apply proton 2D J spectroscopy to t y p i c a l organic molecules; development of that insight was chosen as the p r i n c i p a l objective of the studies described here. As w i l l be seen i n the following discussion, t h i s led to recognition of several l i m i t a t i o n s of the method and solutions to them. Ov e r a l l , the general strategy and objective of the study was development of convenient, e f f i c i e n t and v e r s a t i l e procedures for analysis of NMR spectra of complex molecules. 3.2 Applications of proton 2D J spectroscopy i n chemistry 3.2.1 General analysis Some of the general features of proton 2D J spectroscopy w i l l now be i l l u s t r a t e d using as a "model" trideuteriomethyl 2,3,4,6-tetra-O-trideuterioacetyl-ot-D-glucopyranoside (6) (26). The 2D J spectrum, S(f2,f-^), of a 0.1M solution of 6 in benzene-d_g is displayed i n the power mode i n Figure (3.7). Although such multiple-trace or "stacked p l o t " displays often reveal i n t e r e s t i n g new information (for example, i n this case that both H-3 and H-4 are doublets-of-doublets rather than t r i p l e t s ) , considering the time required for the complete plot (ca. two hours i n this case for p l o t t i n g the 128 traces of the 2D J spectrum), the useful NMR information i s best, c e r t a i n l y most r a p i d l y , obtained from the various projections of the 2D J spectrum. Thus the 45° projection y i e l d s the proton-decoupled proton spectrum shown i n Figure 3.7B (and hence the proton chemical s h i f t s ) and a projection onto the axis corresponds to the conventional one dimensional spectrum ( F i g . 3.7A). Projection of d i f f e r e n t " s l i c e s " of the 2D J spectrum onto the f^ axis y i e l d the p a r t i a l J spectra for each m u l t i p l e t as shown i n Figure 3.8. Comparison of these traces with the spectra obtained by conventional Fourier transform NMR ( F i g . 3.7A) shows the enhancement of resol u t i o n due to s t a t i c f i e l d inhomogeneity refocussing e f f e c t of the spin-echo pulse sequence; therefore this approach leads to a H3 H4 H2 HI H6.61 H5 JL CH,OCOCD3 )3C0° VWH CD3CCX)^i4A , CD3COO 0 C D 3 6 u> Figure 3.7: 2D J spectrum of the a-methyl glucoside (fc) plotted m the power mode. A and B are tte normal and proton-decoupled proton spectra r e s p e c t i v e l y . Note the " s o l u t i o n enhancement e f f e c t of the multiplets i n the f x dimension ( c f . F i g . 3.8). Experimental parameters: NA-4, SW1250; AT=0.82 s; N=128; M=4096; T=17.86 ms; SF=270 MHz. H3 H4 H2 HI H6 H61 H5 + 15 0 -15Hz Figure 3.8: Comparison between the normal (C) and p a r t i a l J spectra (B) obtained from the 2D J spectrum shown in Figure 3.7. The improved resolution i s c l e a r l y noticeable, e s p e c i a l l y i n the H-3 and H-5 multiplets which show a long-range coupling of ca. 0.9 Hz. The apparent broadening of the H-l signals in the p a r t i a l J spectra is due to the presence of unresolved long-range couplings to H-3 and H-5. - 75 -more accurate determination of J values.* For example, the mu l t i p l e t due to H-5, which appears as eight lines i n the normal spectrum now appears as sixteen l i n e s , showing the long-range coupling (J~0.9 Hz) across four bonds to H-l which was o r i g i n a l l y obscured by the f i e l d inhomogeneity broadening (29); a small long range coupling i n H-3 i s only p a r t l y resolved because of inadequate d i g i t a l r e s o l u t i o n . In normal p r a c t i c e , however, NMR spectra are often complicated by e i t h e r strong coupling or overlap of resonances, or sometimes both; Figure 3.9 i l l u s t r a t e s the analysis by 2D J spectroscopy of a t y p i c a l example, 2,3,4-tri-O-acetyl-6-deoxy-a-D-glucopyranosyl- 3,4-di-O-acetyl-l,6-dideoxy -B-D-fructofuranoside ( J ) . Figure 3.9A shows a region of the normal ID spectrum below which i s the corresponding 45° skew projection ( F i g . 3.9B). Although the normal spectrum i s complicated by some overlap, most of the i n d i v i d u a l proton chemical s h i f t s can be e a s i l y measured from proton-decoupled proton spectrum ( F i g . 3.9B). The exceptions involve strongly coupled m u l t i p l e t s from the 3-F and 4-F resonances (F and P r e f e r to the furanose and pyranose rings r e s p e c t i v e l y ) , which give more complicated patterns because of the strong coupling within each geminal p a i r ; this i l l u s t r a t e s one of the serious l i m i t a t i o n s of both 2D and conventional NMR spectroscopy and i s one of the several reasons why i t i s preferable to work at the highest magnetic f i e l d strength a v a i l a b l e . A more detai l e d discussion of strong coupling e f f e c t s i n 2D J spectroscopy is given i n Section 3.2.6. Returning now to the disaccharide (7), the normal and p a r t i a l J spectra of the 2-P and 4-P region are shown i n Figures 3.9C and 3.9D r e s p e c t i v e l y . Assignment of the spectral pattern of the ID spectrum i s not immediately T-The NMR parameters are tabulated i n Chapter V along with the ZQT spectroscopy data on compound 6. Figure 3 . 9 : P a r t i a l 2D and ID proton spectra of 7 in C D C I 3 ( 0 . 1 M ) . A, the normal and B, the proton-decoupled proton spectra; in the l a t t e r spectrum the weakly coupled protons appear as s i n g l e t s , but the strongly coupled regions of the 3 F and 4 F protons give more complex patterns, is an expansion of the 2P and 4P region from a ID spectrum and D, the corresponding p a r t i a l J spectrum obtained by projecting the 2D J spectrum onto f^. The P and F s u f f i x e s refer to the pyranose and furanose units respectively. obvious; however, the p a r t i a l J spectrum shows the two m u l t i p l e t s symmetrically disposed with respect to zero-frequency, which can be assigned on the basis of t h e i r d i f f e r i n g l i n e widths. The three broader components constitute the H-4' m u l t i p l e t and the narrower, doubleted doublet are due to the H-21 resonances. In conventional high res o l u t i o n NMR the l i n e widths are usually determined by the instrumental l i n e broadening e f f e c t s rather than the "n a t u r a l " spin-spin relaxation time, which makes assignments based on l i n e widths d i f f i c u l t , or more often impossible; i t w i l l be r e c a l l e d that the p a r t i a l J spectra represent l i n e widths that r e f l e c t the respective " n a t u r a l " spin-spin relaxation times. In both the above two examples the spectra were displayed in the power mode* and as a r e s u l t the t r i p l e t i n t e n s i t i e s i n Figure 3.9D appear i n the r a t i o of 1:4:1 rather than the f a m i l i a r 1:2:1 pattern. Although these example i l l u s t r a t e two p o t e n t i a l advantages of 2D J spectroscopy i n chemistry, namely the s i m p l i f i c a t i o n of a complex spectrum in the form of a proton-decoupled proton spectrum and the r e s o l u t i o n of overlapping signals using p a r t i a l J spectra, these advantages are also associated with a number of p r a c t i c a l l i m i t a t i o n s . Accordingly, an attempt i s made i n the next section to analyse these aspects of 2D J spectroscopy from a p r a c t i c a l standpoint and this is followed by more detai l e d discussions of some s p e c i f i c topics of i n t e r e s t . 3.2.2 The phase twist e f f e c t i n two-dimensional spectroscopy Previous workers have shown (4,21) that double Fourier transformation of the S i t ^ f t ^ ) data matrix obtained from a 2D experiment leads to a complex two-dimensional lineshape given by, Ipower spectrum = {(real)2 + (imaginary) 2}; Magnitude spectrum = { ( r e a l ) 2 + (imaginary) 2} 1* S R ( f l ' f 2 } = A ( a l a 2 " d l d 2 } [ 3 * 2 ] S j C ^ . f j ) = A ( a i d 2 + a 2 d 1 ) [3.3] which represent the r e a l and imaginary components of the 2D spectrum respec-t i v e l y (a and d r e f e r to the Lorentzian absorption and dispersion lineshapes (eq. [1.11]) and the subscripts refer to the two domains). The two-dimensional lineshape was shown i n Figure 3.3 i n the form of a stacked p l o t , corresponding to equation [3.2]; the lineshape at "exact" resonance frequency i n e i t h e r dimension i s represented by an absorption s i g n a l , but the p r o f i l e tends towards a d i s p e r s i o n signal away from the resonance frequency. In the corresponding imaginary part of the 2D spectrum the l i n e s are 90° out of phase with respect to the former showing a dispersion lineshape at resonance frequency and the " t a i l s " approaching absorption lineshape c h a r a c t e r i s t i c s . * Largely as a r e s u l t of these c h a r a c t e r i s t i c s , the major l i m i t a t i o n s of phase-sensitive 2D J spectra are, a) the 45° i n t e g r a l projection leads to net c a n c e l l a t i o n of the signals, b) the dispersive components are characterized by wide " t a i l s " away from exact resonance frequency which can lead to undesirable interference e f f e c t s between neighbouring signals, and c) i t is inconvenient to display such spectra i n suitable form to extract the s p e c t r a l information. A convenient method of avoiding this phase twist problem i s to calculate the magnitude or power spectrum. Unfortunately both these display modes introduce an a d d i t i o n a l array of problems of t h e i r own, a discussion of which is given i n the next section. l-Such complex lineshapes a r i s e as a r e s u l t of double Fourier transformation; a more detai l e d account of lineshape c h a r a c t e r i s t i c s i n 2D J spectroscopy is given i n Section 3.3.3. - 79 -These considerations prompted us to consider methods to obtain absorption 13 1 mode 2D J spectra for protons. For heteronuclear (eg. C - H ) systems, experiments using " a l t e r n a t e " pulse sequences to create "reverse precession"* of the spins to eliminate the dispersive components, have been suggested by Ernst's (30) and Freeman's (31) groups. Unfortunately these methods are not generally applicable to proton, or homonuclear, systems since the pulses i n these cases are usually applied non-selectively to a l l the spins. Bax et a l . (33) have described a whole-echo Fourier transform method to obtain a pure absorption 2D J spectrum, which i s analogous to the SEAS experiment, described i n Section 2.4, for eliminating the dispersive components. Although t h i s procedure appears to be suitable for simple spin systems which have slow spin-spin relaxation rates and narrow spectral widths, these conditions do not often pertain to complex molecules, so this approach appears to lack g e n e r a l i t y . A more p r a c t i c a l and general approach appears to be manual phase correction of the relevant phase-sensitive cross-sections or "sub-spectra". 13 1 In the C - H case, for example, the relevant m u l t i p l e t s can be d i r e c t l y obtained from the 2D J spectrum since the protons can be decoupled during the detection period; the f^ trace at the chemical s h i f t of each resonance y i e l d s a p a r t i a l J spectrum, containing both the r e a l and imaginary parts. Recently an i n t e r a c t i v e , two-dimensional phase correction routine has been demonstrated by L e v i t t et a l . (32), however this has not yet been widely applied. Phase correction i n proton 2D J spectra i s usually more complicated 1-For example, this condition can be achieved in l ^ C - 1H systems by applying a 180° pulse to the carbon-13 spins at the end of the evolution period (30) or by a l t e r n a t i n g the decoupling period between TR and Tn (31) i n the "gated decoupler" method. - 80 -because of the overlap of resonances p a r t i c u l a r l y when dealing with t y p i c a l organic molecules and, also, the multiplets l i e at 45° with respect to each axis. Separation of the multiplets can be achieved i n this case by taking phase-sensitive cross-sections of sub-spectra (34), and Sections 3.3.2 and 3.3.3 deal with more detailed analysis of this procedure. 3.2.3 Problems associated with the magnitude- or power-mode displays of 2D J spectra The major disadvantage i n displaying a 2D J spectrum in the magnitude mode is the associated line broadening ef f e c t . This arises because of the resulting lineshape function which can be represented by, S M ( f ) = ( a 2 + d 2 ) h [3.4] Using equation [1.11] this can be shown to be of the form s M<f> = [3.5] (l+(27rAfT 2) z) l s The lineshape function of the above signal shows broad " t a i l s " c h aracteristic of absolute value mode spectra; these often lead to interference from neighbouring peaks, especially from the t a i l s associated with intense resonances. (The p r a c t i c a l implications of this is discussed i n the next section). The two-dimensional, magnitude value, line shape may be easily derived from equations [3.2] and [3.3] to be, S M ( f 1 , f 2 > = ( S R ( f 1 , f 2 ) 2 + S I ( f 1 , f 2 ) 2 } 1 5 [3.6a] = A f a ^ ] 1 * [3.6b] which on a contour plot has a shape of a four pointed star (Fig. 3.5). Note however, for the condition T ^ = T ^ a diagonal cross-section through a peak gives a pure Lorentzian lineshape (23). - 81 -The power spectrum derived from equation [3.2] and [3.3] has the form, S ( f , , f J = A 2[a-a,] [3.7] p 1 I 1 2 which corresponds to signals with Lorentzian absorption lineshapes along both dimensions; however the i n t e n s i t i e s w i l l be the square of their normal values. When the signals of interest are of similar magnitude, the above procedure yields desirable 2D J spectra with predictable i n t e n s i t i e s (26). Since a l l the signals i n t e n s i t i e s are squared, the 2D spectrum w i l l show an apparent improvement i n s e n s i t i v i t y (signal to noise r a t i o ) . However, both the magnitude- and power-mode spectra w i l l cause distortions and non-linear intensity effects in regions of overlap, which can have serious consequences, p a r t i c u l a r l y i n high resolution 2D J spectroscopy. When dealing with complex spectra, with many overlapping resonances, p a r t i c u l a r l y i n the absolute-value mode, i t is generally desirable to multiply the time-domain signal with suitable ( d i g i t a l ) f i l t e r functions. This type of d i g i t a l f i l t e r i n g can help to enhance the effective resolution of peaks and also minimize the interferences from neighbouring peaks by i t s line-narrowing e f f e c t . I t is also important to be aware that use of f i l t e r functions, such as sine-bell (35), double-exponential (36), etc., invariably introduces some noise thereby causing a loss of effective signal-to-noise, and also leads to intensity distortions within closely spaced or overlapping multiplets. Therefore the use of these functions generally requires that the o r i g i n a l time-domain signals have s u f f i c i e n t l y high signal to noise r a t i o , p a r t i c u l a r l y i f the resolution enhancement i s to be applied i n both t ^ and time domains; i t is also necessary to select the optimum weighting functions. As w i l l be discussed i n Section 3.3.2 and 3.3.3, the phase-sensitive t i l t routine offers a convenient solution to most of the above problems since i t - 82 -makes use of phase-sensitive spectra and provides the option of conventional ID spectrum manipulations on each i n d i v i d u a l multiplet sub-spectrum. 3.2.4 The dynamic range problem i n 2D NMR spectroscopy The r e l a t i v e i n t e n s i t i e s (dynamic range) of the various signals of a spectrum has to be given serious consideration i n 2D J spectroscopy, e s p e c i a l l y when "conventional" 2D data a c q u i s i t i o n and processing methods are employed. Such dynamic range problems are commonly associated with intense solvent r e s i d u a l peaks(37), methyl s i n g l e t s from methylated derivatives (eg. compound 7) or i n t e n s i t y differences between a major and minor component i n a mixture (38), etc. The major causes for this l i m i t a t i o n are associated with the line-broadening e f f e c t of magnitude spectra, and the amplitude deviations in the power spectra; both these e f f e c t s are amplified when dealing with large i n t e n s i t y d i f f e r e n c e s . In the i n t e g r a l projection mode of display, the broad t a i l s of intense resonances are summed over the region of interest and lead to undesirable e f f e c t s for example i n p a r t i a l J spectra of nearby resonances, often causing weak mult i p l e t s to be completely obscured (Ref. 37; Sec. 3.3.1). In the power mode display, each trace i n a 2D spectrum may have to be heavily "under-scaled"* in order to normalize the i n t e n s i t i e s which can lead to the loss of low intense signals from a spectrum. ^The d i g i t i z e d NMR s i g n a l is usually represented by words in a computer. A twenty b i t word can be c o r r e c t l y represented by signals whose i n t e n s i t i e s vary from zero to 2^0-1 integer numbers. I f a si g n a l i s higher than this l i m i t , i t i s usually scaled down by a suitable normalization factor i n order to be represented by the twenty b i t word. This "down-scaling" process can reduce low intense signal to less than unity, and thus r e s u l t i n loss of these s i g n a l s . However the dynamic range of sig n a l i n t e n s i t y can be increased by representing the data by two words (eg. double-precision integer or f l o a t i n g point representation). - 83 -Often, these l i m i t a t i o n s can be avoided by: a) making use of phase-sensitive display modes instead of absolute or power mode display (which was referred to i n Section 3.2.2), b) using suitable d i g i t a l f i l t e r functions to narrow the l i n e widths of (intense) signals, c) the use of analog f i l t e r i n g - i t should be possible to sample frequencies covering a selected band-width with respect to the transmitter by using suitable f i l t e r s , thus minimising the i n t e n s i t y of unwanted signals from outside t h i s frequency range, d) n u l l i n g any intense resonance which has a long spin l a t t i c e r e l axation time by use of an inversion recovery sequence p r i o r to a 2D J pulse sequence (Sec. 3.3.1; Ref. 37), e) n u l l i n g those signals which have a short spin-spin relaxation rate by delayed 2D J spectroscopy (Sec. 3.3.1; Ref. 39), f) s e l e c t i v e e x c i t a t i o n techniques for either pre-saturating the solvent or observing the signals of i n t e r e s t . It should be noted however that the optimum solution depends on the system under consideration, as should become c l e a r with discussion of the various examples that are considered i n this study. 3.2.5 The "overlap" or "hidden resonance" problem in NMR - the use of t i l t e d 2D J spectra Unravelling the overlapping components from many, c l o s e l y spaced, m u l t i p l e t s is one of the more serious problems encountered by chemists attempting to obtain s t r u c t u r a l information from proton NMR spectra. Although the wide dispersion obtained with modern spectrometers (superconducting - 84 -magnets operating at 11.7T, i e . 500 MHz for *H are commercially available) have considerably eased this problem, some of the examples considered in t h i s present work (38) show that straightforward analysis by inspection would s t i l l be d i f f i c u l t -even at higher magnetic f i e l d s far beyond the c a p a b i l i t i e s of present day technology. In the past this problem has been conventionally solved by rather demanding (and time consuming) INDOR ( i n t e r Nuclear DOuble Resonance) studies (40,41) and related double resonance studies such as NOE-difference (42) and spin-decoupling difference methods (43). 2D J spectroscopy o f f e r s a useful s o l u t i o n to the above problem, and w i l l be discussed now. Consider, for example, the p a r t i a l 2D J spectrum of the H - l ' and H-5 resonances of uridine (8) shown i n Figure 3.10 ( c f . F i g . 3.11). The proj e c t i o n of this " u n t i l t e d " spectrum onto the axis gives the normal spectrum, and shows the overlap of the two doublets (Figs. 3.10a; 3.11A). Because of t h e i r close proximity, a projection of the 2D J spectrum onto the f^ axis y i e l d s a p a r t i a l J spectrum i n which the two mul t i p l e t s appear superimposed (Figs. 3.10b; 3.11C). Although in this case the two doublet components can be e a s i l y assigned by inspection, i t is obvious that for more complex m u l t i p l e t s such unequivocal assignment i s rather improbable. Now consider the projections of the t i l t e d 2D J spectrum of Figure 3.10D which was obtained by subjecting the o r i g i n a l data-matrix, S ( f ^ , f 2 ) , to a 45°-tilt i n frequency space (23). Although the projection onto the f'^ axis i s i d e n t i c a l to that i n Figure 3.10A the projection onto the (^ a x ^ s n o w produces a s i n g l e t for each proton at the f^' value corresponding to i t s chemical s h i f t ; t h i s is because components of each m u l t i p l e t now l i e p a r a l l e l to the f n ' axis ( F i g . 3.10c; 3.11B). Traces taken from the 2D J spectrum at Figure 3.10: The t i l t operation to illustrate its advantages in 2D J spectroscopy. A, the 270 MHz proton 2D J spectrum of the H-l' and H-5 resonances of uridine (8) 0.3M in D2O. The f 2 projection of A is equivalent to a conventional spectrum (a) and the projection onto f\ gives the superimposed J spectrum (c). The tilted data matrix, B, when projected onto f ' 2 yields proton-decoupled proton spectrum (c); cross-sections (d, e) at the respective chemical shift frequencies give the partial J spectra of the two protons, thus resolving the overlapping multiplets (c_f. Fig. 3.11). - 86 -OH T 1 1 1 1 1 1 1 r 8 7 6 S(ppm) 5 4 Figure 3.11: The lower trace shows the ID spectrum of 8 i n D2O. The inset shows the conventional spectrum (A), proton-decoupled proton spectrum (B), J spectrum (C), and the cross-sections (D and E) of the H-5 and H-l' resonances, derived from the 2D J spectra i n Figure 3.10. - 87 -the two chemical s h i f t s ( i n f 2)> now give i n d i v i d u a l p a r t i a l J spectra (cross-sections) as shown in Figures 3.10d,e and 3.11D,E. The advantages of using t i l t e d 2D J spectrum become increasingly important for more complex (overlapping) regions of a spectrum; this point is i l l u s t r a t e d i n Figure 3.12 for a,8-D-xylose ( l ) i n D 20. Most of the conventional spectrum can be assigned by inspection, leaving only the region between 63.3-3.5 which contains the overlapping resonances of f i v e , p o t e n t i a l l y inequivalent protons. The proton decoupled spectrum (obtained by projecting the t i t l e d 2D J spectrum onto f 2 ' ) shows the expected sharp sin g l e t s corresponding to the chemical s h i f t of each weakly coupled proton. The region of int e r e s t contains one such si n g l e t at (53.35 (the other four resonances give broad responses which is usually c h a r a c t e r i s t i c of strongly coupled systems); a cross-section at this chemical s h i f t gives the p a r t i a l J spectrum (inset) for this proton; a l l of the v i c i n a l couplings can be e a s i l y measured and the resonance assigned as that of the H-4 proton of the 0-anomer. The importance and usefulness of the above method can be seen in an even more complicated example, namely an anomeric mixture ( a : 8 = l t 3 ) of cellobiose (9) i n D_0. The multiplets corresponding to the eighteen (non-anomeric) protons appear within a region of --200 Hz ( F i g . 3.13B), as a r e s u l t complete analysis of the spectrum using techniques such as double resonance or spectrum simulations are e s s e n t i a l l y impossible. Remembering that i n a proton spectrum, weakly coupled spins give sharp singlets (whereas i l l defined, broad peaks are usually produced by strongly coupled s i g n a l s ) , projection onto f 2 ' of the 2D J spectrum of this sample at 270 MHz provides a convenient spectral s i m p l i f i c a t i o n . Cross-sections taken at these frequencies (corresponding to sharp s i n g l e t s ) give the p a r t i a l J spectra of a t o t a l of eleven protons as 5e HO HO HO | a OH H4* I .[."' I II I II I j I I 14 — i — 0 -14 Hz [H-3,4,5o,5o]a 44 . 36 8 {ppmI Figure 3.12: The lower trace shows the 270 MHz proton spectrum of a,8-D-xylopyranose (1; 0. D2O) and the upper trace the corresponding proton-decoupled proton spectrum obtained by •-- - — - -...«•• inset is the partial J spectrum of H-4P 2D J spectrum onto f ' 2 « projecting the tilted obtained by taking a cross-section af f'2=3.35&. - 89 -Figure 3.13: P a r t i a l 270 MHz proton spectrum (B) and the proton-decoupled proton spectrum (A) of a,8 cellobiose (9,), 0.3M in D2O. The multiplet structures shown as " s t i c k " diagrams and the trace A were obtained from the 2D J spectrum shown i n Figure 3.10. The multiplet structures corresponding to strongly coupled spin systems and from those with low i n t e n s i t y were d i f f i c u l t to resolve and assign (see t e x t ) . - 90 -Figure 3.14: T i l t e d 2D J spectrum of the non-anomeric protons i n ct,S cellobiose (9) i n D2O (0.3M). The top trace i s the projection onto f ' 2 5 cross-sections p a r a l l e l to f ' j yielded the multiplet patterns shown diagrammatically i n Figure 3.13. Sine-bell resolution enhancement was used i n the f2 domain to minimise the line broadening effect of the absolute value display. - 91 -indicated i n Figure 3.13B. (It was not possible to obtain meaningful p a r t i a l J spectra for the strongly coupled resonances.) Providing the chemical s h i f t separation between two m u l t i p l e t s can be resolved in (eg* by increasing the d i g i t i z a t i o n or r e s o l u t i o n enhancement), i t should be possible to resolve those i n d i v i d u a l multiplets by the above procedure. In the above case, for example, the chemical s h i f t B B difference between H-2 and H-2' i s less than 3 Hz. It has been possible i n another study to resolve multiplets which were about 0.5 Hz apart (45). Although i t is possible to "resolve" the NMR spectrum of c e l l o b i o s e in this manner, assignments of the i n d i v i d u a l m u l t i p l e t s based either on matching of coupling constants, or on chemical s h i f t arguments are impossible because each of the ( s i x ) geminal protons and s i m i l a r l y the eight methine protons are a l l expected to have almost i d e n t i c a l multiplet structures (Table 4.1). Given t h i s d i f f i c u l t y and the fact that one-dimensional double resonance methods are not suitable for the analysis of such crowded spectra, i t is fortunate that two-dimensional correlated spectroscopy e x i s t s . As w i l l be discussed l a t e r i n 13 1 Chapter IV C- H chemical s h i f t correlated spectroscopy was used in the above case to assign a l l the proton chemical s h i f t s and thereby complete the sp e c t r a l assignment (38). 3.2.6 Strong coupling e f f e c t s i n 2D J spectra Strong coupling represents a serious l i m i t a t i o n i n ID proton NMR spectral analysis and the same is equally true for 2D spectroscopy (4,46-48). Second order multiplets can be asymmetric about the chemical s h i f t i n a ID spectrum; however a homonuclear 2D J (or the analogous heteronuclear " p r o t o n - f l i p " experiment) y i e l d s a symmetric 2D spectrum with a d d i t i o n a l l i n e s , some with - 92 -negative i n t e n s i t i e s . Since strong coupling often r e s u l t s i n the components of a multiplet being spread over a wider frequency range than when the same nuc l e i are studied under weak coupling conditions (eg. at high magnetic f i e l d s ) , t his often leads to fold-over of peaks i n the f^ dimension. Unlike weakly coupled m u l t i p l e t s , a l l the components of a strongly coupled system may not l i e p r e c i s e l y along a 45° axis with respect to the p r i n c i p a l axes; this r e s u l t s i n more complex patterns i n proton-decoupled proton spectrum (45° pr o j e c t i o n ) , which are often broadened due to overlap of many c l o s e l y spaced l i n e s . These ef f e c t s are demonstrated using 1 1,4,6,6 1-tetrachloro-1',4,6,6 1-tetradeoxy-galacto-sucrose tetramesylate (10) as an example. The weakly coupled methine ri n g protons i n 10 appear i n Figure 3.15 as sing l e t s i n the proton-decoupled proton spectrum, whereas the three pairs of strongly coupled methylene protons show more than nine major l i n e s . C l e a r l y this behaviour could lead to confusion i n attempting to analyze a complex 2D J spectrum. Although such spectra can be analysed by computer simulation (48) this is inv a r i a b l y a tedious and i n e f f i c i e n t process even by the standards of conventional ID second-order spectrum simulations and ana l y s i s . As an example, the 2D J spectrum of the 6-P and 6'-P protons (AB part of an ABX system) i n 10 was simulated using the values, ^, = 11.5, ^ = 7.1, J . - = 6.2 and A c =14 HZ.* The contour diagram along with the j,o 0 , 0 experimental p l o t i n the absolute value mode, i s i l l u s t r a t e d i n Figure 2 3.16; the folded-back (•) and negative peaks (e) are also indicated in the figure (cf_. F i g . 3.17). The d i f f e r e n t projection and the calculated " s t i c k " diagrams are indicated i n Figure 3.17. *A6,6' refers to the chemical s h i f t difference between 6-P and 6'-P 2The computer simulation program was kindly provided by Dr. G.A. Morris. 6F, 6F'6P IF IF'6P' IP 3F 4F 3P 2P 4P 5P 5F H JJJuUdAJV B 60 5.5 5.0 * 4.5 0(ppm) 4.0 3.5 Figure 3.15: The normal 270 MHz proton spectrum (A) and the proton-decoupled proton spectrum of 0.1M solution of 10 i n CDC 13. Sine-bell resolution enhancement was used i n the f 2 domain. Each weakly coupled p'roton gives a singlet i n B, whereas the strongly coupled protons (3.5 to 4.06) give more complex patterns. \ f, Hz Figure 3.16: The plot on the left is an experimental 2D J spectrum of the 6P and 6P' protons \Q, plotted in the absolute value mode. The diagram on the right was constructed by computer simulation of this strongly coupled region using the parameters J5 g t ^ l l . 5 , J6?5=6.2, Jgi 5=7.1 and A5 6'=14 Hz. The numbers represent the absolute intensities. The dark c i r c l e represents fold-over in f j . (The signals associated with an intensity of 0.23 correspond to negative peaks). - 95 -Figure 3.17: A, B and D are the projections of the 2D spectrum shown in Figure 3.16 onto d i f f e r e n t axes, and correspond to the normal, proton-decoupled and J spectra r e s p e c t i v e l y . C and E were constructed from computer simulation data. Since strong coupling usually leads to rather unpredictable cross-sections, i t is advantageous when analysing complex spectra to have some prior knowledge of the regions of a spectrum containing strongly coupled systems. This may be achieved either by viewing the 45° projection (remembering that strongly coupled peaks often give broad responses) or by d i r e c t l y viewing the cross-sections (weakly coupled systems give simpler and symmetric responses i n f ^ 1 at the i r respective chemical s h i f t frequencies i n Various a l t e r n a t i v e methods ex i s t for minimising the ambiguities associated with strongly coupled systems. These include: a) obtaining measurements at the highest possible magnetic f i e l d for larger chemical s h i f t dispersion, b) inducing chemical s h i f t dispersion with the help of paramagnetic s h i f t reagents (49) or solvents; i t should be mentioned that i n a) and b), i t is only necessary to cause a small change i n the r e l a t i v e chemical s h i f t s within a strongly coupled system so as to convert i t to a pseudo f i r s t - o r d e r l e v e l , 13 1 c) using a C- H 2D s h i f t c o r r e l a t i o n experiment to determine the approximate chemical s h i f t of each strongly coupled proton p r i o r to analysing a 2D J spectrum (38), d) analysis of the 2D J spectrum by computer simulation as discussed e a r l i e r , and e) simulation of the strongly coupled NMR spectrum i n ID rather than 2D; since the chemical s h i f t s and coupling constants of weakly coupled protons can be e a s i l y derived by 2D J spectroscopy, i t may now be more convenient to analyse (by simulation) the conventional NMR spectrum. For example, i f the -and J-values of a weakly coupled multiplet from an overlapping strongly coupled region (eg. H-4 i n F i g . 3.12) can be obtained, then i t should be possible to subtract i t s p a r t i a l (simulated) spectrum from the normal spectrum and thereby obtain the spectrum corresponding to the second-order peaks which would thereby be s i m p l i f i e d for ID a n a l y s i s . In the current study attempts were always made to i d e n t i f y any strongly coupled protons, but further analysis was not pursued. 3.3 Miscellaneous topics related to 2D J spectroscopy 3.3.1 Elimination of dynamic range e f f e c t s i n 2D J spectroscopy a) Solvent nulled 2D J spectroscopy The problems a r i s i n g from a large dynamic range of signals were discussed previously i n Section 3.2.4; i n extreme cases, such as when the spectrum has a strong r e s i d u a l solvent peak, a commonly encountered problem with biochemical samples, t h i s can completely jeopardise the usefulness of the 2D J technique by d i s t o r t i n g s ubstantial regions of the 2D spectrum. Fortunately these problems can often be conveniently avoided by modifying the 2D J pulse sequence, using approaches s i m i l a r to those used in ID NMR spectroscopy for solvent suppression (50,51). One example of the problem and i t s solution w i l l s u f f i c e here to make the point. The protons of uridine (8, 0.3M in D 20) have much faster s p i n - l a t t i c e r e l a x a t i o n rates (= 0.4 s *) than the r e s i d u a l proton i n the solvent ( 0.11 s * ) . This difference can be advantageously used to s e l e c t i v e l y n u l l the solvent resonance p r i o r to the 2D J pulse sequence by a p p l i c a t i o n of a non-selective inversion-recovery pulse sequence during the preparation period; this is represented by, {180° - T - 90° - n.T - 180° - n.T - A c q u i s i t i o n ) n u l l M where T^^^ i s set equal to the time required for the HOD signal to reach - 98 -i t s " n u l l - p o i n t " (52). Phase al t e r n a t i o n of both the 180° pulses by 180° is generally recommended to minimize a r t i f a c t s in the f i n a l spectrum (53,19). The r a p i d l y relaxing uridine protons regain t h e i r equilibrium magnetization condition during the time T^.^ and are ready to experience the 2D J pulse sequence. The effectiveness of this approach is c l e a r l y d i s c e r n i b l e by comparison between the 2D J spectra in Figure 3.18. It can be seen in the l a t t e r that the d i s t o r t i o n a r i s i n g from the HOD signal has been completely eliminated from the 2D J spectrum. The impact of this procedure on the corresponding p a r t i a l J spectra i s demonstrated i n Figure 3.19. The various traces were obtained by projecting sections of the 2D J spectra onto the f^ axis; those in Figure 3.19A show a s i g n i f i c a n t signal at zero-frequency due to the t a i l s of the residual solvent resonance, even though i t is about 270 Hz to low-field of the H-5 ' resonance (see F i g . 3.11). For weak signals such as the H4' m u l t i p l e t which also shows signals near the zero frequency in the f^ dimension, the t a i l of the HOD signal completely d i s t o r t s the p a r t i a l J spectrum, so that i t cannot be interpreted ( F i g . 3.19A); i n contrast the equivalent trace obtained by the solvent-nulling 2D J procedure is free from this defect ( F i g . 3.18B). Another useful technique for solvent n u l l i n g in aqueous (D 20) samples, often used i n the course of these studies was s e l e c t i v e i r r a d i a t i o n or pre-saturation (54). This procedure can be used when the sign a l to be i r r a d i a t e d has a relaxation time s i m i l a r to the resonances that are to be studied. b) Delayed 2D J spectroscopy In the previous section elimination of the intense signals was achieved by taking advantage of the large differences in s p i n - l a t t i c e relaxation rates Figure 3.18: (A) Proton 2D J spectrum of the high f i e l d region of uridine (ft) in D20 (cf. Fig. 3.11), showing the distortion at zero frequency in f j due to the "wing" of the HOD peak. (B) The same region, from an experiment in which the solvent resonance was eliminated by an inversion recovery sequence prior to the 2D J pulse sequence. The top and bottom traces show the normal and proton-decoupled proton spectrum respectively. Both spectra are plotted in the power mode with exponential multiplication in both time domains. - 100 -Figure 3.19: (A) P a r t i a l J spectra of the H-4', H-5'A and H-5'B resonances of g obtained by projecting sections of the 2D J spectrum ( F i g . 3.18A) onto the fi axis, each showing, at zero frequency, the signal from the "wing" of the HOD s i g n a l ; note the e f f e c t of the solvent peak on H-4* s i g n a l s . (B) T corresponding regions obtained from Figure 3.18B; each of these p a r t i a l J spectra agree with spectra simulated to include e f f e c t s of strong coupling. - 101 -between the solvent and the protons i n the molecule. In this section another approach, "delayed" 2D J spectroscopy, w i l l be discussed which can be used when the intense signal has a much shorter spin-spin relaxation rate than the resonances of p r i n c i p a l i n t e r e s t ( c f . SEAS). Figure 2.7A shows the ID spectrum of a D 20 sol u t i o n containing 10% (0.01M) dextran T-10 (MW ca. 10,000, a 1 ^  6 ct linked polymer of D-glucopyranose; 3) and methyl B-D-xylopyranoside (0.1M; 4). Comparison with the spectrum of 4 shows the extent of overlap and dynamic range of signals between the polymer and monomer. Use of "conventional" 2D data processing to resolve the xyloside spectrum would r e s u l t i n a predictably d i s t o r t e d 2D J spectrum for the various reasons discussed e a r l i e r (c_f. Sec. 3.2.4), p a r t i c u l a r l y for the H-5e and H-4 resonances due to extreme overlap. This problem may be avoided by acquiring the i n i t i a l 2D J data a f t e r a suitable delay time (T^), during which the transverse magnetization component of the rap i d l y relaxing polymer signals would have decayed due to spin-spin r e l a x a t i o n . (The corresponding spectra from the SEAS experiment ( F i g . 2.7) indicate the extent to which the polymer signals can be eliminated from a spectrum, for a suitable delay time T^.) From the r e s u l t i n g p a r t i a l l y  relaxed 2D J spectrum i t is possible to obtain p a r t i a l J spectra of, for example, the H-5g and H-4 protons as seen in Figure 3.20A and C which are displayed in the phase-sensitive mode; the corresponding regions from SEAS are also shown in the figure for comparison. These cross-sections may be d i f f i c u l t to phase correct* but may be conveniently displayed a f t e r suitable spectrum manipulations (Sec. 3.3.2). Note the res o l u t i o n enhancement associated with ^The phase of each component of the multiplet w i l l be modulated as a function of T^ as discussed i n Chapter I I ; a suitable phase independent display mode may be preferable i n many instances. - 102 -H-5e|> K A B H-4 JUIL AJU l) I C D I -15 i 0 15 Hz Figure 3.20: (B, D) The H-5 e and H-4 multiplets of 6-methyl xylopyranoside (4) obtained from SEAS data for values of 192 and 544 ms re s p e c t i v e l y . (A, C) The corresponding p a r t i a l J spectra obtained from phase-sensitive, t i l t e d , p a r t i a l l y relaxed 2D J spectrum. Note the l i n e narrowing e f f e c t and the lineshapes. The signal near zero frequency i n C is the dispersive t a i l from the methyl resonance. The d i g i t a l r e s o l u t i o n i s 0.49 Hz/point. - 103 -the p a r t i a l J spectra of the H-5g proton - this i s due to the l i n e narrowing e f f e c t i m p l i c i t l y associated with the phase-sensitive t i l t routine. 3.3.2 Phase-sensitive t i l t routine The importance of the "45°-tilt" routine was c l e a r l y demonstrated in the previous sections with the help of a diagrammatic sequence of the data processing steps ( F i g . 3.6), and a few examples using t y p i c a l organic molecules i n Section 3.2.5. It w i l l be r e c a l l e d from previous discussions that the necessary spectral information regarding a weakly coupled multiplet is contained i n the relevant 45° cross-sections of a 2D J spectrum. The f 2 ' and f^' frequencies of this single trace w i l l provide the chemical s h i f t and coupling constants respectively, and the area represents the i n t e n s i t y ; * these are generally the most useful parameters for NMR spectral and s t r u c t u r a l analysis of molecules. It follows from this that any display mode which optimises the information content of cross-sections i s of substantial relevance to p r a c t i c a l applications of 2D J spectroscopy. The above feature makes i t necessary to consider only the cross-sections of equivalent groups of protons at t h e i r respective chemical s h i f t s to obtain phase-sensitive information from a 2D J spectrum. In general the phase-sensitive display mode would be preferred over the absolute value mode, mainly to r e t a i n the Lorentzian c h a r a c t e r i s t i c s of the former, but also to determine the signs of signal i n t e n s i t i e s which have s i g n i f i c a n c e when dealing with 2D J spectra of strongly coupled systems (and in chemical s h i f t correlated ^Because the l i n e widths of i n d i v i d u a l m u l t i p l e t s are often d i f f e r e n t ( p a r t i c u l a r l y i f d i g i t a l f i l t e r i n g is used) and interference of neighbouring l i n e s causes non-linear i n t e n s i t y r e l a t i o n s h i p s , cross-sections cannot be used to provide accurate i n t e n s i t y measurements. In the case of i s o l a t e d m u l t i p l e t s , however, i n t e g r a l projections can be used to provide information on the r e l a t i v e number of protons giving r i s e to each m u l t i p l e t . - 104 -spectroscopy). Unfortunately the methods to obtain phase-sensitive 2D J spectra mentioned i n Section 3.2.2 are not generally applicable to complex proton 2D J spectra obtained from t y p i c a l organic molecules. However, the phase-sensitive t i l t routine (Scheme 2), which w i l l be discussed i n d e t a i l here, o f f e r s a convenient method for analyzing complex 2D J spectra. The c a l c u l a t i o n of the t i l t routine (TILT I) mentioned in the previous sections was performed on the S(f2»f^)* data matrix by f i r s t reading into the computer memory the necessary number of traces from the o r i g i n a l data matrix, followed by a l i n e a r i n t e r p o l a t i o n procedure to construct the t i l t e d trace of cross-sections. The o v e r a l l e f f i c i e n c y of this procedure is determined by the core memory size of the computer, which is a major l i m i t a t i o n when dealing with large data arrays. For that reason, another related procedure (TILT II) was developed which is more suitable for minicomputers; this involves t i l t i n g the Sif^.f^) data matrix by " s h i f t i n g " each trace in the dimension, followed by a (parabolic) i n t e r p o l a t i o n procedure. In this case the size can be almost as large as the core memory size since each i.^ trace is s h i f t e d independent of the other traces.* This operation S(f2»f^) S(t^% , i s i l l u s t r a t e d i n Figure 3.21 which is plotted in the absolute value mode for convenience. Each multiplet i n a 2D J spectrum w i l l be set at a p a r t i c u l a r angle (0 = 45°), with respect to the f^ axis. The o f f s e t by which each trace i s to be s h i f t e d i s given by, A = Tan 6 where n^ is equal to the f^ trace number and h^ the d i g i t i z a t i o n i n the f j dimension. Since the data i s d i g i t i z e d the s h i f t i s followed by a ^Although each operation involves a " s h i f t " of an f2 trace, i t s ultimate e f f e c t on the 2D J spectrum is equivalent to " t i l t i n g " i t by 45°. SCHEME 2 S ( t „ t 2 ) - 2 — S ( t „ f 2 ) S(f2,t,) ^ * S(f2,f,) FT DISPLAY transpose transpose 45° tilt o S ( f „ f 2 ) Figure 3 . 2 1 : (A) The 2D J spectrum of the quartet i n diethylmalonate i n C D C I 3 . The t i l t operation transforms the S ( f i , f 2 ) matrix into S ( f ' i , f ' 2 ) , B. A cross-section of B at the chemical s h i f t yields C, the p a r t i a l J spectrum shown in the absolute value mode. A similar trace from the corresponding phase-sensitive 2D J spectrum yields a sub-spectrum representing the real (D) and imaginary (not shown) parts. Note that the f j t a i l s (including the noise and a r t i f a c t s ) are t i l t e d at "135°" to the f\ axis. - 107 -parabolic interpolation procedure which may be of c r i t i c a l importance, particularly when dealing with limited digitization of signals or when attempting to resolve closely spaced lines. However for many practical cases in the current work, the interpolation procedure was omitted in order to minimize the total data processing time.* The original computer programme written in Nicolet 1180 BASIC is given in Appendix A. It can be seen from Appendix A that both the real and imaginary parts of the 2D J spectrum are processed independently. As a result, the final t i l t e d cross-section of a multiplet contains the real and the corresponding imaginary parts; in effect, this is equivalent to a spectrum obtained by selective excitation of that proton. This "sub-spectrum" can be inverse Fourier transformed to yield the corresponding time domain signal SCtj'jt^'). This data processing method has a number of advantages over "conventional" 2D J data processing routines, particularly because now each sub-spectrum can be individually subjected to the various data manipulation procedures in the time domain ( t ^ ' ) , such as z e r o - f i l l i n g , digital f i l t e r i n g , etc. For example Figure 3.22D shows a sub-spectrum of a doublet (J = 2.65 Hz) obtained by zer o - f i l l i n g and "sine-bell" resolution enhancement; the corresponding region from a normal spectrum is shown in Figure 3.22A. In practice, the NMR time domain signals are often zero-filled to improve the digitization (and hence the lineshapes) of the resulting Fourier transformed spectrum. In 2D spectroscopy this invariably leads a larger data matrix, and hence w i l l increase the total data processing time, which can be lAs written by the author, the t i l t routine was the most inefficient step of a l l the 2D J data processing steps because of the limited capabilities of the Nicolet 1180 BASIC programme; recently D. Dalrymple (Nicolet) provided us with a more efficient assembly language version of TILT II incorporated into the standard NTCFT programme. - 108 -D 4 V 40 Hz Figure 3.22: (A) The normal spectrum of a doublet (j=2.65 Hz) having a d i g i t a l r e s o l u t i o n (DR) of 0.34 Hz/point. (B) The same region with DR=1.37 Hz; this was the f 2 r e s o l u t i o n that was used i n the 2D J experiment which yielded the p a r t i a l J spectra C and D. C i s the (phase-sensitive) sub-spectrum with DR^=0.34 Hz. Trace D was derived from C, by inverse Fourier transforming the spectrum d i g i t a l f i l t e r i n g for enhancing the res o l u t i o n z e r o - f i l l i n g and another (forward) Fourier transformation. (The negative peak i n trace C is an a r t i f a c t from a neighbouring s i g n a l ) . - 109 -s i g n i f i c a n t when dealing with, for example, natural products such as steroids (43,55) which have wide s p e c t r a l - and multiplet widths.* The procedure described e a r l i e r , i n which only the relevant sub-spectra are z e r o - f i l l e d , i s a p r a c t i c a l l y useful feature. Some of the features regarding phase-sensitive cross-sections are summarised below: a) the need for eit h e r magnitude-or power-mode spectra are eliminated and so, thereby, are the li m i t a t i o n s a r i s i n g from those display modes, b) phase-sensitive information, such as (p o s i t i v e and negative) peak i n t e n s i t i e s , can be obtained, c) the sub-spectra show a re s o l u t i o n enhancement (line-narrowing) e f f e c t which i s i m p l i c i t l y associated with the t i l t routine, d) data manipulations ( d i g i t a l f i l t e r i n g , convolution, etc.) can be performed on each i n d i v i d u a l sub-spectrum at the f i n a l stage ( a f t e r double Fourier transformation) rather than on the o r i g i n a l data matrix; as a r e s u l t the weighting function for each mu l t i p l e t can be i n d i v i d u a l l y optimised, e) since i t is unnecessary to z e r o - f i l l the time domain signals of the o r i g i n a l matrix, t h i s can minimize both data processing time and l i m i t a t i o n s in handling large data arrays. The phase-sensitive t i l t routine i n homonuclear 2D J spectroscopy r e s u l t s 2 in non-Lorentzian lineshapes and this i s discussed i n the next section. ^The f i s p e c t r a l width i n this case may be over 50 Hz, therefore the t i signals may have to be z e r o - f i l l e d to give an f i spectrum with 256 or 512 points i n order to improve the lineshapes and resolve small, long range couplings. 2 I t should also be mentioned that Lorentzian absorption mode p a r t i a l J spectra can be d i r e c t l y obtained from 13C_*H (heteronuclear) 2D J spectrum since the signals are generally acquired under proton decoupled conditions and y i e l d a S(6,j) matrix. - 110 -3.3.3 Lineshape c h a r a c t e r i s t i c s i n phase-sensitive, t i l t e d 2D J spectra Fourier transformation of time-domain NMR signal (FID) generates both an absorption and a dispersion s i g n a l , which are 90° out of phase with respect to each other; i f the o r i g i n a l FID is exponential then the r e s u l t i n g frequency domain s i g n a l w i l l be Lorentzian i n shape. In contrast, each 2D signal in a spectrum r e s u l t i n g from double Fourier transformation contains a mixture of absorption and dispersion components which together give r i s e to the so c a l l e d "phase-twist" e f f e c t as i l l u s t r a t e d i n Figure 3.23. As we have already noted this problem due to the phase-twist can be conveniently eliminated by dis p l a y i n g absolute value spectra; however, this r e s u l t s in the c h a r a c t e r i s t i c , and undesirable l i n e broadening e f f e c t . The above feature often leads to interference from neighbouring signals which can be a major l i m i t a t i o n i n the a p p l i c a t i o n of 2D J spectroscopy in high r e s o l u t i o n studies, p a r t i c u l a r l y in proton NMR spectroscopy. The nature of this phase twist i s i l l u s t r a t e d i n Figure 3.23; for the r e a l part of the 2D Fourier transform, given by (4), S R ( f 1 , f 2 ) = Mq{ a 1 ( f 1 ) . a 2 ( f 2 ) - d 1 ( f 1 ) . d 2 ( £ 2 ) } [3.8] where a and d refer to the Lorentzian absorption and dispersion terms res p e c t i v e l y in t h e i r corresponding frequency domains a(f) T 2 [3.9] 1+ {2TT Af T'2}2 and d(f) = 2TT Af T 2 2 [3.10] 1+{2TT Af T 2 } 2 T 2 and T 2* are the decay constants in t^ and t 2 r e s p e c t i v e l y and Af = (f-f°), where f° is the o f f s e t frequency from the c a r r i e r (c_f. eq. [1.11]). S R(f 2 ,f,) S,(f2,f,) Real Imoginary Figure 3.23: Experimental traces showing the lineshape c h a r a c t e r i s t i c s i n 2D J spectroscopy - the "phase twist" e f f e c t . (The subscripts R and I refer to the r e a l and imaginary spectra). - 112 -Each trace i n Figure 3.23 refers to a fixed f^ in equation [3.8]. When Af^ i s large ( i e . away from "exact" resonance i n f^) the absorption terms become n e g l i g i b l e , which re s u l t i n the dispersive signals as shown by the S ( f 0 , f . ) traces i n Figure 3.23; note the change in sign (or the sense of rotation) of the dispersion l i n e shape. At exact resonance* however Af = 0, and hence the trace w i l l correspond to a Lorentzian absorption s i g n a l , with a half-height width of ir *R2 Hz, which corresponds to the "natural" line width (neglecting d i f f u s i o n and instrumental e f f e c t s ) . S i m i l a r l y the corresponding imaginary spectrum i n Figure 3.23 is given by, S ] ; ( f 1 , f 2 ) = M Q { a 1 ( f 1 ) d 2 ( f 2 ) + d 1 ( f 1 ) a 2 ( f 2 ) } [3.11] which w i l l be 90° out of phase with respect to S R ( f ^ , f 2 ) , showing a dispersive s i g n a l at the f 2 resonance frequency and absorptive signals with opposite i n t e n s i t i e s away from "exact" resonance. Similar explanations can be offered for the lineshape behaviour when viewed perpendicular to the f 2 a x i s ; the l i n e widths w i l l now be characterized by R2*, which includes the magnetic f i e l d inhomogeneity e f f e c t s . The absolute value 2D J spectrum can be shown to be (4,21,23), S ( £ v t z ) = M o { a 1 ( f 1 ) T 2 . a 2 ( f 2 ) T 2 * } S s [3.12] and i s characterised by the broad " t a i l s " at "exact" resonance i n both dimensions, which are c l e a r l y seen i n a contour plot as in Figure 3.5. The expression for a cross-section taken at angle Q at a fixed f 2 ' from the above spectrum can be represented by (23), S (f ') = M {a. ( f 'cose - f 'sin6)T 0.a-(f,'sin0 + f 'sine)T [3.13] i O i l 2 I I I 2 2 Note that for the condition T 2 = T 2*, a slope at 45° (sine = cose), both lineshape functions become sim i l a r y i e l d i n g a p a r t i a l J spectrum with a l i t should be r e c a l l e d that the f^ frequency is not due to a resonance phenomenon, but rather a modulation. - 113 -Lorentzian absorption lineshape. These features may be v i s u a l i z e d from a contour plot the 2D peak ( F i g . 3.5) in which those sections through the peak that are p a r a l l e l to either f^ or f^ axes are broad (according to eq. [3.12]), whereas the sections taken through the diagonal appear narrow. In p r a c t i c e , however, the cross-sections may also contain the (dispersive) t a i l s from neighbouring resonances. In some previous examples i t was noted that p a r t i a l J spectra, or sub-spectra, from t i l t e d , phase-sensitive 2D J spectra showed a r e s o l u t i o n enhancement e f f e c t with lineshapes s i m i l a r to those obtained by ID r e s o l u t i o n enhancement procedures such as using " s i n e - b e l l " functions (35). This e f f e c t can be e a s i l y v i s u a l i z e d from the 2D lineshape shown i n Figure 3.23. A sub-spectrum w i l l be represented by a diagonal sections through both the r e a l an imaginary parts of the 2D peak; thus, for example, a section at 45° with respect to the f, axis, through the S D(f„,f 1) peak w i l l show a 1 R / 1 Lorentzian absorption c h a r a c t e r i s t i c at "exact" resonance, tending towards "negative" dispersion signa l away from resonance. In e f f e c t the lineshape may be considered as an absorption peak narrowed by two negative halves of a dispersion s i g n a l . The r e a l part of these sub-spectra for a fixed f 2 ' can be given by (eqs. [3.5] and [3.10]), The above equation represents the phase-sensitive f^' traces derived from SR<f{)) « Mc the S ( f 2 ' , f ') 2D spectrum. Figure 3.24 shows phase-sensitive traces which were obtained using equation [3.14]; the 2D plot was simulated using a programme written i n Nicolet 1180 BASIC language (Appendix B). The trace at the f 2 ' resonance Figure 3.24: A phase-sensitive, tilted, 2D J spectrum, simulated «-i»8 the LINSIMprogramme given Appendix B, for values of T*2=1.2 s; T2=1.0 s; DR2=0.5 Hz; DR^O.05 Hz. Note the f l tails set at 135° to the f]_ axis. - 115 -frequency shows the c h a r a c t e r i s t i c lineshape behaviour observed i n e a r l i e r examples. The t i l t routine has the e f f e c t of t i l t i n g the t a i l s of the signals i n the f^ domain ("f-^ t a i l " ) by 45°, as was already seen i n Figure 3.21. This feature can also be seen i n the simulated 2D J spectrum in Figure 3.24. In order to make d i r e c t comparison between the simulated and experimental p l o t s , selected phase-sensitive cross-sections from a 2D J spectrum of a singl e t are shown i n Figure 3.25. A noticeable feature i n the above traces is the band of noise that appears along the " f ^ t a i l " . This noise r e s u l t s from experimental imperfections and appears along the f^ domain at the resonance frequency, and is referred to as " t ^ noise" (21); because this noise i s random, i t can be minimized by signal averaging. For p r a c t i c a l purposes, the re s o l u t i o n enhancement e f f e c t which is i m p l i c i t l y associated with the phase-sensitive t i l t routine often helps with the measurement of high r e s o l u t i o n information which might otherwise be obscured i n an absolute value d i s p l a y . However, one should be aware of the lineshape c h a r a c t e r i s t i c s and also i t s e f f e c t on neighbouring l i n e s . Figure 3.26 shows a comparison of simulated peaks, before and a f t e r the t i l t operation, for d i f f e r e n t l i n e widths. The l i n e narrowing e f f e c t for the broadest peak (Av^ = 0.64 Hz) is p a r t i c u l a r l y noteworthy. This feature has already been i n this laboratory used to advantage i n the study of resonances which have been broadened by paramagnetic reagents (56)^ conventional, absolute mode displays of the above multiplets are so broad that i n d i v i d u a l couplings cannot be detected, whereas those subjected to the phase-sensitive t i l t are c l e a r l y resolved. simulated sub-spectrum also showed a loss i n si g n a l i n t e n s i t y . It should be possible to resolve the mul t i p l e t patterns i n the above example by applying r e s o l u t i o n enhancement i n both fj_ a n d f 2 domains. A B 3 0 - i -V-— . — ^ v -oH 6 2 Hz - 3 0 J -7^- ./v i h- 1 ON I t; HZ Figure 3.25: Experimental 2D J plots of a s i n g l e t . The multi-trace plot B shows the t i l t e d spectrum in the absolute value mode; A and C are selected traces i n the phase-sensitive mode ( c f . F i g . 3.23). - 117 -(a) (b) B A 8 Hz Figure 3.26: Simulated, phase-sensitive, t i l t e d J spectra (A) and normal spectra (B). a, b, and c correspond to T 2 values of 1.5, 1.0 and 0.5 s re s p e c t i v e l y . The d i g i t a l r esolution for the 2D traces were taken as DRi=0.05 and DR2=0.5 Hz. The l i s t i n g of the BASIC programme which was used for c a l c u l a t i n g B i s given i n Appendix B. - 118 -Figure 3.27 i l l u s t r a t e s the influence of neighbouring lines in a multiplet (see F i g . 3.20). Figure 3.27A i s an experimental sub-spectrum of a doubleted doublet, showing the interference from the dispersive t a i l of a methyl resonance located 20 Hz away. The lower trace was obtained by simulation, using the same frequencies as the experimental pl o t , but with a r b i t r a r y T 2 values as indicated. Direct comparison between the experimental and simulated traces i s not possible, both because the experimental data were obtained with limited d i g i t a l r e s o l u t i o n and include unresolved long-range couplings and also because i t is d i f f i c u l t to measure with p r e c i s i o n the T 2-values in both dimensionswhich are necessary for the simulation. However, Figure 3.27 helps to i l l u s t r a t e the undesireable interference of (intense) neighbouring resonances; as mentioned e a r l i e r the f^ t a i l w i l l also carry a band of noise which could further d i s t o r t the sub-spectra of i n t e r e s t . A comparison of the cross-sections obtained by the various methods are given i n Figure 3.28. Although the three p a r t i a l J spectra ( F i g . 3.28B, C and D) show a s i g n i f i c a n t improvement in res o l u t i o n as compared with the normal spectrum ( F i g . 3.28A), the d i s t o r t i o n s towards the base of the peaks in the absolute value mode ( F i g . 3.28D) display become apparent when overlapping peaks are involved. The lineshapes are considerably improved using the power mode display ( F i g . 3.28C) and phase-sensitive cross-sections ( F i g . 3.28B). The lineshape c h a r a c t e r i s t i c of the l a t t e r is as expected, as was noted e a r l i e r i n the simulated cross-sections (eg. F i g . 3.27B). The baseline d i s t o r t i o n , however, does not a f f e c t the measurement of coupling constants. In demonstrating the display of the proton-decoupled proton spectrum we draw attention to the c h a r a c t e r i s t i c l i n e broadening associated with the - 119 -Figure 3.27: B i s an experimental sub-spectrum of a doubleted doublet (J=3 and 11.6 Hz) showing the interference from an intense s i n g l e t (three times the t o t a l i n t e n s i t y of the m u l t i p l e t ) located 20 Hz away. The centre component i s the f 2 t a i l and the outer dispersive component is the f j t a i l (note the noise on the l a t t e r ) . A was simulated using T 2 and T*2 values of 1.1 s and 0.8 s for the m u l t i p l e t , and 1.6 s and 1.3 s for the s i n g l e t r e spectively. (Note: the simulation was not meant to reproduce the exact lineshape c h a r a c t e r i s t i c s of B; see t e x t ) . - 120 Figure 3.28: (A) The three proton multiplets of furoic acid (11) from a conventional 270 MHz spectrum. B, C and D are sections of the p a r t i a l J spectra were obtained from phase-sensitive, power and magnitude mode 2D J spectra, r e s p e c t i v e l y . A l l data processing was done on the same o r i g i n a l time-domain signals with exponential m u l t i p l i c a t i o n i n both time dimensions. - 121 -absolute mode i n Figures 3.29C and D which represent the i n t e g r a l or summed projection and the "maximal" projection ( p r o f i l e ) , r e s p e c t i v e l y (Sec. 3.1.3). In the l a t t e r mode only the maximum point corresponding to each f^' value is plotted, thereby representing a p r o f i l e of the 2D J spectrum, as viewed perpendicular to f^'• "The analogous projections from the power spectrum are i l l u s t r a t e d i n Figures 3.29E and F, and shows the d r a s t i c change in r e l a t i v e peak heights since the i n t e n s i t i e s are now equal to the square of their normal values. Although the i n t e g r a l projection from a phase-sensitive 2D J spectrum cannot be used to obtain a proton-decoupled proton spectrum due to the net can c e l l a t i o n of a l l signals (23), the "maximal" projection can be s a t i s -f a c t o r i l y used to represent this spectrum, and is i l l u s t r a t e d i n Figure 3.29B. 3.3.4 Generalized a c q u i s i t i o n of spin-echo data - Integrated NMR experiments The various experiments discussed so far, namely the SEFT, SEAS and 2D J, a l l u t i l i z e the same basic spin-echo pulse sequence of Carr and P u r c e l l ; only the time at which the data is acquired and the subsequent data processing routines determine the f i n a l outcome of these experiments. With these close s i m i l a r i t i e s i n mind i t is apparent that i t should be possible to acquire a "general" data matrix which could then be " s e l e c t i v e l y " processed i n various ways to provide a number of d i f f e r e n t experimental r e s u l t s such as (half-)SEFT, SEAS, 2D J and delayed 2D J spectra. The u t i l i t y of t h i s experiment w i l l be discussed using as an i l l u s t r a t i v e example, a sample containing a mixture of 10% (0.01M) dextran (M.Wt. ca. 10,000 a l-»6 linked polymer of D-glucopyranose,3) and 0.1M methyl S-D-xylopyranoside. The pulse sequence for this "generalised" experiment i s represented by, {90° - n.T - 180° - Acquisition} Hg H r ^ " ^ c ° 2 H CHCI, B X 7 7 75 7 3 71 6 9 6 7 6 5 8 (ppm) Figure 3.29: (A) The conventional 270 MHz proton spectrum of a mixture of furoic acid (11) and chloroform in C D C I 3 solution. (B) The corresponding proton-decoupled proton spectrum derived from a phase-sensitive 2D J spectrum S ( f ' i , f ' 2 ) by taking a "maximal" projection (see text) onto the f 2 axis. Similarly (C) and (D) show the summed and maximal projections respectively of the Hp and C H C I 3 region derived from a magnitude spectrum; the corresponding power-mode displays are shown in (E) and (F), respectively. A l l processing was done on the same original data and a l l the spectra are scaled with respect to the C H C I 3 peak. Note the line broadening effect of the magnitude mode and the drastic change in the relative intensities in the power mode. - 123 -analogous to the 2D J pulse sequence, where n = 0, 1, 2, , N-1 (N i n this case may not be a binary number). The acquired whole-echo data matrix is represented i n Figure 3.30, showing every twelfth free induction decay (or echo-envelope). The i n i t i a l trace (T = 0 ms) is equivalent to a conventional FID s i g n a l obtained with a 270° f l i p angle and on Fourier transformation i t y i e l d s the conventional ID spectrum. The half-echoes ( ) when subjected e i t h e r i n d i v i d u a l l y to s i n g l e , or c o l l e c t i v e l y to double, Fourier transformations w i l l provide e i t h e r a series of SEFT spectra or the "standard" 2D J spectrum.* It i s apparent from the conventional spectrum of the sample under consideration that no useful information concerning the monomer can be extracted from the 2D J spectrum due to the dynamic range problem; this makes i t e s s e n t i a l to obtain a p a r t i a l l y relaxed 2D J spectrum of methyl B-D-xyloside a f t e r a s u i t a b l e i n i t i a l delay time T^, as discussed in Section 3.3.1. Whole-echo Fourier transformation provides ID p a r t i a l l y relaxed SEAS spectra for s p e c t r a l s i m p l i f i c a t i o n and also approximate values for semi-q u a l i t a t i v e spectral analysis as discussed in Section 2.3. The experimental procedure described here offers a number of advantages over conventional experimental routines which are usually accomplished by subjecting a spin system to a predetermined pulse sequence and data processing cycle. The obvious advantage of the "integrated experiments" approach is the p o t e n t i a l saving of data a c q u i s i t i o n time; c l e a r l y this saving is dependent on the t o t a l number of separate experiments which would have to be performed to obtain the same t o t a l information, and may be considerable for complex systems ^Since the algorithms for the various data processing steps are generally written for data arrays with a size equal to the power of two, the ID or 2D data arrays created i n this experiment may have to be appropriately z e r o - f i l l e d to generate a suitable data s i z e . - 124 -Tmsec 0 176 352 528 704 880 Normol ID Spectrum 2D J Wiffw1  SEAS H 1 W Figure 3.30: The f i r s t , and subsequently every twelfth, spin-echo signal acquired on 4K word-size data blocks with a constant increment in t\ of 16 ms for the solution described i n the text. Data processing of the half-echoes ( ) acquired from T=0 onward gives the conventional 2D J spectrum; processing of those after T^ ( ) gives a p a r t i a l l y relaxed 2D J spectrum. Fourier transformation of i n d i v i d u a l whole echoes ( ) give SEAS information as a function of various delay times. - 125 -when studied at high d i l u t i o n ; this advantage is even more obvious when handling r e l a t i v e l y unstable substances. However, an equally important advantage is that this integrated approach also provides the experimentalist with "independent" methods for analysing spectra which can be chosen a f t e r the data a c q u i s i t i o n has been completed. In practice i t i s often found that the less complicated regions of the spectrum can be analysed by the ID experiments described e a r l i e r , and i t is advantageous to process only the complex regions of the spectrum by the 2D techniques i f data processing time i s to be minimised. The type of experiments mentioned above requires computer systems with r e l a t i v e l y large data storage and f l e x i b l e data processing c a p a b i l i t i e s . The half-echoes can be extracted from the whole data matrix by simply l e f t - s h i f t i n g the time-domain echo-envelope signals by nT/DW number of points (DW = dwell time). The suitable i n i t i a l delay, T^ ,, for the D2D J experiment may be obtained d i r e c t l y by observing the corresponding SEAS traces such as those shown i n Figure 3.30. - 126 -References (Chapter III) 1. Jeener, J . Ampere International Summer School, Basko Polje, Yugoslavia, A p r i l , 1971. 2. Ernst, R. Chimi (1975) 29, 179. 3. Muller, L., Kumar, A., Ernst, R.R. J . Chem. Phys. (1975) 63, 5490. 4. Aue, W.P., Bartholdi, E., Ernst, R.R. J . Chem. Phys. (1976) 64, 2229. 5. Hester, R.K., Ackerman, J.L., Cross, V.A., Waugh, J.S. Phys. Rev. L e t t . (1975) 34, 993. 6. A l i a , M., Lippmaa, E. Chem. Phys. L e t t . (1976) 37, 260. 7. Kumar, A., Welti, D., Ernst, R.R. J . Magn. Reson. (1975) 18, 69. 8. Wokaun, A., Ernst, R.R. Chem. Phy. L e t t . (1977) 52, 407. 9. Pouzard, G., Sukumar, S., H a l l , L.D. J . Am. Chem. Soc. (1981), i n press. 10. Maudsley, A.A., Ernst, R.R. Chem. Phy. L e t t . (1977) 50, 368. 11. Maudsley, A.A., Muller, L., Ernst, R.R. J . Magn. Reson. (1977) 28, 463. 12. Bodenhausen, G., Freeman, R. J . Magn. Reson. (1977) 28, 471. 13. Bodenhausen, G., Freeman, R., Turner, D.L. J . Chem. Phys. (1976) 65, 839. 14. Muller, L., Kumar, A., Ernst, R.R. J . Magn. Reson. (1977) 25, 383. 15. Hoffman, R.A., Forsen, S. "Progress i n NMR Spectroscopy:, Emsley, J.W., Feeney, J . , S u t c l i f f , L.H. Eds.; Pergamon Press: Oxford, 1966; Vol. 1, Chapter 2. 16. Freeman, R., Morris, G.A. B u l l . Magn. Reson. (1979) 1_, 5. 17. Morris, G.A. Ph.D. D i s s e r t a t i o n , Oxford University, Oxford, 1979. 18. Carr, H.Y., P u r c e l l , E.M. Phys. Rev. (1954) 94, 630. 19. Freeman, R., H i l l , H.D.W. "Dynamic Nuclear Magnetic Resonance Spectroscopy", Jackman, L.M., Cotton, F.A. Eds.; Academic Press: New York, 1975; Chapter 5. son. - 127 -20. Rabenstein, D.L., Nakashima, T. Anal. Chem. (1979) 5_1, 1465. 21. Bodenhausen, G., Freeman, R., Niedermeyer, R., Turner, D.L. J . Magn.  Reson. (1977) 26, 133. 22. Freeman, R., H i l l , H.D.W. J . Chem. Phys. (1971) 54, 301. 23. Nagayama, K., Bachmann, P., Wuthrich, K., Ernst, R.R. J . Magn. Res< (1978) 31, 133. 24. H a l l , L.D., Sukumar, S. J . Magn. Reson. (1980) 38, 555. 25. Aue, W.P., Karhan, J . , Ernst, R.R. J . Chem. Phys. (1976) 64, 4226. 26. H a l l , L.D., Sukumar, S., S u l l i v a n , G.R. J . Chem. Soc. Chem. Commun. (1979) 292. 27. Nagayama, K., Wuthrich, K., Bachmann, P., Ernst, R.R. Naturwissenschaften (1977) 64, 581. 28. Nagayama, K., Wuthrich, K., Bachmann, P., Ernst, R.R. Biochem. Biophys.  Res. Commun. (1977) 78, 99. 29. H a l l , L.D., Manville, J.F., Tracey, A. Carbohydr. Res. (1967) 4, 514. 30. Bachmann, P., Aue, W.P., Muller, L., Ernst, R.R. J . Magn. Reson. (1977) 28, 29. 31. Freeman, R., Kempsell, S.P., L e v i t t , M.H. J . Magn. Reson. (1979) 34, 663. 32. L e v i t t , M.H., Freeman, R. J . Magn. Reson. (1979) 34, 675. 33. Bax, A., Mehlkopf, A.F., Schmidt, J . J . Magn. Reson. (1980) 40, 213. 34. H a l l , L.D., Sukumar, S. J . Magn. Reson. (1980) 38, 555. 35. DeMarco, A., Wuthrich, K. J . Magn. Reson. (1976) 24, 201. 36. Fer r i g e , A.G., Lindon, J.C. J . Magn. Reson. (1978) 31, 337. 37. H a l l , L.D., Sukumar, S. Carbohydr. Res. (1979) 74, C l . 38. H a l l , L.D., Morris, G.A., Sukumar, S. J . Am. Chem. Soc. (1980) 102, 1745. 39. H a l l , L.D., Sukumar, S. J . Magn. Reson. (1980) 40, 405. - 128 -40. Kowalewski, V.J. "Progress i n NMR Spectroscopy", Emsley, J.W., Feeney, J. , S u t c l i f f , L.H. Eds.; Pergamon Press: Oxford, 1979; Vol. 5, Chapter 1. 41. Feeney, J . , Partincton, P. J . Chem. Soc. Chem. Commun. (1973) 611. 42. Noggle, J.H., Schirmer, R.E. "The Nuclear Overhauser E f f e c t " , Academic Press: New York, 1971. 43. H a l l , L.D., Sanders, J.K.M. J . Am. Chem. Soc. (1980) 102, 5703. 44. H a l l , L.D., Morris, G.A., Sukumar, S. Carbohydr. Res. (1979) 79, C7. 45. H a l l , L.D., Hunter, B.K., Sanders, J.K.M., Sukumar, S. to be published. 46. Freeman, R., Morris, G.A., Turner, D.L. J . Magn. Re son. (1977) 26^, 373. 47. Bodenhausen, G., Freeman, R., Morris, G.A., Turner, D.L. J . Magn. Reson. (1977) 28, 17. 48. Bodenhausen, G., Freeman, R., Morris, G.A., Turner, D.L. J . Magn. Reson. (1978) 31, 75. 49. Reuben, J . "Progress i n NMR Spectroscopy", Emsley, J.W., Feeney, J . , S u t c l i f f , L.H. Eds,; Pergamon Press: Oxford, 1973; V o l . 9, Part 1. 50. Shaw, D. "Fourier Transform NMR Spectroscopy", E l s e v i e r : Amsterdam, 1976. 51. Martin, M.L., Martin, G.J., Delpuech, J . J . " P r a c t i c a l NMR Spectroscopy", Heyden: London, 1980. 52. Patt, S.L., Sykes, B.D. J . Chem. Phys. (1971) 56, 3182. 53. Demco, D.E., Van Hecke, P., Waugh, J.S. J . Magn. Re son. (1974) l j i , 467. 54. Jessen, J.P., Meakin, P., Kneissel, G. J . Chem. Phys. (1973) 59, 1775. 55. H a l l , L.D., Sanders, J.K.M., Sukumar, S. J . Chem. Soc. Chem. Commun. (1980) 366. 56. J.K.M. Sanders, unpublished data. - 129 -CHAPTER IV ASSIGNMENT OF NMR SPECTRA BY 2D FOURIER TRANSFORM METHODS - 130 -4.1 Introduction Methods for assigning complex proton spectra contribute an important element i n the s t r u c t u r a l e l u c i d a t i o n of molecules using NMR spectroscopy. Simple molecules or spectra (which are usually weakly coupled and well dispersed) are generally assigned on the basis of chemical s h i f t s , coupling constants and r e l a t i v e l i n e i n t e n s i t i e s . S p i n - l a t t i c e r e laxation times of i n d i v i d u a l groups of protons may also be used to assign spectra of complex molecules since they are related i n most cases to (dipole-dipole) relaxation contributions from neighbouring protons. The d i f f e r e n t i a l i n relaxation 1 13 properties may also be used to simplify spectra (eg. H or C) v i a the use of p a r t i a l l y relaxed spectra (1). One of the most useful and widely used assignment techniques is s e l e c t i v e , spin-decoupling which is available as a standard feature i n most modern high-resolution spectrometers. The success of this technique i s to a great extent dependent on the r e l a t i v e dispersion of the signals, which must be s u f f i c i e n t so that the i r r a d i a t i o n frequencies can be applied s e l e c t i v e l y to just one chosen resonance. Although spectra complicated by overlap such as that shown in Figure 3.13 may be analysed by the INDOR technique (2), this cannot yet be regarded as a routine experiment mainly because i t i s demanding i n terms of time and instrumental s t a b i l i t y . However, i t i s worthwhile noting that the improved s e n s i t i v i t y and s t a b i l i t y of modern h i g h - f i e l d spectrometers does enable nuclear Overhauser enhancement (NOE) e f f e c t s to be observed conveniently and accurately, and to provide s t r u c t u r a l information on molecules; because proton NOE and s p i n - l a t t i c e r e l a x a t i o n studies are related to interproton interactions "through space", they provide information on interproton distances and hence the stereochemistry of complex molecules (3,4). - 131 -Recently, novel assignment techniques based on homonuclear (5,6,7) and heteronuclear (8,9) 2D Fourier transform spectroscopy have been reported. The r e s u l t i n g 2D spectra provide in a rather unique way c o r r e l a t i o n between two frequencies, analogous to information obtained by double resonance techniques. In the present study, just two of these double Fourier transform techniques 13 1 have been evaluated namely carbon-13-proton ( C- H ) chemical s h i f t c o r r e l a t i o n spectroscopy (9) and zero-quantum t r a n s i t i o n (2D) spectroscopy (10,11,12). The l a t t e r w i l l be presented in the next chapter and includes ZQT c o r r e l a t i o n experiment provides a 2D spectrum in which the and f^ dimensions represent carbon-13 chemical s h i f t s and the corresponding d i r e c t l y bonded proton chemical s h i f t s , r e s p e c t i v e l y . The (homonuclear) proton zero-quantum t r a n s i t i o n 2D spectrum represent i n the f^ dimension, ZQT frequencies which are related to the frequency " d i f f e r e n c e s " of scalar coupled protons. A method based on homonuclear 2D J spectroscopy which distinguishes between peaks that arise from homo- and heteronuclear scalar couplings is also presented l a t e r i n this chapter. 13 1 4.2.1 C- H chemical s h i f t c o r r e l a t i o n (2D) spectroscopy Maudsley and Ernst (8) have described an experiment to i n d i r e c t l y detect carbon-13 resonances using a spectrometer which is designed to detect proton resonance frequencies; this is based on the "coherent transfer of transverse magnetization" between carbon-13 and proton spin-systems and u t i l i s e s the concept of double Fourier transformation. The main disadvantage of t h i s technique for p r a c t i c a l applications arises because the r e s u l t i n g 2D spectrum contains p o s i t i v e and negative lines which re s u l t s i n the net c a n c e l l a t i o n of sp e c t r a l analysis based on the density matrix formalism. s h i f t - 132 -signals when the whole 2D spectrum is integrated (or projected onto the 13 1 or a x i s ) . The C- H s h i f t c o r r e l a t i o n experiment described here is that of Freeman et al_. (13) and is based on a pu b l i c a t i o n by Maudsley et» a l . (9); the f i n a l display is a 2D spectrum with the f^ and £^ axes representing "decoupled" proton, and carbon-13 spectra, r e s p e c t i v e l y . Although the features of chemical s h i f t c o r r e l a t i o n experiments such as i n t e n s i t i e s and frequencies of lines can be predicted by using the density matrix approach, i t may be convenient to understand the experiment i n terms of a " s e m i c l a s s i c a l " approach (14,15), which is presented i n the next section.* In these discussions the magnetization vector model i s used i n conjunction with the energy levels and spin population de s c r i p t i o n for a simple explanation of the r e s u l t i n g 2D spectrum. 4.2.2 The experiment The pulse sequence used i n this study to obtain carbon-13-proton chemical s h i f t c o r r e l a t i o n maps i s given i n Figure 4.1A. The features and the modifications of this experiment are best understood by f i r s t considering the o r i g i n a l experiment of Maudsley and Ernst (8) as represented i n Figure 4.IB. The i n i t i a l 90° pulse applied to the proton spin system creates a transverse magnetization i n a reference frame rot a t i n g at the proton transmitter frequency. During the evolution period the proton magnetization accumulates a phase angle with respect to the y' d i r e c t i o n equal to 2 T r f Q t ^ (rad.), where f Q i s the of f s e t frequency with respect to the proton transmitter. The second 90° proton pulse f l i p s the y 1 component of this magnetization onto the l o n g i t u d i n a l a x i s ; the component thus created w i l l be a function of the ISuch semiqualitative arguments cannot be used i n the case of homonuclear s h i f t c o r r e l a t i o n experiments. 9 0 ° 9 0 c 1H Noise-decoupling 1 8 0 ° 9 0 ° 13, c Detection 1/2 t, 1/2t, A , A 2 t2 9 0 ° 9 0 ° LO 00 9 0 ° B „ I Detection _ I 1 3 C 2 Figure 4.1: (A) The pulse sequence used for obtaining 1 3 C - 1H c o r r e l a t i o n maps (Aj-3.3 ms; A2=2.2 ms). (B) The o r i g i n a l pulse sequence by Maudley and Ernst (8) for coherent transfer of transverse magnetization i n heteronuclear systems. - 134 -evolution period t^, and is given by c o s 2 T r f Q t ^ . It w i l l be recalled from Chapter I that the longitudinal magnetization is related to the population difference between two energy levels; hence the effect of the two proton pulses is to perturb the proton spin populations in a coherent fashion, related to the (proton) frequency f Q . Since carbon-13 nuclei share a common energy level with the protons (assuming they are scalar coupled), the spin populations across the carbon levels w i l l be indirectly changed from their equilibrium values by the proton pulses. The net effect therefore is a coherent transfer of (proton) transverse magnetization into the carbon-13 system. This is analogous to population transfer experiments in ID NMR (16). These experiments provide an improvement in sensitivity of nuclei with low gyromagnetic ratio (INEPT, Insensitive Nuclei Enhanced by Polarization Transfer). This coherent perturbation of spins across the carbon-13 energy levels can be monitored by detecting the carbon signals, which causes amplitude  modulation as a function of t^.* The modulation frequencies are revealed by an experiment performed in accordance with 2D spectroscopy. The f^ axis of the resulting 2D spectrum represents the conventional proton-coupled carbon-13 spectrum and the f^ axis will represent the carbon-13 sa t e l l i t e proton spectrum. Although such an experiment provides a l l connectivity information regarding the carbon-13-proton sub-systems i t may often be d i f f i c u l t to extract this information for complex molecules for the following reasons: ^The 13C longitudinal magnetization prior to the, 90°, 13(j sampling pulse is proportional to the amplitude of the detected signal; hence the latter w i l l be amplitude modulated as a function of t\. This behaviour should be compared with the (^ H) 2D J experiment where the evolution of the transverse magnetization is monitored, producing a phase modulated signal as a function of tj_. - 135 -a) for each (proton-coupled) carbon-13 resonance i n f2» the trace represents a carbon-13 s a t e l l i t e proton spectrum; t h i s complicates the 2D spectrum by introducing many overlapping l i n e s , b) the i n t e n s i t i e s of the m u l t i p l e t components deviate from the conventional patterns with h a l f the signals along an f^ trace being p o s i t i v e and the rest negative, 13 1 c) a d d i t i o n a l l i n e s due to long range C- H couplings may also appear in the 2D spectrum. C l e a r l y for chemical a p p l i c a t i o n purposes i t i s desireable to simplify such a 2D spectrum by, for example, by (some sort of) decoupling in both dimensions; this should provide a simple c o r r e l a t i o n map between proton and carbon chemical s h i f t s . Unfortunately, decoupling during e i t h e r the detection period (eg. broad band noise decoupling of protons), or the evolution period (eg. by applying a 180° carbon pulse at Ht^) causes the p o s i t i v e and negative signals to coincide, thereby leading to t h e i r c a n c e l l a t i o n . Solutions to these problems were suggested, and r e a l i z e d in pr a c t i c e , by Maudsley et aj_. (9) and by Bodenhausen et_ a_l. (14). The v a r i a t i o n of Freeman et a_l. (13) which appears to be more suitable for chemical applications is given in Figure 4.1A. The p r i n c i p l e behind this experiment i s to introduce suitable phase s h i f t s i n both time domains in order to reinforce the signals ( a r i s i n g from one-bond spin-spin couplings), rather than cancel them. The high- and low-frequency carbon components (due to C-H coupling) in the detected signal using the pulse sequence shown in Figure 4.IB have opposite phase; the delay ^ (=1/2J) introduces a phase s h i f t between the corresponding high- and low-frequency components so that they are brought together i n phase. As a r e s u l t , the noise decoupling which is subsequently - 136 -employed during the detection period does not cancel the s i g n a l . S i m i l a r l y , a phase-shift i s introduced i n the t^ domain by the delay A in order to prevent s i g n a l c a n c e l l a t i o n . In practice A i s optimised for the one-bond carbon-13-proton spin-spin couplings; as a r e s u l t , the signals due to 13 1 long-range C- H couplings are cancelled, which r e s u l t s i n further s i m p l i f i c a t i o n of the 2D spectrum. In the example chosen in t h i s study, compromise settings of A^=3.3 ms and A 2=2.2 ms were used.* (The one-bond coupling constants in the examples chosen were 130-150 Hz). 4.2.3 Experimental r e s u l t s It w i l l be r e c a l l e d from Chapter III that although chemical s h i f t s and coupling constants of m u l t i p l e t s can be e a s i l y measured from complex spectra by 2D J spectroscopy, assignment of these resonances may be p r a c t i c a l l y 13 1 impossible by conventional methods. C- H s h i f t c o r r e l a t i o n spectroscopy o f f e r s a convenient means of assigning these resonances. Thus i n the case of the anomeric mixture of cellobiose ( F i g . 3.13) the previously assigned carbon-13 spectrum was used to assign the correlated protons (Table 4.1). 13 1 The combination of proton 2D J spectroscopy and C- H s h i f t correlated spectroscopy provides a powerful method for resolving and assigning 13 1 complex proton spectra. Since the C- H s h i f t correlated spectroscopy is e s s e n t i a l l y a low resolution technique, the main purpose of the experiment is to obtain the approximate (£a. + 0.01-0.02 ppm) values for of the chemical s h i f t s of those protons which are associated with i n d i v i d u a l carbons by a 13 1 one-bond C- H coupling. *It should be noted that increasing r e 8 u l t s i n the loss of i n i t i a l points of the detected signal r e s u l t i n g i n a loss of s e n s i t i v i t y . Table 4.1 Proton and Carbon-13 NMR Parameters for Cellobiose 1 2 3 B-D-glucopyranosyl 103.37 73.97 76.31 70.28 76.80 61.41 Carbon-13 s h i f t 6-D-glucopyranose 96.56 74.70 75.10 79.43 75.60 60.87 a-D-glucopyranose 92.63 72.04 72.15 79.56 70.92 60.74 Proton s h i f t B-D-glucopyranosyl 4.52 3.33,3.32° 3.52 3.41 3.51 3.93,3.74 B-D-glucopyranose 4.67 3.29 3.63 d 3.63 d 3.59 d 3.96,3.81 a-D-glucopyranose 5.23 3.58 3.83 3.65 3.96 3.88d J l , 2 J2,3 J3,« J«,5 J5,6A J5,6B J6A,6B Proton c o u p l i n g 6 B-D-glucopyranosyl 7.9 9.5 8.8 9.9 2.4 5.8f 12.5 constant B-D-glucopyranose n Q g g 2.3 4.8f 12.3 7.9 9 . J a-D-glucopyranose 3.8 9.8 8.6 g g g g a+ 0 02 nnm referred to external TMS v i a i n t e r n a l dioxane at 67.406 b ±0.02 ppm, referred to i n t e r n a l T SP! c ^ ^ ^ ^ r e s p e c t i v e l y . <> a n i m a t e s h i f t ; strongly coupled, e ± 0 3 Hz, signs not determined. f assignment of reference 21 reversed. 8 strongly coupled m u l t i p l e t . A l l values are reported f o r a 0.3M so l u t i o n in D 20 at 22±2°C. - 138 -In a second example, 5epi-sisomycin (12), the proton spectrum shows ten out of the t o t a l seventeen " m u l t i p l e t s " well dispersed at 400 MHz. Therefore i n t h i s case, conventional homonuclear spin-decoupling and NOE studies provided most of the proton spectral assignments. A point of in t e r e s t i s the symmetry of the central cyclohexane r i n g . As expected, H-4 and H-6 (although they have d i f f e r e n t chemical s h i f t s ) are almost i d e n t i c a l l y oriented in r e l a t i o n to the neighbouring protons to which they are coupled; s i m i l a r l y , H-l and H-3 also show i d e n t i c a l s p a t i a l r e l a t i o n s h i p with the rest of the protons i n the r i n g . This feature makes i t impossible to assign these protons by spin-decoupling techniques. Nuclear Overhauser enhancement studies can be used to assign the H-4 and H-6 m u l t i p l e t s , by es t a b l i s h i n g the s p a t i a l r e l a t i o n s h i p (eg. using molecular models) of these protons with those of the two neighbouring rings (see the structure of 12 given in Figure 4.4). Thus i r r a d i a t i o n of H - l " induced an NOE i n H-6; s i m i l a r l y the H-4 resonance was assigned by H-l'. With H-4 and H-6 assigned, spin decoupling of H-4 (because i t i s well dispersed, see F i g . 4.3) gave the assignment of H-3, and hence H-l. The t o t a l assignment of the proton resonances are s i m p l i f i e d to a great extent by analysing the r e s u l t s from both double resonance and 2D J spectroscopy (Table 4.2). With the completed assignment of the proton resonances i t was a t r i v i a l 13 1 matter to assign the carbon-13 spectrum by the use of C- H s h i f t c o r r e l a t i o n spectroscopy. Figure 4.2 shows the normal carbon-13 spectrum obtained at 68 MHz together with traces corresponding to the proton spectrum associated with each carbon obtained from the s h i f t c o r r e l a t i o n spectrum. In this example, the wide sp e c t r a l width of the carbon-13 spectrum (eau 6300 Hz 13 1 from the transmitter, in the C- H c o r r e l a t i o n experiment) exceeded the A U 8(ppm)140 120 - 1 — 100 80 60 40 - r -20 Figure 4.2: (A) The 68 MHz l 3 C spectrum of 5,epi-sisomycin (12). (0.26M i n D2O). (B) The z e r o - f i l l e d i n d i v i d u a l traces obtained from the 2D spectrum, corresponding to the proton spectrum are shown above; the f^ scale represents the frequency o f f s e t with respect to the transmitter. The trace corresponding to a CH 2 sub-system with non-equivalent protons show peaks representing both the geminal protons. Some of the d i s t o r t i o n s i n lineshapes and a r t i f a c t s i n some of the cen t r a l traces are due to imperfections i n the 180° pulse on carbon. Experimental parameters: DRj=13 Hz; DR2=6.2 Hz; t^ increment=150 ps; si z e of data matrix (t 2xti)=2048x256; SW2=6300 Hz; SW^+1667 Hz. B A S(ppm) 6 4 Fieure 4.3: (A) The 400 MHz proton spectrum of 5,epi-sisomycin (0.1M D 20). (B) prfton-d c o p i e d proton spectrum and (O the cross-sections correspondingj t.> each proton v - a n d H-3'fl have i d e n t i c a l chemical s h i f t s . D i g i t a l f i l t e r i n g * DR 2=U17 Hz; t x increment=13.33 ms; size of data matrix (t 2x t l)=4096xl28; SW1-2400 Hz, SW1=+18.7 Hz. (* correspond to spikes from the transmitter). - 141 -Figure 4.4: The *3C- s h i f t c o r r e l a t i o n 2D spectrum of the h i g h - f i e l d region of 5,epi-sisomycin (12) plotted i n the absolute value mode. The zero-frequency i n f i corresponds to the proton transmitter frequency; the signals along t h i s frequency correspond to the unmodulated carbon-13 component. Some of the asymmetry of the two halves may be due to inadequate d i g i t a l r e s o l u t i o n ( c f . F i g . 4.2) and imperfections i n the 180° pulse. - 142 -Table 4.2: Proton and Carbon-13 NMR parameters for 5,epi-sisomycin. a b c Carbon s h i f t s Proton s h i f t s Coupling constants C - l " 102.49 6 H-l " 5.05 6 l " - 2 " 4.2 Hz C-2" 69.95 H-2" 3.78 2"—3" 10.8 C-3" 64.07 H-3" 2.70 5"-5" 12.5 a e C-4" 73.02 — C-5" 68.40 H-5" a 3.40 H-5" 3.92 1 3 C H V -C 22.33 e CH -C 1.25 1 3CH3--N 37.59 3 CH3-N 2.56 C - l ' 96.79 H-l' 5.17 l ' - 2 ' 2.6 C-2' 47.06 H-2' 3.10 • 2 f-3' 10.4 d a C-3' 25.70 H-3' 2.05 2'-3' 6.4 a e H-3' 2.24 d 3'-3' 16.6 e a e C-4' 98.89 H-4' 4.98 3'-4' a 1.9 C-5* 147.65 — 3*-4' e 6.4 C-6' 42.72 H-6' 3.27 C- l 45.1 H-l 3.19 1-2 a 12.5 C-2 35.97 H-2 1.15 1-2 4.5 a e C-3 H-2 2.05 2 -2 12.5 e a e C-3 47.06 H-3 3.11 2 -3 e 4.6 C-4 80.30 H-4 3.58 2 -3 a 12.5 C-5 69.51 H-5 4.36 3-4 10.4 C-6 85.5 H-6 3.37 4-5 2.8 5-6 3.0 6-1 10.1 3 68 MHz data; r e f . external TMS v i a i n t e r n a l dioxane. 400 MHz data; c d r e f . TSP. ca.+0.2 Hz. Strongly coupled. - 143 -a b i l i t y of our spectrometer* to apply a uniform 180° pulse to a l l carbon-13 spins (17) this introduced a r t i f a c t s i n the 2D spectrum corresponding to the resonances about 3000 Hz away from the transmitter. The traces from the 2D spectrum i n Figure 4.2 were obtained from two separate experiments, with the transmitter placed on either side of the spectrum (the low - f i e l d quarternary carbon was ignored in this experiment since i t does not show any response i n f ^ ) . Even so, the e f f e c t of imperfections can be noticed i n some of the f^ traces corresponding to the carbon-13 signals i n the central region of the spectrum. It should be mentioned here that phase a l t e r n a t i o n of the 180° pulse, which is generally used i n the spin-echo 13 1 sequence to suppress imperfections cannot be applied i n the C- H experiments (18). 13 Based on the above experiments we i n f e r that the advantages of the C-*H s h i f t c o r r e l a t i o n for the a p p l i c a t i o n i n chemistry are summarised below: a) Unlike i t s ID equivalent, s e l e c t i v e spin-decoupling (19), the 2D, 13 1 C- H s h i f t c o r r e l a t i o n experiment is not limited by overlap of proton resonances. Insofar that i t can be performed using a single instrumental setting to provide simultaneously a l l the correlated frequencies. b) For molecules such as carbohydrates, for example, where most of the proton chemical s h i f t s are s i m i l a r , the wider dispersion of the carbon-13 resonances can be advantageously used to improve the e f f e c t i v e chemical s h i f t IWork i s nearing completion on the present spectrometer to provide: a) quadrature detection of the signals so that the transmitter could be placed i n the centre of the spectrum, thereby doubling the band width of the carbon-13 pulse, b) sin g l e - , rather than double-tuning of the carbon observe-coil, which could improve the e f f i c i e n c y of the probe, c) computer control of the transmitter frequency, so that the 180° carbon pulse can be applied at the centre of the spectrum. These features when implemented should produce 1 3C pulses of adequate homogeneity to perform c o r r e l a t i o n experiments with compounds such as "natural products" which have resonances spread over wide spe c t r a l widths. - 144 -separation, often by a factor of about f i f t y (20); this is much greater than any increase i n dispersion l i k e l y to become available i n the foreseeable future from an increase in magnetic f i e l d strength. Providing that the carbon-13 resonances are resolved, protons which have i d e n t i c a l chemical s h i f t s can be resolved and i d e n t i f i e d (eg. H-2 and H-3' in Fig. 4.2). e a 13 1 c) Prior to analysing a complex proton 2D J spectrum, a Cj- H correlation experiment can provide approximate chemical s h i f t s of both weakly and strongly coupled protons; this could help i n analysing proton spectra with strong coupling (see Sec. 3.2.6). d) Because ^ 0 and protons that are not d i r e c t l y bonded to carbon atoms do not give responses i n the s h i f t correlation experiment, proton chemical s h i f t s can be measured i n aqueous solution; this can be p a r t i c u l a r l y useful i n b i o l o g i c a l studies. e) It can be used to assign either proton or carbon resonances providing the chemical s h i f t of one or of the other is known. f) Although the spectrometer is tuned to detect carbon-13 resonances, the relaxation of the excited system is governed by s p i n - l a t t i c e relaxation of the protons and the s e n s i t i v i t y of the method is governed by population differences between the proton energy l e v e l s ; as a result the overall s e n s i t i v i t y of the experiment i s substantially greater than of an experiment designed to excite and observe carbon-13 signals. 4.3 D i s t i n c t i o n between homonuclear and heteronuclear couplings: the use of 2D J spectroscopy to achieve broad-band heteronuclear decoupling It has already been c l e a r l y established that a major advantage of 2D J spectroscopy i n chemistry i s that separation of chemical s h i f t s and coupling - 145 -constants onto two axes increases the ease with which analysis of complex molecules can be effected. The basic phenomenon on which this approach depends is due to J modulation of signals as a function of t ^ , as for example when a homonuclear spin system is subjected to non-selective pulses as described i n Sections 2.3 and 3.1. Consider now a d i f f e r e n t system, i n which the pulses are applied s e l e c t i v e l y to just one group of spins (A), as for example in a heteronuclear AX system. The course of the spins in the x-y plane of the rotating frame i s as i l l u s t r a t e d i n Figure 2.3a-d,g,h. Since the X n u c l e i do not experience the e f f e c t of the 180° pulse, the " i d e n t i t y " of the A magnetization vectors remains unchanged and they continue to precess at t h e i r o r i g i n a l precession frequencies and are refocussed at the end of the evolution period. It follows from this that i n a homonuclear 2D J experiment, the chemical s h i f t s and a l l the heteronuclear spin-spin couplings w i l l be simultaneously refocussed; this w i l l be r e f l e c t e d i n the f^ domain of the 2D J spectra which w i l l show only the frequencies corresponding to homonuclear spin-spin couplings. This feature may be used to d i s t i n g u i s h between homo- and heteronuclear spin-spin couplings, without the need for any broad-band spin-decoupling apparatus such as those used i n double resonance studies. Figure 4.5 shows regions from ID and 2D J spectra of a bicycloheptenol d e r i v a t i v e (13)* in benzene-d^; the normal spectrum indicates the complexity of the spectrum p a r t i c u l a r l y when the homo- and heteronuclear couplings are of s i m i l a r order of magnitude. The proton 2D J experiment performed on this compound would y i e l d p a r t i a l J spectra in the f^ domain, showing only the proton-proton couplings. This procedure therefore allows one IUPAC name for this compound is l,2,3,4,7,7-hexachloro-6-exo-fluoro-bicyclo[2.2.1] hept-2-ene. A B J V m c H-2 13 M 1H decoupled" spectrum " 1 9 F decoupled" f T or 0 spectrum 25 Hz 6.0 3.5 3.0 Normal spectrum 2.5 S Figure 4.5: A, B and C correspond to H-l, H-2 and H-3 protons of L3 (0.1M in CgDg) res p e c t i v e l y . The p a r t i a l J spectra and the proton decoupled spectra were obtained from a phase-sensitive, t i l t e d 2D J spectrum, but taking cross-sections along f'\- and f 1 2 - d i r e c t i o n s respectively (SF=270 MHz). - 147 -to e a s i l y separate the homonuclear spin-spin couplings i n this example. Although one could now obtain the heteronuclear couplings by comparing the normal spectrum with that of the p a r t i a l J spectra, a more elegant procedure would be to measure these couplings d i r e c t l y from the proton-decoupled proton spectrum as shown i n Figure 4.5. ( J J Q p =^4.2; H2=7"*"'' "*H1 H3 =** 7' JH2 F = 1 2 * 3 ; JH2 H 3 = l 3 * 5 ' JH3 F = 2 5 * 5 H Z ^ " ^ p a r t i a l J s P e c t r a w e r e obtained by taking cross-sections p a r a l l e l to the f^ axis from a phase-sens i t i v e 2D J spectrum; note the resolution enhancement and l i n e shapes (Sec. 3.3.3). The "proton-decoupled" proton spectra were obtained by taking traces p a r a l l e l to the f ^ axis at the appropriate f 1 ^ frequencies; the l i n e shapes i n th i s case w i l l be pure Lorentzian. The r e s u l t s for a second example, the difluoro-sugar, 3,4,6-tri-O-acetyl-2-deoxy-2-fluoro-8-D-glucopyranosyl f l u o r i d e (14) are i l l u s t r a t e d i n Figure 1 19 4.6; although the large geminal H- F couplings (^50 Hz) are obvious i n the normal spectrum ( F i g . 4.6B), d i s t i n c t i o n between the v i c i n a l *H-*H 19 1 and F- H couplings i s less c l e a r . As can be seen the p a r t i a l J spectra obtained by proje c t i o n of the appropriate regions of the 2D spectrum onto the f^ axis, gives the *H-*H couplings; the 45° summed projections give 1 19 the H- F couplings. An important p r a c t i c a l point to note is that the equivalent information cannot be simultaneously obtained by the conventional decoupling procedures because of the large chemical s h i f t separation between the two fl u o r i n e resonances. (J . =55.7; J - =13.5; J „ =4.1; F l , n l r l , H Z r z , r l l J F 2 , H 2 = 5 1 ' 7 ; J F 2 , H 3 = 1 6 , 6 ; J H 1 , H 2 = 6 , 9 ; J H 2 , H 3 = 9 * ° ' JH3,H4 = 9' 7 ; JH4,H5 = 9' 7 H z ) ' Another example which demonstrates the cha r a c t e r i z a t i o n between *H-*H 1 31 and H- P s p l i t t i n g s i s shown i n Figure 4.7, using 4,4-dideuterio-2-oxo-2-phenoxy-5- henyl-l,3,2-di xaphosphorinane (15). As expect d, the 45° skew Figure 4 .6 : (B) Region of a normal proton spectrum J4 (0.1M in CgDg) at 270 MHz. A and C are respectively the proton-decoupled spectra and p a r t i a l J spectra obtained by projecting the absolute value (u n t i l t e d ) 2D J spectrum onto the diagonal and Fj axes. S i n e - b e l l r e s o l u t i o n enhancement was used in the t 2 domain. The h i g h - f i e l d methyl peaks were suppressed by using an analog f i l t e r . Figure 4.7: (B) The 270 MHz proton spectrum of 15 (0.1M in C 6D 6). (A) The proton decoupled and (c) the p a r t i a l J spectra of the respective protons obtained by projecting regions of a (u n t i l t e d ) 2D J spectrum i n the absolute value mode. Note the broad " t a i l s " i n the 45° skew proj e c t i o n , (A). - 150 -p r o j e c t i o n ( F i g . 4.7A) and the p a r t i a l J spectra ( F i g . 4.7C) enables the easy d i s t i n c t i o n between *H-*H and *H-3*P couplings ( J . =11.1; A, a J A , C = 1 2 - ° ; J B , C = 4 ' 8 5 J P , A = ^ ' ^ J P , B = 1 2 ' 5 H z ) -As mentioned e a r l i e r , the projections from the l a s t two examples were derived from the absolute value spectra; the indesirable features of this display mode are evident in the skew i n t e g r a l projections which show c h a r a c t e r i s t i c line-broadening e f f e c t s . Obviously these may lead to the same li m i t a t i o n s described i n Section 3.2.3; in contrast the cross-sections obtained from the phase-sensitive display i l l u s t r a t e d for the f i r s t example are c l e a r l y superior, p a r t i c u l a r l y when attempting to resolve c l o s e l y spaced lines i n the f' ^  doma i n . Another i n t e r e s t i n g a p p l i c a t i o n of this procedure i s i l l u s t r a t e d i n Figure 4.8 using diphenyl-1,1,1-trifluoro-isopropyl-phosphate (16), in which the 1 19 homonuclear couplings are separated from the heteronuclear H- F and 1 32 . . . . H- P couplings. The l i m i t a t i o n s of the absolute value mode and the 45° summed projection mode are i l l u s t r a t e d i n Figure 4.9; the many c l o s e l y spaced lines and the dynamic range of the peaks within the m u l t i p l e t of H-2 causes the interference of neighbouring lines causing a d i s t o r t i o n of the r e s u l t i n g p r o j e c t i o n ( F i g . 4.9). In contrast the Lorentzian line-shape c h a r a c t e r i s t i c s of the phase sensitive £'^ traces y i e l d desirable line-shapes from which the two overlapping quartets may be e a s i l y i d e n t i f i e d for the measurement of the heteronuclear couplings (J =6.1; J =6.4; J P ) R=9.2 Hz). The technique described above i n e f f e c t provides "complete decoupling" over an i n f i n i t e band-width simultaneously for a l l heteronuclear species. The very general nature of this experiment may prove invaluable for simplifying - 151 -i ' 3 FH ill CF,-CH-CH 3 6 (PhOJ^O 16 H decoupled spectrum normal spectrum , , 1 9Fand 3 1 P decoupled" (or partial 3)spectrum 30 Hz Figure 4.8: (B) The normal 270 MHz spectrum of the proton attached to C-2 16 (0.1M i n CgDg). The p a r t i a l J spectrum (sub-spectrum), A, gives the proton-proton coupling constants and the cross-section along f ' 2 (C) gives both the ^ l p - l f l a n d I'F-^H couplings. A and C are phase-sensitive traces. - 152 -B A 30 Hz Fieure 4.9: A and B were obtained from the absolute value 2D J spectrum for the sample 16. The interference of neighbouring lines makes i t impossible to obtain u s e f u l information from the 45<> skew projection, B. A i s the p a r t i a l J spectrum of H-2. Compare the phase-sensitive traces i n Figure 4.8. - 153 -spectra and for measuring and assigning coupling constants, p a r t i c u l a r l y because i t avoids the hardware r e s t r i c t i o n s based on decoupling power and frequencies; furthermore the experiments can be performed using a conventional, single frequency proton probe and without the need for any spin-decoupling apparatus. Probably the most useful application of this technique i s i n organometallic chemistry, where i t is not uncommon to have spin systems with many different nuclei. - 154 -References (Chapter IV) 1. Preston, CM., H a l l , L.D. Carbohydr. Res. (1974) 37, 267. 2. Moniz, W.B., Gutowsky, H.S. J . Chem. Phys. (1963) 38, 1155. 3. Noggle, J.H., Schirmer, R.E. "Nuclear Overhauser e f f e c t " , Academic Press: New York, 1971. 4. Wong, K.F. Ph.D. Di s s e r t a t i o n , The Univ e r s i t y of B r i t i s h Columbia, Vancouver, Canada, 1979. 5. Aue, W.P., Bartholdi, E., Ernst, R.R. J . Chem. Phys. (1976) 64, 2229. 6. Nagayama, K., Wuthrich, K., Ernst, R.R. Biochem. Biophys. Res. Commun. (1979) 90, 305. 7. Bain, A.D., B e l l , R.A., Everett, J.R., Hughes, D.W. J . Chem. S o c , Chem.  Commun. (1980) 256. 8. Maudsley, A.A., Ernst, R.R. Chem. Phys. L e t t . (1977) 50, 368. 9. Maudsley, A.A., Muller, L., Ernst, R.R. J . Magn. Reson. (1977) 28, 463. 10. Wokaun, A., Ernst, R.R. Chem. Phys. L e t t . (1977) 52, 407. 11. Wokaun, A., Ernst, R.R. Mol. Phys. (1978) 36, 317. 12. Pouzard, G., Sukumar, S., H a l l , L.D. J . Amer. Chem. Soc. i n press. 13. Freeman, R., Morris, G.A. J . Chem. S o c , Chem. Commun. (1978) 684. 14. Bodenhausen, C , Freeman, R. J . Magn. Reson. (1977) 28_, 471. 15. Freeman, R., Morris, G.A. B u l l . Magn. Reson. (1979) 1, 5. 16. Morris, G.A., Freeman, R. J . Amer. Chem. Soc. (1979) 101, 760. 17. Meakin, P., Jesson, J.P. J . Magn. Reson. (1973) 1_0, 296. 18. Morris, G.A. Ph.D. Di s s e r t a t i o n , U n i v e r s i t y of Oxford, Oxford, England, 1978. - 155 -Hoffman, R.A., Forsen, S. "Progress i n NMR Spectroscopy", Emsley, J.W., Feeney, J . , S u t c l i f f , L.H. eds.; Pergamon Press: Oxford, 1966; Vol. 1, Chapter 2. H a l l , L.D., Morris, G.A., Sukumar, S. J . Amer. Chem. Soc. (1980) 102, 1745. - 156 -CHAPTER V HIGH RESOLUTION, ZERO QUANTUM TRANSITION (2D) SPECTROSCOPY - 157 -5.1 Introduction Thus fa r , the p r i n c i p a l thrust of the discussion has been towards the use of two-dimensional NMR experiments for resolving and subsequent assignment, of individual proton resonances. A l l of the experiments have had in common the fact that the observed transitions have involved (observable) single quantum 13 1 tra n s i t i o n s , as for example, 2D J or C- H chemical s h i f t correlation spectroscopy. These experiments were described i n Chapters I I I and IV using a "semiclassical" model for an understanding of the principles and features involved. One of the more exciting new opportunities associated with two-dimensional NMR spectroscopy (1-5) is the p o s s i b i l i t y of observing, for weakly coupled systems, transitions which would otherwise be "forbidden", such as combination lines or multiple quantum transitions (6,7). For example, i t has recently been demonstrated that zero- and multiple quantum transitions (ZQT and MQT) of simple spin systems can be selectively detected (6,8) or, even, excited (9). Study of ZQT spectra, and their e x p l i c i t analysis i s of particular interest for many reasons; thus, such spectra can provide additional information on the spin system of interest which does not appear in the conventional single quantum tra n s i t i o n (SQT) spectrum. ZQT spectra generally exhibit fewer lines than either conventional SQT spectra (7) or 2D chemical s h i f t correlated spectra (10,11) and furthermore, the widths of the resulting lines are independent of magnetic f i e l d inhomogeneity effects. Perhaps the most appealing feature for the practicing chemist i s that a l l of the frequency information encoded i n a ZQT spectrum is correlated v i a differences i n both chemical s h i f t s and coupling constants; the l a t t e r includes information concerning the r e l a t i v e signs of coupling constants. As w i l l be now shown, - 158 -these features can be recognised i n the ZQT proton spectra of complex organic molecules and provide a p o t e n t i a l l y useful method for assigning the resonances of a conventional spectrum. Although the properties of MQT spectra (more s p e c i f i c a l l y , those involving double quantum tr a n s i t i o n s ) have been described previously (12,13), no e x p l i c i t analysis of ZQT spectra has appeared in the l i t e r a t u r e . Because i t should be of general i n t e r e s t , that analysis for spin h nuclides i s presented and a demonstration i s given of how i t can be applied, i n the form of a type of sub-spectral analysis, to a more complex spin system. I t i s appropriate to preface that analysis with a b r i e f reminder of how ZQT (or MQT) are created and observed i n a multiple pulse Fourier transform (FT) experiment. As we have previously mentioned, most NMR experiments involve single quantum t r a n s i t i o n s and can be simply understood i n terms of the e f f e c t of pulses on c l a s s i c a l magnetization vectors and subsequent precession (and relaxation) of these vectors in the r o t a t i n g frame of reference. In contrast, ZQT (and MQT) cannot be v i s u a l i z e d i n the same sense, mainly because they are not observed d i r e c t l y i n an FT experiment, and t h e i r creation and detection are best explained using the density matrix formalism, as summarised in the next section.* 5.2 Creation and observation of ZQT's i n pulsed NMR The two spin (h) systems can be conveniently represented as a 4x4 matrix (a) written i n the eigenbasis of the Zeeman hamiltonian (and F ) ( i e . ++, z +-, -+, — ) ; Table 5.1 gives the energy l e v e l s and a l l the possible t r a n s i t i o n frequencies for the AB case. The e f f e c t of a strong radiofrequency (RF) pulse *The reader i s referred to any standard text (eg. Ref. 15) on NMR for the basic equations and d e f i n i t i o n s on quantum mechanics. Table 5.1:The energy l e v e l representation and the possible n-quantum t r a n s i t i o n frequencies for a weakly coupled AB spin 1/2 system. M Level a Energy A M Transition Frequency -1 4 - - (f A+f B)/2 + J/4 0 2 + 3 fA" fB 0 3 - + (fA-fB)/2 - J/4 1 1 + 2 V 3/2 0 2 + - -(fA-fB)/2 - J/4 1 3 + 4 £B+ J/2 1 1 + 3 f - J/2 A +1 1 + + -(f A+f B)/2 + J/4 1 2 + 4 f.+ J/2 A 2 1 + 4 A B Expressed in frequency units. - 160 -of angle a applied along the x axis of the rotating frame of reference can be described by the r o t a t i o n operation which transforms the matrix o into [ o ] + such that [ o ] + = exp(-ictF x)aexp(ictF x) [5.1] where the angular momentum operator projection F x = F^ + F^. Expanding the exponential form of the r o t a t i o n operator y i e l d s e x p l i c i t expressions for the elements of the new matrix (14). It should be noted however that the new elements w i l l also depend on the phase, <f>, of the RF pulses, and hence the r o t a t i o n operator should be written for a general case as, R(ct,<j>) = exp(-i<)>F )exp(ictF )exp(i«J)F ) [5.2] 2* X Z For the present arguments a zero pulse phase (along the x axis) i s assumed for convenience, but i t w i l l be noted l a t e r that for s e l e c t i v e detection of n-quantum t r a n s i t i o n s i t w i l l be necessary to vary the phase, <J>, of the RF " e x c i t a t i o n " pulses (6,8) as shown i n Figure 5.1.* The NMR observable along the y axis of the rotating frame is given by <My> = i / 2 [ ( o 1 2 - a 2 1 ) + ( a 1 3 - a 3 l ) + ( o 2 4 - o 4 2 ) + ( a 3 4 - o 4 3 ] + [5.3] i n d i c a t i n g that the detected signal contains only SQC's of the density matrix. However, the ZQT information is contained i n the non-diagonal ZQC's of the density matrix; thus to detect ZQT (or MQT) spectra i t i s not only necessary to create ZQC's (or the MQ equivalent), but that information has to be trans-ferred into the observable SQT by means of suitable pulse sequences (6,16). Of the methods a v a i l a b l e for creation and detection of ZQC's (6,16-19), the pulse sequence shown in Figure 5.1 has proven to be both convenient and of general a p p l i c a b i l i t y and w i l l be described here on a weakly coupled AB spin system. ^The f i r s t two pulses i n Figure 1 are necessary to " e x c i t e " or create ZQC. Preparation Evolution Detection 9QO 90J 90' t, I l2 i ON time 0 0* T T * t, t* • 7 \ Figure 5.1: The basic pulse sequence for creation and detection of n-quantum t r a n s i t i o n spec The phase <f> of the " e x c i t a t i o n " pulses can be varied for s e l e c t i v e detection of ZQT spectra ( t e x t ) . The notation on the time-scale is used in Table 5.2. - 162 -In order to understand the creation and detection of ZQC's one can express just two elements, o^CSQC) and ^^(ZQC), of the density matrix and follow the consequences of the RF pulses and the evolution of those matrix elements at various stages of the pulse sequence (Table 5.2). The i n i t i a l (Boltzmann) state of the density matrix contains only the diagonal elements (a ) corresponding to the equilibrium populations. The nn i n t i a l 90° pulse equalises a l l diagonal elements and creates only SQC, and no ZQC (or MQC), as indicated by the t a ] Q + elements i n Table 5.2; the e x p l i c i t expressions for the corresponding elements may be derived from equation [5.1] (14). The non-diagonal SQC's when allowed to develop during the preparation period T, give elements of the form, a (T) = a (0 +)exp(-ia T ) e x p ( - r / T 0 ) [5.4] nm nm nm 2nm a i s the angular v e l o c i t y of the o s c i l l a t i n g a coherence, with an nm nm exponential decay due to transverse relaxation ( T ^ ^ ) ; the damping term of the coherences have been omitted i n Table 5.2 for convenience, since i t does not contain frequency information. I t can be seen from Table 5.2 that the second pulse can create ZQC (and MQC) and that these elements can now be non-zero and can evolve during the evolution period, t ^ , each at t h e i r appropriate ZQT (or MQT) frequencies. Since the signal observable during the detection period ( t 2 ) can arise only from the single quantum coherences (eq. [5.3]) i t i s necessary to transfer the ZQC (or MQC) information into these elements by a th i r d (mixing) pulse. This can be seen i n the f i n a l expression for the [a.~].. element i n Table 5.2 which contains terms of the type 1 2 a ( T ) . b ( t 1 ) . e x p ( - i o 1 2 t 2 ) [5.5] The amplitude of each l i n e i n the f i n a l 2D spectrum w i l l be governed by the function a ( x), which i s c r i t i c a l for the p r a c t i c a l applications of this - 163 -TABLE 5.2: a " d a 23 e l e m e n t s o f t n e (4x4) density matrix of an AB system, following the pulse sequence shown i n Figure 5.1. Energies are expressed i n terms of angular v e l o c i t i e s a)(=2irf) and J '(=2TTJ). The relaxation (T 2) terms have been omitted for convenience (see t e x t ) . Time E x p r e s s i o n s f o r t h e m a t r i x e l e m e n t s , o 1 2 and o 2 3 0° [ o 1 2 ] 0 - 0 [o 2 3 ] o - 0 [ ° 1 2 ] T * [ 0 i 2 ] o + « P ( - i « * > l 2 T ) " i A P { e x p - i ( u B - J ' / 2 ) T } / 2 [ o 2 3 ] T " t ° 2 3 ] 0 + e x P ( - i u 2 3 T ) * 0 T + f ° 1 2 ] T + * [ ( 0 1 2 + 0 2 l ) + ( ° 3 i . + O i » 3 ) - ( ° 1 3 - 0 3 l ) + ( 0 2 M - < ' i « 2 ) ] T / 4 - A P { s i n ( a) BT/2 ) . c o s ( J'T/2 ) + i s i n ( u AT/2) . i s i n ( J'T/2) }/2 [ ° 2 3 l T + " i [ ( ° 1 2 + O 2 l ) - ( 0 3 ' i + o ' » 3 ) - ( 0 1 3 + 0 3 l ) + ( 0 2 M + 0 ' 4 2 ) ] T / A = i A P { s i n ( J ' T / 2 ) . s i n ( ( u . + a ) E ) T / 2 ) . s i n ( ( a ) -UID)T/2)} A D A D t j t°12l t l " [°12l T + e x P(- i "12 t l ) - & P { B i n ( u ) B T / 2 ) . c o s ( J ' T / 2 ) + i s i n ( u A T / 2 ) . i s i n ( J ' T / 2 ) . e x p ( - i u 1 2 t 1 ) } / 2 I ° 2 3 ] t " [ f 2 3 ] T + e x P ( - l l l l 2 3 t l ) - i A P { s i n ( J ' i / 2 ) , s i n ( (U.+Ui1)T/2) . s i n ( (u -U b )T/2) . e x p ( - i u 2 3 t 1 ) } A C A o + c E i [ ° i 2 l t l + " U(o12^2i)+(o3^+o,>3)-(o13+031)+(o2, (-o, (2)] t. + i [ (clk-akl)+(o2i-a32) ] )/* t 2 [012!,. " [°12]. . e x p ( - i u j 2 t 2 ) d t 2 t j + 3 Boltzmann equilibrium state. b AP = [ ( a 1 1 - a 2 2 ^ 0 = ^ a 3 3 ~ ° 4 4 ^ 0 c At t h i s stage i t i s only necessary to know the e x p l i c i t form of the observable. d Form of the detected s i g n a l . - 164 -experiment. The function b(t^) w i l l contain terms involving zero, single and multiple quantum t r a n s i t i o n frequencies and w i l l show a complex amplitude modulation of the detected signal as a function of t . . The form of [ <j] 1 t 2 indicates that a double Fourier transformation with respect to t 2 and t^ w i l l show only the observable SQT i n the f 2-domain while the f^-domain includes, i n addition, a l l "forbidden" t r a n s i t i o n s . Thus the x-domain (preparation period) and the t^-domain (evolution period) re s p e c t i v e l y influence the amplitudes and frequencies of the n-quantum t r a n s i t i o n s studied by a 2D NMR experiment. The present work deals s p e c i f i c a l l y with the ZQT s p e c t r a l analysis (jie. the f^ domain) and w i l l be discussed for weakly coupled AB, ABC, AB 2 ABCD and AB^ spin systems. 5.3 Spectral analysis of zero quantum t r a n s i t i o n s 5.3.1 Generalization ABCD... refers to a weakly coupled spin h system having energies f^, f , ( f >f >... i s assumed) resp e c t i v e l y expressed in frequency B A B units with respect to the transmitter frequency, and coupling constants J Ag> J A C The basic product functions and corresponding energy le v e l s are described i n standard NMR texts (15,20,21), usually i n the context of analysis for the allowed single quantum t r a n s i t i o n s . These basic analyses are e a s i l y extended to predict the frequencies of the ZQT spectra. The " s e l e c t i o n r u l e " for ZQT is A M = 0 where M is the projection of the t o t a l spin angular momentum in the z d i r e c t i o n . Spin functions w i l l be represented by standard + and - symbols in non-degenerate systems (a and 8 w i l l be used in the case of degeneracy). - 165 -It has already been noted by Wokaun and Ernst (17) that d i f f e r e n t types of ZQT can be defined, depending on whether one or several pairs of spins are involved i n a t r a n s i t i o n for which AM = 0. For the purpose of the present discussion the terms " t r a n s i t i o n of the f i r s t - k i n d " w i l l r e fer to the ZQT invol v i n g only one pair of spins (the other spins being unchanged), ZQT of the second-kind w i l l r e f e r to a change of two pairs of apins, and so on. The following t r a n s i t i o n notation, which is convenient for predicting the frequencies involved, i s also introduced: for example, a t r a n s i t i o n of the f i r s t kind i n an A B C D system, +-++ -»• ++-+ w i l l be denoted by ( A + ) B C + ( D + ) , where the parentheses around the A and D nuclei imply that the + spins corresponding to these n u c l e i remain unchanged, while the B and C spins, which are involved i n the t r a n s i t i o n , change from - to + and + to - res p e c t i v e l y . The signs i n the above notation r e f e r to the i n i t i a l states.* 5.3.2 AB system This is the simplest case of a coupled spin % system which w i l l be expected to show a single ZQT, as can be seen i n Table 5.1. Since ZQT appear as a complex amplitude modulation of the NMR observable ( i e . S Q C i n the density matrix), the frequencies corresponding to both 2-K3: A + B and 3-*2: B + A (opposite i n sign) are expected i n the ZQT spectrum, but for convenience only the p o s i t i v e (absolute) frequencies w i l l be presented i n the following discussions. The ZQT, A + B , in this example w i l l appear with the frequency ^ ^ - f g ) a n a " is independent of J Ag« It can be noted from Table I A d i f f e r e n t nomenclature i s used when equivalent groups of n u c l e i are involved, as w i l l be seen l a t e r for the A B 2 and A B 3 case. - 166 -5.1 that the double quantum t r a n s i t i o n (DQT) appearing at ( f A + f g ) > corresponds to a higher frequency than the ZQT. In th i s simple case, the ZQT spectrum w i l l not provide more information than the conventional SQT spectrum. 5.3.3 ABC system Table 5.3 gives the energy levels for the ABC system and the possible ZQT frequencies, which are centred at the chemical s h i f t d i f f e r e n c e between each pair of n u c l e i . The ZQT spectrum w i l l show three doublets centred at ( f ^ -fg)» ( f A" f c)» a n d ^ fB~ fC^' t h £ s P l i t t i n & s b e i n 8 ( J A C ~ J B C ^ ' (J. -J__) and (J A T,-J.„) r e s p e c t i v e l y . Inspection of these ZQT A D D C AB AC frequencies w i l l indicate that the chemical s h i f t difference between two n u c l e i , for example A and B, is associated with the coupling constants and J but not th e i r mutual coupling, J . _ . This feature is quite general D C A D to ZQT's of the f i r s t kind and can be e a s i l y extended to other systems which show mu l t i p l e t s of the form, ( V V ± ( J A C - J B C ± ( \ D - V ± The appearance of chemical s h i f t and coupling constant differences i n ZQT spectra is very d i f f e r e n t from conventional NMR spectroscopy and i t i s this feature which provides a technique for c o r r e l a t i n g chemical s h i f t s and coupling constants. Because the coupling constant terms appear as dif f e r e n c e s , t h e i r r e l a t i v e signs have si g n i f i c a n c e i n the ZQT spectra and hence can be evaluated by intercomparison between the normal (SQT) and ZQT spectra. The AB 2 system is a s p e c i a l case of a three spin system, and the corresponding energy l e v e l s are given i n Figure 5.2, i n which the functions of n u c l e i B are separated according to their symmetry. ZQT's w i l l be expected only within each of the M=+^ 5 submanifolds and, since elements of d i f f e r e n t M -3/2 6 MP Figure 5.2: Energy level representation for an AB 2 spin h system; S and AS refer to the symmetric and anti-symmetric functions respectively. The possible ZQT's are indicated by the arrows. TABLE 5.3: The energy levels and the ZQT frequencies for an ABC system. M Level Energy -3/2 8 < F A + F B + F C ) / 2 + ( J A B + J A C + J B C ) M 7 - - + (f A+Vf c m + ( J A B - J A C - J B C ) / 4 -V2 6 " + " <VVV /2 " ( J A B - J A C + J B C ) / 4 5 + - ~ - < F A - V F C ) / 2 " ( J A B + J A C " J B C ) / 4 4 _ + + ( f A - f B " f c ) / 2 - (J A B+J A C-J B C)/4 +1/2 3 + - + -(£ A-£ B+f c)/2 + ( J A B - J A C « B C ) / ^ 2 + + - - ( F A + V F C ) / 2 + ( J A B - J A C - J B C ) / 4 +3/2 1 + + + - ( * A + F B + F C ) / 2 + ( J A B + J A C + J B C ) M ZQT ( A " ) B + C 6 + 7 A + ( B _ ) C : 5 + 7 A + B * ( C ~ ) : 5 + 6 A + B " ( C + ) : 3 + 4 A + ( B + ) C ~ : 2 + 4 ( A + ) B + C " : 2 + 3 Frequency (VV " < J A * - J A r V 2 A B A C <W " ( J A B - J B C ) / 2 <VV ' ( J A C f W / 2 < W + < J A C f W 2  ( F A " F C ) + < J A B " W 2 (VV + ( J A B " J A C ) / 2 oo a Expressed in frequency units. - 169 symmetry do not mix in the density matrix, only elements belonging to the same i r r e d u c i b l e representation within a given M submanifold w i l l give r i s e to ZQT l i n e s . Therefore i n th i s case we would expect the ZQT's 2-* 3 and 4*5 at frequencies ( f - f g ^ ^ g - N o t e t h a t t h e coupling J A f i appears i n the above term but not J t 'BB 5.3.4 ABCD system Table 5.4 gives the levels and the i r corresponding energies, i n frequency u n i t s , for an ABCD case, including a l l possible ZQT frequencies. I f we f i r s t consider the t r a n s i t i o n s within the M=+l submanifold, s i x ZQT's are expected (due to the six possible chemical s h i f t d i f f e r e n c e s ) , each of the form, ( fC- fD ) + l 5 [ ( JAC- JAD ) + ( JBC- JBD ) ] ( A + ) ( B + ) c V : 2+3 The corresponding t r a n s i t i o n s i n the M = -1 submanifold w i l l be of the form, ( fC- fD )- J s [ ( JAC- JAD ) + ( JBC- JBD ) ] ( A - ) ( B - ) c V : 14+15 Taken together, these twelve t r a n s i t i o n s correspond to the s i x doublets i n the ZQT spectrum only p o s i t i v e frequencies being considered, a r i s i n g from the M = +1 l e v e l s . S i m i l a r l y one can expect f i f t e e n ZQT's a r i s i n g from the M = 0 l e v e l , of these, three are ZQT's of the second-kind, involving the simultaneous change of two pairs of spins, namely A +B +C D , A +B C +D and A +B C D + and occurring at frequencies ( f ^ - f g ) + ( f ^ - f p ) , ( f . - f _ ) + ( f ^ - f j and ( f . - f n ) + ( f ^ - f , , ) ; note that the A C B D A D B C tr a n s i t i o n s appear at r e l a t i v e l y higher frequencies and are s i n g l e t s . The remaining twelve ZQT's are of the f i r s t - k i n d , and the t r a n s i t i o n s involving the chemical s h i f t d i f f e r e n c e s , for example between C and D n u c l e i , w i l l be of the form, - 1 7 0 -TABLE 5 . 4 A : The energy le v e l s f o r an ABCD system, expressed i n frequency units. M Level Energy - 2 1 6 - - - -( F A + F B + F C + V 12 + ( J A B + J A C + J A D + J B C + J B D + J C D ^ / 4 1 5 - - - + ( W W 12 + ( J A B + J A C " J A D + J B C " J B D " J C D ' / 4 - 1 1 4 - - + -( F A + F B - F C + F D > 12 + ( J A B " J A C + J A D " J B C + J B D " J C D ' / 4 1 3 - + - -( F A " F B + F C + F D ) 12 -( J A B " J A C " J A D + J B C + J B D " J C D ' Ik 1 2 + - - - - ( W W 12 - ( J A B + J A C + J A D " J B C " J B D " J C D ' / 4 1 1 - - + + ( F A + F B " F C - F D ) 12 + ( J A B " J A C " J A D " J B C " J B D + J C D ] / 4 1 0 - + - + ' W W 12 - ( J A B - J A C + J A D + J B C - J B D + J C D ^ / 4 0 9 - + + -( F A - F B " F C + F D > 12 -( J A B + J A C - J A D - J B C + J B D + J C D ] / 4 8 + - - + " ( W W 12 - ( J A B + J A C - J A D - J B C + J B D + J C D > / 4 7 + - + - " ( W W 12 - ( J M - J A C + J A D + J B C - J B D + J C D > / 4 6 + + - - " ( W W 12 + ^ A B ^ A C ^ A D ^ B C ^ B D ^ C D ^ / 4 5 - + + + ( F A - F B - F C - F D > 12 -( J A B + J A C + J A D " J B C ~ J B D ~ J C D ] / 4 4 + - + + - ( F A - F B + F C + F D ) 12 - ( J A B " J A C " J A D + J B C + J B D " J C D ) / 4 + 1 3 + + - + - ( F A + F B - F C + V 12 + ( J A B " J A C + J A D " J B C + J B D " J C D ) / 4 2 + + + -- ( F A " F B - F C + F D > 12 + ( J A B + J A C " J A D + J B C " J B D " J C D ) / 4 + 2 1 + + + + " ( F A + F B + F C + F D > 12 + ^ A B ^ A C ^ A D ^ B C ^ B D ^ C D ) Ik - 171 -T A B L E 5.4B : The Z Q T frequencies for an A B C D case. Transitions of the f i r s t - k i n d Transitions of the second-kind ( V V +" ^ ( J A C " J B C ) ± ( J A D - J B D ) } < F A " V + ( f c " F D ) ( F A " F C ) 1 ^{ ( J A B " J B C ) ± ( J A D - J C D ) } + ( W ( W +" ^ { < J A B - J B D ) ± ( J A C - J C D ) } ( F A " F D ) + ( F B " F C ) <W 1 ^ ^ J A B - J A C ) ± ( J B D - J C D ) } <w +- H U J A B - J A D ) ± ( J B C - J C D ) } <fc-v +- * ( J A C - J A D ) ± ( J B C - J B D ) } - 172 -( fC- fD ) + i 5 t ( JAC- JAD ) + ( J B C - V ] ( A + ) ( B - ) C V : 7 ,8 ( fC- fD ) + i 5 [ ( JAC- JAD ) + ( JBC- JBD ) ] ( A ~ ) ( B + ) c V : 9+10 Thus the f i n a l ZQT spectrum w i l l contain 27 l i n e s (Table 5.4) composed of s i x quartets (doublets of doublets), one centred at each of the si x possible frequency differences A A g , . . . with the s p l i t t i n g pattern _+CJ^ ,^—Jg^ ,) + ( j - J ),... and three s i n g l e t s corresponding to the ZQT's of the AD BD second-kind. (Note that the corresponding SQT spectrum consists of 56 l i n e s , 24 of which are combination l i n e s ) . Another four-spin system of interest i s the AB^ case; three of the nu c l e i are equivalent and hence the B^ sub-system may be represented according to the symmetry group. The basic symmetry functions may be c l a s s i f i e d with respect to the A^ or E i r r e d u c i b l e representations as shown in Table 5.5 (the subscripts refer to the M values). The ZQT's o r i g i n a t i n g from the various l e v e l s are indicated i n Table 5.6. The ZQT spectrum w i l l show signals at frequencies, (f - f )+J. and ( f - f ).^ A D — AB A a The above discussions can be e a s i l y extended to more complicated spin systems to predict the ZQT spectra by following procedures s i m i l a r to those of conventional NMR spectral analysis. F i r s t , the stationary state wave functions should be determined and t h e i r energies calculated; then the frequencies of the ZQT's can be predicted by considering only the tr a n s i t i o n s between states of a given M sub-manifold (AM=0) and function of same symmetry, as discussed e a r l i e r . lIt i s i n t e r e s t i n g to note that although for molecules i n i s o t r o p i c solution ZQT's occur only between l e v e l s belonging to the same i r r e d u c i b l e representation, Tang and Pines have recently demonstrated how this rule can be broken i n the case of an "oriented" C H 3 group (22), - 173 -TABLE 5.5: Energies and basic (symmetry) functions corresponding to an AB^ system. The A and E states of the C 3 symmetry group are indicated in the left hand column; the subscripts here indicate the M values. The E states are doubly degenerate but only one of the functions is represented. State Basic function Energy" A.2 BBBB (f +3f )/2 + 3J/4 1A_! B { B B c t + BaB + aB6)/v/3 ( f A + f )/2 + J/4 2A_! aBBB - ( f A ~ 3 f )/2 - 3J/4 1A 0 B{aaB + aBa + Baa}//3 (f - f )/2 - J/4 A IJ 2A 0 a{BBa + BaB + aBB)//3 - ( f - f )/2 - J/4 IA, Baaa (f -3f )/2 - 3J/4 2Aj a{aoB + aBa + Baa}//3 - ( f A + fv)/2 + J / A A D A 2 oaaa - ( f +3f )/2 + 3J/4 E _ i B(BBa - BaB}//2 (f + f )/2 + J/4 1E 0 B(aaB - aBa}//2 ( f A ~ f g ) / 2 - J/4 2E 0 a(BBa - BaB)//2 - ( f A ~ f )/2 - J/4 E i a{aaB - afia}//2 - ( f + f )/2 + J/4 J refers to J - 174 -TABLE 5.6: The ZQT's and their energies given in frequency units for an AB3 case (see Table 5.5). ZQT Energy 2A! + IA, ( f A - f B ) - J A B 2A0 - 1A0 ( f A" fB } 2A.x- 1A_4 ( f A - f B ) + J A B 2E 0 - 1E 0 ( f A - f B ) - 175 -5.4 Applications of ZQT spectroscopy i n chemistry It might have been anticipated that e x p l i c i t analysis of the ZQT-spectrum of the multiple spin-systems of a t y p i c a l , complex organic molecule would be both cumbersome and time-consuming. However, i t w i l l be noted from the above formalism that since ZQC can only be created between spins which have mutual spin-spin coupling, a type of sub-spectral analysis i s i n v a r i a b l y possible.... long-range couplings (across four, or more, bonds) are frequently of small- or zero-magnitude and so i t is generally possible to consider i n i s o l a t i o n only those spins which have a v i c i n a l or geminal coupling; as w i l l be seen, t h i s s u b s t a n t i a l l y s i m p l i f i e s analysis of ZQT spectra in p r a c t i c a l cases. We s h a l l i l l u s t r a t e this point, and hence some of the diagnostic p o t e n t i a l of ZQT spectroscopy in organic chemistry, by a study of trideuteriomethy1 2,3,4,6-tetra-O-trideuterioacetyl-Ct-D-glucopyranoside (6), which i s a seven spin system (Figure 5.3; Table 5.7). The 2D spectrum r e s u l t i n g from the three-pulse experiment ( F i g . 5.1) described e a r l i e r w i l l contain the conventional SQT frequencies i n the f 2 domain and a l l possible n-quantum t r a n s i t i o n frequencies in the f^ domain. However by use of suitable phase-shifted sequences i t i s possible to s e l e c t i v e l y observe only the ZQT spectrum in f^ (6). This point i s i l l u s t r a t e d i n Figure 5.4 which shows t r a n s i t i o n s , corresponding to the HI proton ( i n f 2 ) . Spectrum A, is an f^ trace obtained using the basic pulse sequence (<j)=0°) and shows the responses due to zero, single and multiple (double) quantum t r a n s i t i o n s . Figure 5.4B shows that phase s h i f t i n g the two e x c i t a t i o n pulses by 180° (eg. <)>=90o and 270°) r e s u l t s i n c a n c e l l a t i o n of the SQT's (odd-n-quantum t r a n s i t i o n s ) while r e t a i n i n g the zero and double (even-n-) quantum t r a n s i t i o n s i n the f i n a l spectrum. In t h i s p a r t i c u l a r case, Figure 5.3: The normal 270 MHz FT NMR spectrum of trideuteriomethyl 2,3,4,6-tetra-0-trideuteriomethyl-ot-D-glucopyrano8ide (6) i n benzene-d_6 (0.1M); the scale represents the o f f s e t from the transmitter frequency. TABLE 5.7: The conventional and ZQT spectral data for trideuteriomethyl 2,3,4,6-tetra-0-(trideuterioacetyl)-a-p-glucopyranoside (6) . Frequency 3 Coupling constants S h i f t separations 0 ZQT r e s u l t s f l • 316 (Hz) J12 " 3.8 (Hz) A12 = 41 (Hz) J12 = 4 f2 " 275 J23 * 10.6 A23 = 219 J23 = 10.5 f3 = 56 J34 - 9.5 A34 = 144 J34 = 9.5 f4 " 200 J45 = 10.6 A45 = 411 J45 = 10.5 f 5 " 611 J56- " 4.7 A56' = 127 KJ56. - J 6 t 6 . . ) | • 16.5 £6' " 484 J56" = 2.5 A56" = 72 1 ( J 5 6 „ - J 6 . 6 . . ) l = 14 v- 539 J6'6" = 12.5 A6»6" = 55 | ( J 5 6 . " J56"^ 1 2 6 Offset from the transmitter frequency. From reference 23. cThe chemical s h i f t differences obtained from the conventional spectrum; a d i r e c t comparison of these separations between the protons can be made by matching the conventional spectrum with the ZQT traces (eg. ( f i - 1 ^ ) i n Figure 5.3 js^equel to the separation between the A^^ m u l t i p l e t s i n Figure 5.SB. Obtained from ZQT spectra with 1.5 Hz d i g i t a l r e s o l u t i o n . eNot well resolved due to limited r e s o l u t i o n and overlap.(See Fig.5.5C). f,(Hz) Figure 5.4: Trace (A) was obtained using the basic pulse sequence 90°- T-90° -tj-90°-A c q u i s i t i o n , (T=200 msec, 4>=0°) and represents the f j domain corresponding to the HI proton. (B) shows the selective suppression of the SQT's, achieved by s h i f t i n g the phase of the two i n i t i a l pulses by 180°. The DQT were suppressed, as seen i n trace (C), by co-adding signals from two separate experiments i n which the i n i t i a l pulses were phase s h i f t e d from 90° to 270°. The incomplete cancellations are probably due to pulse (phase) imperfections, and long-term i n s t a b i l i t i e s (see Experimental section). - 179 -suppression of the double-quantum t r a n s i t i o n s , and hence the s e l e c t i v e detection of the ZQT spectrum can be obtained by s h i f t i n g the pulse phase by 0°, 90°, 180° and 270° and is shown in Figure 5.4C.1 2 The ZQT spectrum corresponding to the HI proton gives a simple pattern because H-l is coupled to only one other proton, H2(j^2 =3.8 Hz). The ZQT spectrum is expected to show a m u l t i p l e t centred at the chemical s h i f t difference + ( f ^ - f 2 ) (which i s denoted by A^)» The structure of this m u l t i p l e t can be predicted by considering these t r a n s i t i o n s as a r i s i n g from and ABC "sub-spin system" (see Table 5.3), involving Hi, H2 and H3: A 1 2 ^ ( J 1 3 - J 2 3 ) The multiplet i s observed as a doublet, separated by ^ 3 = 1 0 . 6 Hz (23); the t r a n s i t i o n s corresponding to A 3 do not appear in the ZQT spectrum since 3 there i s no appreciable spin-spin coupling between HI and H3. Similar arguments may be used to predict the possible ZQT's corresponding to the H3 proton. Since H3 i s coupled to H2 (j=10.5 Hz) and H4 (j=9.5 Hz), two m u l t i p l e t s centred at A^^ and A ^ w i l l be i n the ZQT spectrum, a r i s i n g from the sub-spin systems, HI, H2, H3, H4 and H2, H3, H4, H5 r e s p e c t i v e l y . l l n t h is instance the trace C i n Figure 5.4 was obtained by adding the time domain signals (interferograms) from two separate experiments (<t>=0°, 180° and 90°, 270°). After completion of this work, we have acquired a 293B pulse programmer which enables the above experiment to be performed in a single experiment; the long term i n s t a b i l i t i e s i n this case are minimised, which gave better c a n c e l l a t i o n of higher order t r a n s i t i o n s (c_f. F i g . 5.4). 2"ZQT spectrum of the HI proton", refers to the (ZQT) traces i n the f^ domain corresponding to the HI frequencies in f 2 . The ZQT spectrum may be obtained as a single trace from the 2D spectrum or an i n t e g r a l projection of the selected (Hi) region onto f]_. 3Long-range, four-bond couplings (c_a. 0.8 Hz) can be detected in these type of molecules between 1,3-axial, equatorial protons, however the choice of the preparation delay x (=200-300 msec) is generally too short to allow for any s i g n i f i c a n t contribution from protons more than three bonds away. The limited d i g i t a l r e s o l u t i o n and line-broadening in f 2 further decrease the detection of the ZQT's associated with these couplings. - 180 -The m u l t i p l e t patterns for these signals are given by (Table 5.4), A 2 3 ± H [ ( J 1 2 - J 1 3 ) ± (J 2 4-V] = A 2 3 i l 5 ( J 1 2 ± J 3 4 ) and, A 3 ^ [ ( j 2 3 - J 2 4 ) i ( J 3 5 - J 4 5 > 1 = A34^ s ( J23i J45 ) These m u l t i p l e t s are i l l u s t r a t e d i n the ZQT traces i n Figure 5.5B. The above examples demonstrate a p o t e n t i a l use for ZQT spectra i n s t r u c t u r a l analysis namely by e s t a b l i s h i n g c o n n e c t i v i t i e s between weakly coupled protons. In addition, the s p l i t t i n g patterns provide a method for i n d i r e c t l y obtaining coupling constants; for example, i t should be possible i n p r i n c i p l e , to determine the coupling constants J45 by analysing the ZQT spectrum of H3 (J34 and w i l l appear i n the domain, corresponding to the conventional SQT's). The H6" proton i s part of the H6', H6", H5, H4 sub-spin system, and is coupled to H61 (J=12.5 Hz) and H5 (J=2.5 Hz). Following the e a r l i e r discussion the ZQT spectrum corresponding to the H6" proton would be expected to show the signals S 6 » ^ [ ( J 4 5 - J 4 6 ^ ( J 5 6 ' - J 6 ' 6 " ) ] = ^ e ^ ^ s ^ s e - " - ^ ^ " ^ and A 6 , 6 „ + 1 £ ( J 5 6 , - J 5 6 „ ) In addition to these chemical s h i f t d i f f e r e n c e s , another m u l t i p l e t centred at A,jg, i s seen i n Figure 5.5C with the frequency pattern, A5 6.1 55[(J45-J4 6.)±(J 5 6«-J 6. 6")] - A 5 6 „ f s t ( J 4 5 ) ± ( J 5 6 « - J 6 . 6 M ) ] This m u l t i p l e t , unlike i n the previous examples, would be expected when observing H6" since there is a f i n i t e coupling (J^^,=4.7 Hz) between H5 and H6" protons, which are also coupled to H6". - 181 -Figure 5.5: ZQT (absolute value) spectra for the protons indicated, each corresponding to a single trace in fj_. The appropriate "interferograms" (512x2 words) were zero-filled, and apodised to improve the effective resolution. The trace shown as an inset was obtained for H3 by halving the f j width to achieve higher d i g i t a l resolution. The experimental parameters were: digitization in f 2 , 0.68 Hz; increment in t\f 625 psec; number of acquisitions, 8; preparation delay (T), 200 msec, (except trace B, 260 msec.) - 182 -An i n t e r e s t i n g feature i n the ZQT spectrum of H6" i s the appearance of the geminal (negative) coupling J,,,„, as a d i f f e r e n c e . This enables the o o d i s t i n c t i o n to be made between po s i t i v e and negative coupling constants,^ which is r a r e l y used i n conventional spectral analysis mainly because of the d i f f i c u l t y i n obtaining this information. This could help in d i s t i n g u i s h i n g between the geminal (negative) and t r a n s - d i a x i a l ( p o s i t i v e ) couplings of ster o i d s , which are of s i m i l a r magnitude (24). The delay times T(200, 260 and 200 msec respectively) used to obtain the ZQT spectra shown i n Figure 5.5A, B and C were selected to give optimum signal i n t e n s i t i e s to i l l u s t r a t e the expected spectral patterns. However, i t should be noted that the ZQT s i g n a l i n t e n s i t y is a rather complicated function of both coupling constants and chemical s h i f t frequencies, which makes i t d i f f i c u l t to simultaneously optimise conditions for a l l protons in the spectrum. For example, the ZQT spectra ( F i g . 5.5D and E) corresponding to the H2 and H3 protons for T=200 msec show r e l a t i v e l y weak signals for the mu l t i p l e t A^^ (£f. Trace B), i n d i c a t i n g the s i g n i f i c a n c e of the preparatory delay i n these experiments for optimum signal i n t e n s i t i e s . Although in a l l the previous discussions only the protons with v i c i n a l or geminal r e l a t i o n s h i p were considered, Figure E, which corresponds to the H3 proton, shows a doublet at A^2» this r e f l e c t s the fact that H3 is i n d i r e c t l y connected to HI v i a H2. Such responses from the i n d i r e c t l y connected protons were generally found to be weak in the present study and hence they have not been emphasised. (This should be compared with the e a r l i e r discussion on the (absence of) signals at due to small long-range couplings.) *For example the multiplet at A 5 6 1 , shows two large couplings of about 10 and 14 Hz, the l a t t e r a r i s i n g from the J difference [2.5-(-12.5)]. - 183 -Although we have deliberately chosen a weakly coupled multi-spin system, with r e l a t i v e l y simple sub-spin systems, i t i s evident from Table 5.4 that ZQT of the second kind could well give r i s e to additional peaks for more complicated spin systems. In general these lines may be expected to appear at r e l a t i v e l y higher frequencies i n f^ than those of the f i r s t kind and they should therefore, be easily i d e n t i f i e d . In this chapter a preliminary study regarding a two-dimensional correlation (or assignment) technique was presented which involves forbidden transitions i n a homonuclear (proton) system. I t was evident from the discussions i n the previous chapters that more v e r s a t i l e and convenient assignment techniques are needed for the study of complex molecules. The relat i v e merits and limitations of the various assignment techniques are discussed i n the f i n a l chapter. - 184 -References (Chapter V) 1. Aue, W.P., Bartholdi, E., Ernst, R.R. J . Chem. Phys. (1976) 64, 2229. 2. A l i a , M., Lippmaa, E. Chem. Phys. L e t t . (1976) 37, 260. 3. Hester, R.K., Akerman, J.L., Neff, B.L., Waugh, J.S. Phys. Rev. L e t t . (1976) 36, 1081. 4. Vega, S., Shattuk, T.W., Pines, A. Phys. Rev. L e t t . (1976) 37, 43. 5. Bodenhausen, G., Freeman, R., Niedermeyer, R., Turner, D.L. J . Magn. Re son. (1977) 26, 133. 6. Wokaun, A., Ernst, R.R. Chem. Phys. L e t t . (1977) 52, 407. 7. Wokaun, A., Ernst, R.R. Mol. Phys. (1978) 36, 317. 8. Bodenhausen, G., Void, R.L., Void, R.R. J . Magn. Reson. (1980) 37, 93. 9. Warren, W.S., Sinton, S., Weitekamp, D.P., Pines, A. Phys. Rev. L e t t . (1979) 43, 1791. 10. Nagayama, K., Wuthrich, K., Ernst, R.R. Biochem. Biophys. Res. Commun. (1979) 90, 305. 11. Bain, A.D., B e l l , R.A., Everett, J.R., Hughes, D.W. J . Chem. Soc. Chem.  Commun. (1980) 256. 12. Kaplan, J . I . , Meiboom, S. Phys. Rev. (1957) 106, 499. 13. Yatsiv, S. Phys. Rev. (1958) 113, 1522. 14. Schaublin, S., Hoehner, A., Ernst, R.R. J . Magn. Re son. (1974) 1_3, 196. 15. S l i c h t e r , C P . " P r i n c i p l e s of Magnetic Resonance", 2nd ed., Spinger-Verlag: B e r l i n , 1978. 16. Maudsley, A.A., Wokaun, A., Ernst, R.R. Chem. Phys. L e t t . (1978) 55, 9. 17. Vega, S., Pines, A. J . Chem. Phys. (1977) 66, 5624. 18. Hatanaka, H., Terao, T., Hashi, T. J . Phys. Soc. Japan (1975) 39, 835. - 185 -19. S t o l l , M.E., Vega, A.J., Waughan, R.W. J . Chem. Phys. (1977) 67, 2029. 20. Emsley, J.W., Feeney, J . , S u t c l i f f , L.H. "High re s o l u t i o n Nuclear Magnetic Resonance Spectroscopy", V ol. I; Pergamon Press: London, 1966. 21. Pople, J.A., Schneider, W.G., Bernstein, J . "High r e s o l u t i o n Nuclear Magnetic Resonance", McGraw-Hill: New York, 1969. 22. Tang, J . , Pines, A. J . Chem. Phys. (1980) 72, 3290. 23. H a l l , L.D., Sukumar, S., S u l l i v a n , G.R. J . Chem. S o c , Chem. Commun. (1979) N6, 292. 24. H a l l , L.D., Sanders, J.K.M.; J . Amer. Chem. Soc. (1980) 102, 5703. - 186 -CHAPTER VI SUMMARY AND DISCUSSION - 187 -5.1 Summary and Discussion In this Section, an attempt w i l l be made to b r i e f l y summarize the p r i n c i p a l findings of this study, to place them into a chemical context, and to speculate about future p o s s i b i l i t i e s with the numerous recent advances in h i g h - f i e l d , superconducting magnet technology and (mini)-computer technology. NMR has proven to be an increasingly powerful and widely used a n a l y t i c a l tool i n chemistry. In addition to the conventional (single-pulse) NMR experiment, the l i t e r a t u r e describes a wide range of NMR techniques which have p o t e n t i a l for solving chemical problems, ei t h e r by providing more information on molecular properties (eg. relaxation time measurements) or by s i m p l i f y i n g spectral a nalysis. The main thrust of this thesis has dealt with the l a t t e r aspect and i t should be clear from the examples chosen that several v e r s a t i l e and convenient NMR techniques now exist for resolving and assigning NMR spectra. Although NMR spectroscopy is used extensively in chemistry, p a r t i c u l a r l y i n synthetic organic chemistry, r e l a t i v e l y less work has been done in biochemistry. Proton NMR spectra of b i o l o g i c a l (or macromolecular) systems are usually too complicated to be analysed by conventional means; however some s i m p l i f i c a t i o n can be achieved by studying, for example, carbon-13 or phosphorous-3l resonances which e x h i b i t a wider range of chemical s h i f t s than protons. One method of simp l i f y i n g proton NMR spectra of biomolecular systems is by s e l e c t i v e suppression of signals, for example by SEFT methods. However the major l i m i t a t i o n of the method arises from the phase and i n t e n s i t y anomalies as discussed i n Chapter I I . SEAS o f f e r s a convenient solution to this problem, by providing e s s e n t i a l l y a high r e s o l u t i o n proton spectrum, independent of the phase problem encountered in SEFT spectroscopy. The f i r s t - 188 -applications of SEAS in chemistry and biology have been presented in this thesis (Sec. 2.5 and 2.6) and serve to demonstrate the potential use of this method in biology. Since the above technique is more suitable for studying the more slowly relaxing (high resolution) components in the spectrum, mobile units of a macromolecule or small molecules in a biological system, for example, can be used as "probes" to study aspects of the system under consideration. Most of this thesis has dealt with an exploration study of the use of double Fourier transform methods for solving NMR spectral analysis; these techniques, in a rather unique way, provide methods to resolve and assign complex spectra and could well revolutionize the use of NMR spectroscopy in many areas of chemistry. Chapter III dealt with proton 2D J spectroscopy mainly from an experimentalist's point of view. Most of the limitations in displaying the 2D J spectral data arise from the complex 2D lineshapes associated with each signal. In the past these spectral traces were displayed in the absolute value mode; however, in the presence of large differences in signal intensities this can cause distortion in a 2D J spectrum and can often lead to loss of information. Several methods were suggested in Chapter III to alleviate this problem such as by selective suppression of unwanted signals and by displaying phase-sensitive (tilted) traces or sub-spectra. Since both chemical shift and coupling constant information of a resonance are contained in the appropriate 45° cross-section of a 2D J spectrum the t i l t routine is a v i t a l step in the 2D J data processing procedure. It is suggested that the phase-sensitive t i l t routine provides a means of manipulating the (sub-) spectrum of each individual multiplet, at the - 189 -f i n a l stage a f t e r the double Fourier transformation, thus optimising the display of each multiplet separately. 2D J spectroscopy provides a method of obtaining e f f e c t i v e l y "broad-band homonuclear-decoupled" spectrum i n one dimension and homonuclear spin-spin coupling constants i n the other dimension. This p r i n c i p a l can be used to achieve "broad-band heteronuclear decoupling" and thus d i s t i n g u i s h homonuclear and heteronuclear spin-spin coupling constants (Sec. 4.3), without the l i m i t a t i o n s imposed by high-power i r r a d i a t i n g frequencies. Usually proton NMR s p e c t r a l assignments have been achieved v i a various ID methods including spin-decoupling and related double resonance techniques such as NOE studies and INDOR techniques. Although in p r i n c i p l e these techniques should provide a l l connectivity information between the spin system of i n t e r e s t , t h e i r success i s c r i t i c a l l y dependent on the r e l a t i v e dispersion of the proton chemical s h i f t s , which can be a serious l i m i t a t i o n when dealing with complex spectra. Furthermore, the decoupling power or the band-width of the i r r a d i a t i n g f i e l d may have to be i n d i v i d u a l l y optimised for each resonance or m u l t i p l e t to achieve the s e l e c t i v i t y needed. Assignment techniques based on two-dimensional Fourier transform spectroscopy have a major advantage over these double resonance methods because they are not l i m i t e d by the spectral dispersion or the i r r a d i a t i n g f i e l d . Although these experiments simultaneously provide, usually i n a single experiment, a l l connectivity information t h e i r general p o t e n t i a l in chemistry remains to be f u l l y explored. 13 1 C- H s h i f t correlated spectroscopy is an elegant assignment technique which uses the wider dispersion of the carbon-13 spectrum to resolve and correlate the proton chemical s h i f t s . This work has shown for the f i r s t - 190 -time that, i n conjunction with 2D J spectroscopy, t h i s provides a powerful t o o l for s p e c t r a l analysis and s t r u c t u r a l e l u c i d a t i o n (Sec. 4.2). The f i r s t a p p l i c a t i o n of zero-quantum t r a n s i t i o n (2D) spectroscopy for NMR s p e c t r a l assignment was demonstrated i n Chapter V, along with an explanation of the features involved, based on the density matrix approach. ZQT spectroscopy is unique i n that i t provides a 2D c o r r e l a t i o n information based on chemical s h i f t s and coupling constants, and also that the ZQT frequency information cannot be d i r e c t l y obtained by conventional methods. Further discussions on the a p p l i c a t i o n of the various assignment techniques are given i n the l a t t e r part of this chapter. Given that most p r a c t i c i n g chemists have r e s t r i c t e d access to the type of sophisticated instruments required for these experiments i t is clear that "time" considerations are c r u c i a l to the extent to which these experiments w i l l be used. Accordingly, the next few paragraphs w i l l be concerned with t h i s s i t u a t i o n . For studies of complex organic molecules, the main p r a c t i c a l l i m i t a t i o n of most 2D NMR experiments arises from the time required for the large data matrix that has to be generated and processed to y i e l d the f i n a l 2D spectrum. For example, the sample of 0.1M 5,epi-sisomycin (12) used in this study (Sec. 4.2) required a 4096 by 128 word-size data matrix, corresponding to the and t^ domain resp e c t i v e l y for the 2D J experiment (the experimental parameters are given along with the figure caption i n F i g . 4.4), 13 1 and required about an hour for data a c q u i s i t i o n . The C- H s h i f t c o r r e l a t i o n experiment on 0.26M solution of the compound was performed on a 2048 by 256 data matrix corresponding to the two domains, and t^ respectively, which required about 4% hours for data a c q u i s i t i o n (see experimental parameters l i s t e d with F i g . 4.2). Data processing for the 2D J - 191 -and s h i f t correlation experiments took about 3 and lh hours respectively. Furthermore the time spent i n pl o t t i n g and obtaining frequency measurements was also substantial; i t is not possible to generalize these times because i t is determined by the complexity of the molecule. For example, the 2D J spectrum shown i n Figure 3.7 took about two hours. Although the experimental times are not substantial, i t must be remembered that for better d i g i t i z a t i o n , p a r t i c u l a r l y in the f^ domain, i t w i l l be necessary to increase both the data acquisition and processing times. On the other hand i f i t is only necessary to obtain approximate chemical 13 1 s h i f t s for spectral assignments as i n the C- H s h i f t correlation experiments, poor d i g i t i z a t i o n can be used i n both dimensions. The experimental times given above are for processing the whole data matrix. In practice, however, only the regions bearing the signals need to be processed, and the frequency information obtained from the appropriate traces (note, for example, most regions of the 2D spectrum in Fig. 4.4 consists of noise). Although 2D NMR experiments are rather time consuming and complex, considering the immense quantity and variety of information that they provide, usually in a single experiment, the time scale of these experiments should not be regarded as p r o h i b i t i v e . Furthermore these techniques can provide information that i s unique, and which i s otherwise often tedious or impossible by conventional means; thus ZQT spectroscopy and "wide-band" homonuclear and heteronuclear decoupling are experiments which have no equivalent in conventional NMR spectroscopy. For any chosen experiment, the t o t a l data acquisition time i s governed p r i n c i p a l l y by the s e n s i t i v i t y of the spectrometer and concentration of the - 1 9 2 -sample. Present day, h i g h - f i e l d spectrometers have considerably eased t h i s problem.* Data processing times depend to a great part on the type of computer system (eg. memory size) available and on the e f f i c i e n c y of the computer program (soft-ware). With the rapid growth of computer technology data handling and processing may be expected to be performed more rap i d l y and e f f i c i e n t l y i n the future. A new method for e f f e c t i v e l y increasing the o v e r a l l e f f i c i e n c y of c e r t a i n NMR experiments was suggested i n Section 3.3.4; t h i s involves the concept of an "integrated" NMR experiment. In the example chosen, several d i f f e r e n t sets of NMR spectral information were obtained from a single experimental data matrix; portions of the o r i g i n a l data matrix were appropriately processed to y i e l d SEFT, SEAS, 2D J and D2D J spectral information. Similar procedures can be adapted for s e l e c t i v e detection of n-quantum t r a n s i t i o n spectra. It seems l i k e l y that further extensions of this concept could s u b s t a n t i a l l y decrease the t o t a l time required for a complete NMR study of complex molecules. It si. ^ld also be possible to improve the o v e r a l l e f f i c i e n c y of 2D NMR experiments by performing data processing simultaneously with data a c q u i s i t i o n ("foreground-background operation") or by automating the whole experimental procedure. It was evident from this study that v e r s a t i l e , new techniques for assigning proton resonances are necessary to complement the high resolving 13 1 power of proton 2D J spectroscopy. One such technique is C- H s h i f t c o r r e l a t i o n spectroscopy; t h i s provides a simple method for assigning or c o r r e l a t i n g resonances providing that either the proton or carbon-13 signal i s previously known. A new assignment technique that was described i n this ^The s e n s i t i v i t y i s proportional to the s t a t i c magnetic f i e l d . - 193 -thesis was that based on ZQT (2D) spectroscopy. In contrast to the 13 1 C- H s h i f t c o r r e l a t i o n experiment ZQT- and "conventional" homonuclear (^H-^H) s h i f t c o r r e l a t i o n (1,2,3) 2D-spectroscopy may be regarded as "high r e s o l u t i o n " experiments; for both the homonuclear techniques the f^ domain represents frequencies of the order of chemical s h i f t s (or "differences") and hence this domain must be s u f f i c i e n t l y d i g i t i z e d which in v a r i a b l y leads to a larger data matrix. In e i t h e r experiment, handling of large data arrays should be given serious consideration, both from the viewpoint of signa l a c q u i s i t i o n times and data processing c a p a b i l i t i e s . The use of ZQT spectra to obtain c o n n e c t i v i t i e s appears to have the following advantages over the homonuclear (^H) s h i f t c o r r e l a t i o n methods: a) the ZQT's are independent of f i e l d inhomogeneity, enabling one to obtain high-resolution spectra ( i n f^) which are limited mainly by "natural" line-widths ( c f . J spectra; Ref. 4), b) the t r a n s i t i o n frequencies (of the f i r s t - k i n d ) appear as chemical s h i f t d i f f e r e n c e s , which may considerably reduce the spectral width i n the f^ domain; this has a number of p r a c t i c a l advantages - since the si z e of the data matrix can now be reduced to achieve the suitable d i g i t i z a t i o n i n the f i n a l 2D spectrum (<cf. Ref. 1, 2 and 3), this could i n turn lead to s i g n i f i c a n t time saving i n data a c q u i s i t i o n and processing, and also minimise the problems associated with the handling of large data assays, c) i t should be possible, as described i n the previous section, to i n d i r e c t l y determine the r e l a t i v e signs of coupling constants, d) ZQT spectra generally exhibit fewer lines than the corresponding SQT spectra, which could help s i m p l i f y s p e c t r a l a n a l y s i s , and e) i t is known that i n 2D c o r r e l a t i o n spectroscopy there is no net magnetization transfer (Sec. 4.2) and that i t r e s u l t s in m u l t i p l e t s which have - 194 -both p o s i t i v e - and negative-going signals; i t i s conceivable that limited d i g i t a l r e s o l u t i o n i n e i t h e r dimension could r e s u l t in c a n c e l l a t i o n of these signals, however, i n spite of the limited d i g i t a l r e s o l u t i o n used to obtain the traces i n Figure 5.5 a l l ZQT's show f i n i t e i n t e n s i t i e s . Since ZQT's are independent of magnetic f i e l d inhomogeneity e f f e c t s , the higher order n-quantum t r a n s i t i o n s may be eliminated by applying a f i e l d gradient pulse during the evolution period (5), thereby obviating the need for elaborate phase c y c l i n g procedures. On the other hand i f one needs to s e l e c t i v e l y study, for example, SQT's or DQT's i t i s only necessary to add or subtract signals r e s u l t i n g from the appropriate phase s h i f t i n g of the e x c i t a t i o n pulse. Although DQT's also contain connectivity information, the r e l a t i v e l y higher frequencies i n f^ (sums of chemical s h i f t s ) and the greater s e n s i t i v i t y to f i e l d inhomogeneity e f f e c t s makes DQT spectra less desirable for p r a c t i c a l a p p l i c a t i o n s . A p o t e n t i a l l i m i t a t i o n of ZQT spectroscopy is the dependence of the i n t e n s i t y of the signals i n the f i n a l 2D spectrum on the preparation delay,t . For example, i t was necessary i n this study of 15 to perform several i n d i v i d u a l experiments to select s uitable values of x to maximise ZQT signa l i n t e n s i t i e s , and thus obtain high r e s o l u t i o n information. On the other hand i t may be that t h i s T-dependence of signal i n t e n s i t i e s can be used to s i m p l i f y ZQT spectra by reducing the t o t a l number of li n e s i n a complex 2D spectrum. In either event i t w i l l be necessary to have more experience of the experimental practice of ZQT spectroscopy and a deeper t h e o r e t i c a l understanding of the signa l i n t e n s i t y dependencies. - 195 -At the time the author started the studies described in this thesis, the 13 1 three different NMR techniques namely 2D J - C- H s h i f t correlated- and n-QT-spectroscopy were already described i n the l i t e r a t u r e , however their diagnostic potential i n the context of studies by a practicing chemist of complex molecules was less obvious. Although 2D NMR spectroscopy is s t i l l not widely used, the work included i n this thesis has demonstrated the potential of 2D NMR techniques is exc i t i n g . Ernst's group i n Switzerland have described a 2D NMR technique for studying NOE (6) and also a method for studying chemical exchange (7), which appear to have many useful p r a c t i c a l advantages over the conventional ID methods for obtaining the same information. These techniques are yet to be f u l l y explored for the study of chemical systems. - 196 -References (Chapter VI) 1. Aue, W.P., Bartholdi, E., Ernst, R.R. J . Chem. Phys. (1976) 64, 2229. 2. Nagayama, K., Wuthrich, K., Ernst, R.R. Biochem. Biophys. Res. Commun. (1979) 90, 305. 3. Bain, A.D., B e l l , R.A., Everett, J.R., Hughes, D.W. J . Chem. S o c , Chem.  Commun. (1980) 256. 4. Freeman, R., H i l l , H.W. J . Chem. Phys. (1971) 54, 301. 5. Wokaun, A., Ernst, R.R. Mol. Phys. (1978) 36, 317. 6. Kumar, A., Ernst, R.R., Wuthrich, K. Biochem. Biophys. Res. Commun. (1980) 95, I-7. Jeener, J . , Meier, B.H., Bachman, P., Ernst, R.R. J . Chem. Phys. (1979) 71, 4546. - 1 9 7 -CHAPTER VII EXPERIMENTAL SECTION - 198 -7.1 The spectrometer The spectrometer used i n this study was assembled at U.B.C. from components which o r i g i n a l l y comprised a Nicolet TT-23 (100 MHz) console, and a narrow bore superconducting solenoid (6.3T) from Oxford instruments. The i n i t i a l experiments were performed using a 293A pulse c o n t r o l l e r , which was l a t e r updated to a 293A'unit. The spectrometer i s controlled by a Nicolet 1180 computer (40K); the standard NTCFT (NMR) programme was used for data a c q u i s i t i o n and processing. Data processing and storage of large (2D) data arrays was f a c i l i t a t e d by two Diablo disk drives (model-30), each with a disk capable of storing one megawords of information. In i t s recently updated configuration, the spectrometer i s f i t t e d with a Nicolet 293B pulse programmer. In addition to the 1180 computer used for the basic data-acquisition and processing an independent data processing system comprising another Nicolet 1180 (40K) computer, a disk drive and a d i g i t a l p l o t t e r has been i n s t a l l e d . Although each of the Nicolet computers has c a p a b i l i t i e s for simultaneous "foreground-background" operation, the two-computer system described here was found to be far more v e r s a t i l e and s u b s t a n t i a l l y increased the o v e r a l l e f f i c i e n c y of the 2D NMR experiments. It is possible with the 293B pulse programmer to programme pulse sequences which include up to 128 steps; i n contrast the 293A-series allows a maximum of only 16 steps. This confers many advantages for programming experiments which involve many pulses; i t i s now possible, for example, to include r e l a t i v e l y sophisticated phase-cycling procedures into multipulse experiments for the can c e l l a t i o n of instrumental imperfections. The Bruker WH-400 (9.4T) with an Aspect 2000 computer was also used i n some experiments. - 199 -7.2 The chemicals used Most of the carbohydrate derivatives used in this study were laboratory samples. The mono- and di-saccharides were obtained from standard laboratory suppliers such as A l d r i c h Chemical Co., or P f a n s t i e h l Lab. Inc. A l i s t of the source of the rest of the chemicals are given below:^" Dextran T-10 - Pharmacia Ltd. BSA, lysozyme - Worthington Biochemicals Co. Compound (j - Laboratory sample (1) Compound 7 and 10 - Gifted by Prof. L. Hough Uridine - Pf a n s t i e h l Lab. Inc. Furoic acid - A l d r i c h Chemical Co. 5,epi-sisomycin - G i f t from Schering Pharmaceutical Co. 1,1,1 t r i f l u o r o propan-2-ol - PCR Research Chemicals, Inc. Compound 13 - Hooker Chemical Co. Compound 15 - Laboratory sample Compound 16 - 1»1>1 t r i f l u o r o propan-2-ol (1 m) and diphenylphosphorochloridate (1.2 m) were reacted in pyridine (solvent and base) according to standard procedures (2,3). The product (16) was obtained by evaporating the solvent and was used for the NMR study without further p u r i f i c a t i o n . Although the sample contained residual pyridine and traces of unreacted material, the s p e c t r a l region of interest was not affected by the impurities. The deuterated solvents used i n the study were purchased from Merck Sharpe and Dohme. The samples when studied i n aqueous medium were usually l y o p h i l i z e d three times i n 98% D2O and made up i n 100% D2O for proton NMR ^Refer to the l i s t of compounds for the names of the respective compounds. - 200 -studies. However this procedure was not necessary in the latter part of the work since i t was possible to presaturate the solvent peak in 2D J NMR experiments when using the 270 MHz spectrometer. NMR spectra measured in aqueous solvents and organic solvents are referenced with respect to internal TSP (sodium 3-trimethylsilylpropionate-2,2,3,3-d^) and TMS (tetramethylsilane) respectively. The 2D NMR experiments described in the following sections is an accurate but brief description of the experimental procedures and not intended to be a detailed instruction manual. 7.3 Red blood c e l l s , sample preparation Red blood cells (RBC) were prepared from freshly drawn venous blood (from Mr. Rob Snoek) and collected in EDTA (10.5 mg Na2EDTA/7 ml blood; anti-coagulant). The whole blood was centrifuged and the red cells washed three times in phosphate buffered saline, with or without added glucose (10 mM). The cells were then washed in Kreb Ringer solution (4) which was made up in D20, with or without glucose (10 mM) at pH 7.2. The samples that were to be exposed to glucose were incubated in Kreb Ringer solution containing 10 mM glucose in D20 for two hours at room temperature (haematocrit ~40%). They were then centrifuged and the supernatant separated from the "pellet" (procedure B). Part of the pellet (haematocrit ~90%) was used in the SEAS studies. Another portion of the RBC-glucose sample was lysed by adding D20 (5 ml/1 ml blood). The sample was then centrifuged at 20,000 g and the pellet, separated from the supernatant, was used in the NMR studies. The RBC which were not exposed to glucose were centrifuged (20,000 g) and the pellet (haematocrit ~85%) made available for NMR studies (procedure A). - 201 -Sample spinning was not employed during the NMR measurements of the RBC samples. 7.4 2D J spectroscopy The pulse sequence used i n proton 2D J spectroscopy with phase alternation of the 180° pulse is as follows: 1. Preparation delay 2. 90° pulse 3. Incremental delay 4. 180° pulse (<f=0°) 5. Incremental delay 6. Signal a c q u i s i t i o n 7. Relaxation delay 8. Preparation delay 9. 90° pulse 10. Incremental delay 11. 180° pulse (<f>=180°) 12. Incremental delay 13. Signal a c q u i s i t i o n 14. Relaxation delay 15. Signal average by repeating (1) through (14) The incremental delay is equal to (T\+n.T) where T\ is an i n i t i a l delay (-50 us); n=0, 1, 2, (N-1). A b r i e f summary of the data processing procedures used in 2D J spectroscopy i s : 1. FT with respect to - 202 2. Transpose e i t h e r a section of, or the whole , data matrix 3. FT with respect to t^ 4. Transpose data 5. T i l t 6. Transpose data 7. "Pick-out" cross-sections (or sub--spectra) 8. Inverse Fourier transform 9. Manipulate data (eg. z e r o - f i l l i n g , d i g i t a l f i l t e r i n g ) 10. "Forward" Fourier transform 11. Phase correct 12. Plot and take measurements Using the Nicolet 2D NMR spectroscopy software the normalization constants for s c a l i n g the spectra were obtained by f i r s t locating the largest s i g n a l , and then setting the sc a l i n g factor with respect to this spectrum p r i o r to Fourier transformation. Depending on the circumstances, suitable d i g i t a l f i l t e r i n g of time-domain signals was employed. Selective i r r a d i a t i o n was employed during the preparation (and relaxation) delay when solvent suppression was needed. In the case of solvent n u l l i n g by inversion recovery, the preparation delay included the following sequence: 1. 180° (non-selective) pulse ($=0°) 2. Delay (equal to the " n u l l point") and the 2D J pulse sequence repeated with phase al t e r n a t i o n (<j>=180°) of the 180° pulse. For the D2D J experiment the i n i t i a l delay (T^) was set to a suitable value (Sec. 3.3.1). - 203 -In the Bruker 2D NMR spectra software, steps ( l ) through (7) of the data processing procedure are automated. This makes the whole operation rather more convenient than that using the Nicolet software. However, the Bruker system does not provide phase-sensitive sub-spectra, nor can i t be modified for the d i f f e r e n t 2D NMR experiments described i n the text; t h i s lack of f l e x i b i l i t y is a regrettable, serious l i m i t a t i o n . 13 1 7.5 Cj- H s h i f t c o r r e l a t i o n spectroscopy The carbon-13 measurements were performed using a home b u i l t probe,* with the receiver c o i l double tuned for observing carbon-13 and deuterium "lock". The 60 watt amplifier provided a 22 us 90° pulse. The proton pulses (and noise-decoupling) were applied using the decoupler c o i l ; the proton 90° pulse was 45 ps using a 10 watt a m p l i f i e r . It was necessary to cool the probe (because of the heat generated by noise-decoupling) by passing a i r through i t at ambient temperature (~20°C). The pulse sequence used is summarised below: 1. Preparation delay 2. 90° proton pulse 3. Incremental delay 4. 180° carbon pulse 5. Incremental delay 6. delay ( 3.3 ms) 7. 90° proton pulse 8. 90° carbon pulse ^The probe construction and e l e c t r o n i c s was done by Tom Markus (Ele c t r o n i c s section, Chemistry Department, U.B.C.) based on a prototype design by Dr. G.A. Morris. - 204 -9. t2 delay ( 2.2 ms) 10. Signal a c q u i s i t i o n (and noise-decoupling) 11. Relaxation delay 12. Repeat (1) through (11) for signal averaging During the preparation delay the carbon-13 signals were saturated by using two long pulses (~450°) with a delay of 150 ms between them; this minimised the unmodulated component (zero-frequency in f^) in the 2D spectrum. The data processing steps are summarised below: 1. FT with respect to t ^ 2. Transpose 3. "Pick-out" the appropriate interferograms 4. FT (a f t e r data manipulation) with respect to t^ 5. Take measurements (eg. a f t e r p l o t t i n g ) From the r e s u l t s i n the present study i t was noted that a non-ideal 180° pulse caused d i s t o r t i o n s and a r t i f a c t s i n the spectrum. This can be a serious l i m i t a t i o n when dealing with carbon-13 spectra whose spe c t r a l widths are >ca. 3000 Hz. In the example chosen i n Section 4.2 (SW=6000 Hz), i t was necessary to perform two experiments each with the transmitter at one end or other of the spectrum to produce the f^ traces i n Figure 4.3. 7.6 Zero-quantum (2D) spectroscopy The pulse sequence used for the s e l e c t i v e detection of odd-n-quantum tr a n s i t i o n s i s given below (where ij> =0°): 1. 90° pulse (phase=<t°) 2. Preparation delay ( "0 3. 90° pulse (phase=<t>°) - 205 -4. Incremental delay 5. 90° pulse (phase=0°) 6. Signal a c q u i s i t i o n 7. Relaxation delay 8. Repeat sequence (1) to (7) with <)>=(<)>+180)° 9. Signal average by repeating sequence (1) through (8) The s e l e c t i v e detection of ZQT's (Figs. 5.4 and 5.5) was achieved by adding the time-domain signals (interferograms) from a separate experiment, si m i l a r to the sequence ( l ) to (9), but with <f> being equal to 90°. The signals S(t^,t2) were acquired on 2048-word size blocks, for 512 increments (625 usee.) in t ^ . After the f i r s t Fourier transformation with respect to t2 and transposition, i n d i v i d u a l interferograms were z e r o - f i l l e d and Fourier transformed with respect to t ^ , to give the traces, S(f2»f^) shown i n Figures 5.4 and 5.5. The preparation delay x was set to ca. 100-300 msec, (which is of the order of the inverse, average coupling constant) for optimum signal i n t e n s i t i e s i n the f i n a l spectrum. Aft e r the completion of the experimental work on ZQT spectroscopy described i n this t h e s i s , which used a 293A' pulse c o n t r o l l e r , the above experiment was repeated using the Nicolet 293B pulse programmer. With the l a t t e r i t is possible to program the whole pulse sequence described above into a s i n g l e , composite experiment and the f^ traces thus obtained showed complete c a n c e l l a t i o n of higher order t r a n s i t i o n s . In contrast, those traces obtained from a combination of two separate experiments showed imperfect c a n c e l l a t i o n of double quantum t r a n s i t i o n s ( F i g . 5.4); i t seems l i k e l y that this i s due to long-term i n s t a b i l i t i e s i n the spectrometer. A further advantage of using a composite pulse sequence or single experiment for - 206 -detecting the ZQT spectum is that i t avoids the limitations (eg. time, storage, etc.) i n handling two large data sets. The data processing for obtaining the individual traces (eg. F i g . si m i l a r to that given i n the previous section. - 207 -References (Chapter VII) 1. Wong, K.F. Ph.D. D i s s e r t a t i o n , University of B r i t i s h Columbia, Vancouver, Canada, 1979. 2. H a l l , L.D., Malcolm, R.B. Can. J . Chem. (1972) 50, 2092. 3. Vogel, A.I. "A text book of p r a c t i c a l organic chemistry", 3rd ed.; Longmans: London, 1956. 4. Cohen, P.P. "Manometric Techniques", Burgess Publishing Co: New York, 1975. - 208 -APPENDICES 2o9. APENDIX A PROGRAM TO TILT PHASE SENSITIVE 2D J DATA 100 DIM B1(7500),A<7500) 110 DIH N1t(3>,N29(3) 120 PRINT "INPUT FILE NAHE \" 130 INPUT N1»(0),N1t(1)»N1f(2) 140 PRINT "OUTPUT FILE NAHE \" 150 INPUT N2«(0),N2<(1),N2t(2) 160 CALL BDEFINE(3,N1t) 170 CALL BDEFINE<4,N2») 180 CALL FREAD(3,B1,352) 190 CALL FURITE(4,B1,352) 200 PRINT "F2 SU = " 210 INPUT U2 220 PRINT "F2 SIZE = " 230 INPUT S2 240 PRINT "CURRENT BLOCK SIZE<REAL+INAG) 250 INPUT S3 260 LET H=352 270 CALL FAINT(H, 1) 280 CALL IAFLT<B1,N) 290 PRINT "F1 SIZE AFTER 2F =" 300 INPUT S1 310 LET T1=S1 320 PRINT "18 = " 330 INPUT 18 340 LET Ul=250000/18 350 LET H1=2»U1/T1 360 LET H2=2«U2/S2 370 LET X=S3/352 380 LET T2=(1+INT(X>>*352 390 LET H2=T2 400 CALL FAINT(H2,1) 410 LET T=S3 420 CALL FDISPI(Bl,7,200) 430 PRINT "NO. OF BLOCKS TILTED" 440 FOR B=0 TO T1-1 450 CALL FREAD(3,B1,72) 460 CALL IAFL7(B1,M2) IF B>=(S1/2) THEN 600 LET X=H1*((S1/2)-0.5-B) Y=X/H2 /Allocate space and f i l e s 470 480 490 500 510 520 530 540 550 560 570 580 LET LET FOR LET IF Z=IN7(Y) P=0 70 72-A1«P-Z A1>=0 7HEN 1 LET A(P)=0 60 TO 580 IF A1>=S2 THEN LET A(P)"B1(A1) NEXT P 560 540 /Write parameters onto output f i l e /Size of data ( f 2 ) to be t i l t e d /±f, width / f d i g i t i z a t i o n / i\ /Number of points to read per block /Display array /Do " r i g h t " s h i f t /Calculate o f f s e t and do " l e f t 1 s h i f t to nearest point 2 1 0 590 60 TO 700 400 FOR P=0 70 T2-1 610 LET X1=H1*(B+0.5-(S1/2)) 420 LET Y1=X1/H2 630 LET Z1=INT<X1/H2) 640 LET A1=P+Z1 650 IF A1>=S2-Z THEN 680 660 L E T A(P)=B1(A1) 670 60 TO 690 680 LET A(P)=0 690 NEXT F 700 FOR P=0 TO T2-1 /Quadratic i n t e r p o l a t i o n routine 710 LET 0=P-1 720 LET R=P 730 LET S=P+1 740 IF R=0 THEN 870 750 IF S>=S2 THEN 870 760 LET E=(Y-Z)*H2 770 LET D2=H2+E 780 LET D3=D2+H2 790 LET L1=<<A<R)*D3*D3)-<A<S)*D2*D2>> 800 LET L2=<P2*A(S))-<D3*A<R)*D2) 810 LET L4= (A(R)-A(Q))/D2 820 LET L3=(A(S)-A<R))*A(G)*D2 830 LET J=((L1*L4)-L3)/(L1+L2) 840 LET K=(A(R)-A<Q)-U-*D2) )/<D2*D2) 850 LET B1 (P) = (A<Q>) + (J*H2) + <K-*H2*H2) 860 60 TO 880 870 LET B1(P)=A(R) 880 NEXT P 890 CALL FAINKB1 ,T2) 900 CALL FURITE(4,B1,T2) /Write t i l t e d block 910 LET S4=B+1 920 PRINT S4, 930 NEXT B 940 CALL D1SP0F 950 PRINT "TILT FINISHED" 960 END 2 1 1 APPENDIX B PROGRAM TO SIMULATE PHASE SENSITIVE TILTED TRACES 100 DIH S(?50) 110 DIM U f ( 3 ) , X » ( 3 ) 120 PRINT "INPUT FILE NAME— 130 INPUT U » ( 0 ) , U I ( 1 ) , U $ < 2 ) HO PRINT "OUTPUT FILE NAHE-150 INPUT Xf(0),X«<t)vXt<2) 160 CALL BDEFINE(11,U$) 170 CALL BDEFINE(12,X$) 180 CALL FREAD<11,S,352) 190 CALL FWRITE(12,S,352) PRINT "T1=" INPUT Tl PRINT "T2=" INPUT T2 LET K=8000 LET U1=-7 LET U2=93 LET N=512 LET H2=0.5 LET H1=0.05 PRINT "H=" INPUT H 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 -\" 380 390 400 410 420 430 440 460 470 480 490 500 510 FOR LET LET LET LET LET LET NEXT /Allocate space and f i l e s /Write parameters onto output f i l e /T 2 i n f± /T 2 i n f /Constant - unit amplitude / f ^ frequency / f 2 frequency /Number of points i n f ^ / f 9 d i g i t i z a t i o n . Ii[ / f 2 trace number LET R1=1/T1 LET R2=1/T2 LET 0=352 . . . LET Q2=Q 360 CALL FDISPKS,Q2,200) 370 LET E=6.2832 P=0 TO Q-1 A0=<P-UN-1)/2))*H1 A1=(A0-W1)*E V1=T1/<1+(A1*A1*R1*R1)) A2=((H*H2)+A0-U2)*E V2=T2/(1+(A2*A2*R2*R2)> S<P)=K»<(V2*V1)-(T1*T2*A1-»V1*A2*V2)) P /Display /Calculate t i l t e d trace LET Q1=Q CALL FAINT(S,Q1> CALL FURITE(12,S,QD BENDFILE H12 END /Write onto output f i l e 212 APPENDIX C PROGRAMME TO SIMULATE A PHASE SENSITIVE-TILTED CROSS-SECTION TO SHOW THE EFFECT OF INTENSE NEIGHBOURING SIGNALS 100 DIN S(1056),J<1056), 1(1056),LU056) 110 DIN U* (3 ) ,X« (3 ) 120 PRINT "INPUT FILE NAME \ " 130 INPUT Ut(0),Uf(1) f Uf(2) 140 PRINT "OUTPUT FILE NAME V 150 INPUT X « ( 0 ) , X * ( 1 ) , X « < 2 ) 160 CALL BDEFINE<11,U*) 170 CALL BDEFINE<12,X*) 180 CALL FREAPd 1 ,S,352) 190 CALL FURITE(12,S,352) 200 BENDFILE *11 210 PRINT "T1=" 220 INPUT T1 230 PRINT "T2=" 240 INPUT T2 250 LET K=16000 260 PRINT "T3=" 270 INPUT T3 280 PRINT "T4=" 290 INPUT T4 300 LET N=1002 310 LET n=200 320 LET H1=0.05 330 LET H2=0.5 340 LET R1=1/T1 350 LET R2=1/T2 360 LET R3=1/T3 370 LET R4=1/T4 380 LET Q=1056 390 LET Q2=Q 400 CALL FDISPKS,02,200) 410 LET E=6.2832 420 LET U4=120 430 LET U3=0.0 440 LET J(P)=0 450 LET U1=-7.366 460 60SUB 540 470 LET UJ=-4.318 480 BOSUB 540 490 LET U1=4.31B 500 60SUB 540 510 LET U1=7.366 520 60SUB 540 530 GOTO 730 /Allocate space and f i l e s /Read and write parameters onto output f i l e /T 2 of mult i p l e t /T* of mult i p l e t /Constant /T 2 of s i n g l e t /T* of si n g l e t /Number of points i n f^ /Cross-section at 200tn point i n f, / D i g i t i z a t i o n i n f ^ / D i g i t i z a t i o n i n f ^ /Display c a l c u l a t i o n /Chemical s h i f t o f f s e t of singlet /Frequency components of the mul t i p l e t 21 3_ 540 LET 550 FOR 560 LET W2=U1+(M*H2) P=0 TO Q-1 I(P)=0 /Calculate t i l t e d trace for each l i n e and sum them 570 LET L<P)=0 580 LET A0=(P-((N-1>/2>)*H1 590 LET A1=(A0-U1)*E 600 LET V1=T1/(1+(A1*A1*R1*R1)) 610 LET A2=(A0-U1)*E 620 LET V2=T2/<1+(A2+A2*R2*R2)> 630 LET I(P)=K*((V2*v1)-(T1*T2*A1*VUA2*v2)) 640 LET A3=(A0-U3)*E 650 LET V3=T3/( 1 + <A3*A3=*R3*R3)) 660 LET A4=<(M*>H2)+A0-U4)*E 670 LET V4=T4/(1 + (A4-*A4*R4*R4>) 680 LET L<P)MK*3)*<<v3*V4>-<T3*T4*A3*V3*A4*V4)) 690 LET J(P)=I(P)+L(P)+J(P) 700 LET S<P)=J<P) 710 NEXT P 720 RETURN 730 LET Q1=Q 740 CALL FAINT(S,Q1) 750 CALL FURITE(12,S,Q1) /Write onto output f i l e 760 BENDFILE #12 770 CALL DISP0F 780 END .214. APPENDIX D PROGRAMME TO SHIFT FID'S IN INTEGRATED NMR EXPERIMENTS -\" 1O0 DIM 6(9000),R(9000) 110 DIN N1t(3),N2t(3) 120 PRINT "INPUT FILE NAME \ " 130 INPUT N 1 « ( 0 ) , N U ( 1 ) , N 1 * ( 2 ) 140 PRINT "OUTPUT FILE NAME 150 INPUT N2$(0),N2$(1),N2*<2) 160 CALL BBEFINE(11,N1$) 170 CALL BDEFINE(12,N2*) 180 CALL FREAD(11,Q,352) 190 CALL FURITEU2,0,352) 200 PRINT "I8(USEC)=" 210 INPUT 18 220 PRINT "DUELL TIME=" 230 INPUT D1 233 PRINT "D8(USEC)=" 240 INPUT D8 250 PRINT "SIZE=" 260 INPUT S2 270 PRINT "NO. OF BL0CKS=" 280 INPUT S1 290 LET T1=S1 300 LET T=(S2/352)+0.6 310 LET T2=(INT(T))-*352 320 LET M2=T2 330 FOR B=0 TO T1-1 340 LET J=(((B*I8HD8)/D1 )+0.5 350 LET J4=0 360 LET J1 = INTU) 370 LET J4=J1 380 CALL FREAD(11,Q,M2) 390 CALL IAFLT(U,M2) 400 LET J3=(T2-J1) 410 FOR P=0 TO T2-1 420 LET J5=(J4+P) 430 IF J5>=S2 THEN 460 440 LET R(P)=Q(J5) 450 GO TO 470 460 LET R<P)=0 470 NEXT P 472 CALL FAINT(R,M2) 480 CALL FUR1TE(12,R,H2) 490 NEXT B 500 PRINT "END OF EXPT" 510 END /Allocate space and f i l e s /Read and write parameters onto output f i l e /Tau value / I n i t i a l delay /Number of points to read per block /For each block / F i r s t point of new block /Write s h i f t e d block onto output f i l e - 215 -APPENDIX E ABBREVIATIONS1 NMR Nuclear Magnetic Resonance CW Continuous Wave FT Fourier Transform RF Radio Frequency 2D Two-D imen s i ona1 FID Free Induction Decay SPD Single Phase Detection QPD Quadrature Phase Detection C-P Carr-Purce11 CPMG Carr-Purcell-Meiboom-Gill ZQT (or C) Zero-Quantum T r a n s i t i o n (or Coherence) SQT Single-Quantum T r a n s i t i o n MQT Multiple-Quantum T r a n s i t i o n INDOR Inter-Nuclear Double Resonance NOE Nuclear Overhauser Enhancement B Q S t a t i c magnetic f i e l d B^ Applied radio-frequency magnetic f i e l d i (-I)'* a°. x, ot¥y A pulse which corresponds to a " f l i p - a n g l e " of ot°; the — subscript refers to the applied d i r e c t i o n x,y,z The Laboratory coordinates x',y',z' The rota t i n g frame coordinates ct,B Ct and 8 nuclear spin state wave functions ^See also Appendix F - 216 -[ a j j l t The i j coherence of the density matrix at time t Chemical s h i f t in parts per m i l l i o n (ppm) ij,,,, Chemical s h i f t separation between n and m nuclei in Hz Efljjj Summation of the precession frequencies of the nuclei n and m i n the rotating frame h Planck's constant y Magnetogyric r a t i o k Boltzmann's constant AT Acquisition (sampling) time SR Sampling rate SWi 2 Spectral width; the subscripts refer to the f^ or f 2 domain DR^?2 D i g i t a l resolution BS Block size NA Number of acquisitions RD Relaxation delay VD Variable delay SF Spectrometer frequency RBC Red Blood Cells - 217 -APPENDIX F NOMENCLATURE One-dimensional (NMR) spectroscopy -The standard or conventional NMR experiment i n which the time domain signals a r i s i n g from a system which has been subjected to a pulse sequence i s Fourier transformed to y i e l d a si g n a l i n t e n s i t y versus frequency spectrum. Two-dimensional (NMR) spectroscopy -A technique by which an NMR spectrum i s displayed i n two frequency dimensions. It involves the a c q u i s i t i o n of a data matrix, S ( t i , t 2 ) , as a function of two time variables ( t ^ and t2) which when subjected to Fourier transformation with respect to t^ and t 2 y i e l d s a 2D spectrum S ( f ^ , f 2 ) , with the orthogonal frequency axes f j and f 2 r e s p e c t i v e l y . The f 2 domain corresponds to the observable NMR signals. J modulation -A resonance, whose amplitude or phase is modulated as a function which is related to i t s coupling constant, with time. Proton 2D J spectroscopy -A 2D NMR experiment i n which the f^ dimension represents coupling constants only (J spectrum); the chemical s h i f t s and magnetic f i e l d e f f e c t s are eliminated i n the f^ domain; the f 2 domain represents the conventional spectrum (see 45°-tilt routine). " P r o t o n - f l i p " l^C 2D J spectroscopy -The carbon-13 2D J experiment i n which a 180° pulse is applied to the proton spins simultaneously with the carbon refocussing pulse. "Gated-decoupler" 13 C 2D J spectroscopy -The carbon-13 2D J experiment where the decoupler is gated on or o f f during the evolution period ( t ^ ) . Chemical s h i f t correlated spectroscopy -2D NMR experiment which give a c o r r e l a t i o n between spin-spin coupled n u c l e i . Such experiments may involve homonuclear or heteronuclear systems, and include allowed SQT's or forbidden t r a n s i t i o n s . MQT (2D) spectroscopy -2D NMR experiments which enable the measurement of (forbidden) multiple quantum t r a n s i t i o n frequencies. Selective detection of t r a n s i t i o n s of a s p e c i f i c order is also possible. The f^ domain represents the n-QT spectrum. - 218 -Delayed 2D J experiment -A 2D J experiment i n which the broad, r a p i d l y relaxing components from a 2D J spectrum are eliminated. Interferogram -The t \ , time domain s i g n a l , S(f2»fi). The corresponding signal obtained from the spin-echo experiment is often referred to as the echo-in t e r ferogram. 45°-tilt routine -A transformation i n frequency space, which re s u l t s i n a proton 2D J spectrum, S ( J , < 5 ) , i n which the two orthogonal axes represent coupling constants and chemical s h i f t s r e s p e c t i v e l y . In the phase-sensitive t i l t routine the r e a l and imaginary parts of the spectra are independently subjected to the t i l t . P r ojection -A display procedure which is obtained by summing a 2D data matrix, along a s p e c i f i e d d i r e c t i o n . This should be compared with the "maximal" projection which represents the highest point along a s p e c i f i e d d i r e c t i o n . Cross-section -A trace taken along a s p e c i f i e d d i r e c t i o n from a 2D spectrum. Usually this refers to a 45° cross-section of a multiplet taken from a 2D J spectrum and is equivalent to a p a r t i a l J spectrum. Sub-spectrum -A phase-sensitive cross-section, which includes both the r e a l and imaginary parts. Proton-decoupled proton spectrum -A 45° projection of a proton 2D J spectrum (or a 0° projection of a t i l t e d 2D J spectrum S ( f ' i , f ' 2 ) ) which represents the chemical s h i f t spectrum for a weakly coupled proton spin system. " t i - n o i s e " -A band of noise which appears along each "resonance" frequency in the f^ d imension. "phase-twist" -A complex 2D lineshape r e s u l t i n g from double Fourier transformation - 2 1 9 -T1IR -Refers to the inversion recovery pulse sequence used for s p i n - l a t t i c e r e l axation time measurements. Car r - P u r c e l l pulse sequence (T2CP) -The basic C-P pulse sequence which involves a 90° pulse and a 180° pulse separated by a delay, t (method A). A modification which minimises the e f f e c t of d i f f u s i o n i n T 2 measurements involves a series of 180° pulses each separated by 2 x , a f t e r an i n i t i a l 90° pulse (method B). Spin-echo Fourier transform (SEFT) spectroscopy -This involves the Fourier transformation of the half-echo signals obtained from a T2CP pulse sequence. Spin-echo absorption spectroscopy (SEAS) -This involves the Fourier transformation of the whole-echo signal obtained from a T2CP pulse sequence and the display of the magnitude spectrum which shows an absorption mode NMR spectrum. Phase a l t e r n a t i o n -The change of the phase of a pulse by 180° on every alternate pulse sequence. This i s usually performed i n order to minimize the e f f e c t s of pulse imperfections. Spin-echo correlated spectroscopy (SECSY) -A homonuclear chemical s h i f t correlated experiment, including phase-cycle of the two 90° pulses so as to obtain a 2D spectrum where the f j axis is represented by only "frequency d i f f e r e n c e s " of correlated protons. The e f f e c t i v e d i g i t i z a t i o n i n f^ may be improved and the experimental time decreased when compared to the o r i g i n a l experiment which uses just two 90° pulses. The pulse-sequence for SECSY i s : {90° - hti - 90° - hti - Acquisition} Two-dimensional nuclear Overhauser enhancement (2D NOE) experiment -A 2D technique for obtaining, i n the f\ domain, c o r r e l a t i o n between protons which couple v i a d i p o l a r i n t e r a c t i o n s . This i s analogous to the NOE studies used i n ID NMR. The pulse sequence used i s {90° - ti - 90° - x m ~ 90° - Acquisiton) where t m is the mixing period - 220 -Transposition -A operation which "exchanges" the rows and columns of a data matrix. In 2D NMR experiments, r e a l and imaginary components are transposed independently. J spectrum or p a r t i a l J spectrum -A spectrum which contains only coupling constant information, eg. the proj e c t i o n of the whole 2D J spectrum onto the f^ axis, is a J spectrum, and a p a r t i a l J spectrum corresponds to one which contains signals corresponding to a single m u l t i p l e t . PUBLICATIONS 1. Forrest,T.P., Sukumar,S. Can. J . Chem. (1977) 55, 3686: "A comparison of Substituent E f f e c t s on V i c i n a l Proton-Proton and Carbon-Proton Coupling Constants". 2. Hall.L.D., Sukumar,S., Sullivan,G.R. J . Chem. S o c , Chem. Commun. (1979) 293: "Two-dimensional J Spectroscopy: *"H NMR Spectra of Mono- and Di-saccharides". 3. Hall.L.D., Sukumar,S. J . Amer. Chem. Soc. (1979) 101, 3120: "Applications of Homonuclear Two-dimensional J Spectroscopy:an a l t e r n a t i v e to Heteronuclear and Homonuclear Decoupling". 4. Hall,L.D., Sukumar,S. Carbohydr. Res. (1979) 7^4, C l : "Nulling of residual-solvent resonance during proton Two-dimensional J NMR experiments:Uridine i n water". 5. Hall.L.D., Morris,G.A., Sukumar,S. Carbohydr. Res. (1979) 76, C7: "Resolution of complex, proton-N.M.R. spectra of Carbohydrate d e r i v a t i v e s by using " T i l t e d " Two-dimensional J spectra". 6. Hall.L.D., Morris,G.A., Sukumar,S. J . Amer. Chem. Soc. (1980) 102, 1745: "Resolution and Assignment of the 270-MHz Proton Spectrum of Cellobiose by Homo- and Heteronuclear Two-dimensional NMR". 7. Hall,L.D., Sukumar,S. J . Magn. Reson. (1980) 38, 559: "Applications of Absorption-mode Spin-Echo Spectra". 8. Hall.L.D., Sukumar,S. J . Magn. Reson. (1980) 38, 555: "Phase-Sensitive Displays f o r Proton 2D J Spectra". 9. Hall.L.D., Sukumar,S. J . Magn. Reson. (1980) 4X), 405: "A v e r s a t i l e strategy for the Generalised A c q u i s i t i o n of Proton Spin-Echo DataMeasurement of P a r t i a l l y relaxed Two-dimentional J Spectra". 10. Hall.L.D., Sanders,J.K.M., Sukumar,S. J . Chem. S o c , Chem. Commun. (1980) 366: "Measurement of V i c i n a l arid Geminal Proton Coupling Constants of Steroids using Proton Two-dimensional J Spectroscopy". 11. Hall.L.D., Sukumar,S. Relaxation Times, (1980) 1, 3: "Two-dimensional NMR for the P r a c t i s i n g Chemist". 12. Pouzard,G. Sukumar,S. Hall.L.D. J . Amer. Chem. S o c (1981), i n press: "High Resolution Zero-Quantum T r a n s i t i o n (Two-dimensional) NMR Spectroscopy: Spectral Analysis". 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0060722/manifest

Comment

Related Items