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hemical and Stereochemical applications of paramagnetic lanthaipe Chelate complexes Armitage, Ian MacLeod 1972

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CHEMICAL AND STEREOCHEMICAL APPLICATIONS OF PARAMAGNETIC LANTHANIDE CHELATE COMPLEXES BY IAN MACLEOD ARMITAGE B.Sc. (Hon.), Bishop's University, 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November, 1972 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver 8, Canada Date $-r\ 2 C, J - i i -ABSTRACT Paramagnetic substances can produce two principal effects on the high resolution nuclear magnetic resonance (n.m.r.) spectra of any substrate molecule that will associate with them in solution. First of a l l the unpaired electrons can cause changes in nuclear relaxation times and secondly, paramagnetic substances produce changes in chemical shifts as a result of a pseudocontact or contact interaction or both. This thesis describes some ways in which the chemical shift changes induced by paramagnetic chelate complexes of some lanthanide metals can be used to study the chemical and stereochemical properties of organic molecules. The predominance (for protons at least) of the pseudo-contact interaction coupled with the rapid reversible equilibrium between lanthanide complex and organic substrate accounts for the unique suitability of these reagents for the present study. In Chapter I, the "^H n.m.r. spectra of a series of 1,2:5,6-di-0_-isopropylidene-a-D-hexofuranose systems have been studied in solution with tris(dipivaloylmethane)-(dpm)-derivatives of europium, thulium and praseodymium. All three reagents were found to induce large stereospecific "^H chemical shifts in the carbohydrate spectra. Eu(dpm).j was particularly suitable; producing the optimum shift to line broadening ratio. The induced shifts were found to vary linearly with the amount of added lanthanide reagent thus facilitating the recovery of the "normal" chemical shift data. Some experimental optimizations for the use of these lanthanide shift reagents to induce chemical shift - i i i -dispersion, with the minimal amount of broadening and hence the maximal number of measurable coupling constants, have been discussed. The utility of lanthanide shift reagents to assist in assigning 13 C n.m.r. spectra has also been discussed. The model system, 2,2-dimethyl-l-propanol was used for this study. In Chapter II, a detailed theoretical analysis of the equilibrium which exists between a lanthanide shift reagent, L, and a substance, S, is presented and tested on several suitable substrate molecules interacting with a variety of lanthanide shift reagents. Using this novel approach, i t was possible to completely characterize the lanthanide-substrate equilibrium in terms of three parameters: the equilibrium binding constant, K^ ; the bound chemical shift, A , for each proton of a substrate; the solution stoichiometry, a n. Subsequent use of this knowledge was applied to studies of complex stability and to determination of molecular structure. The dependence of K , A and n on the basicity of the donor group, B B the lanthanide reagent, the intramolecular steric hindrance at the substrate donor atom and the organic solvent has been thoroughly described. Substrates used for these studies included a variety of amines, alcohols and ketones and the organic solvents consisted of carbon tetrachloride, benzene and chloroform. Lanthanide shift reagents consisted of the tris(dipivaloylmethane) derivative of europium thulium and praseodymium for which typical K -values were <100 liter mol and the tris(2,2-dimethyl-6,6,7,7,8,8,8-heptafluoro-3,5-octanedionato)-europium(III), [Eu(fod)^], complex for which corresponding K^-values were increased by at least 10-fold. - iv -Perhaps the most important parameter to be unambiguously determined is the "bound" chemical shift for each proton of an organic substrate bound to a lanthanide shift reagent. This parameter reflects the stereospecific nature of the induced chemical shifts and can be used to determine the geometry of the lanthanide-substrate complex and thus presumably the conformation of the substrate its e l f . In Chapter III, the potential use of lanthanide shift reagents in the determination of complex conformation has been rigorously investigated using a series of detailed computer programs which have been listed in the Appendices. Particular emphasis (from both a chemical and a mathematical point of view) is placed on the importance of internal rotation to the success of this approach to molecular conformations in solution. A variety of new models for free or hindered internal rotation is proposed and tested on four organic substrates (both alcohols and amines) which are rigid except at the point of attachment to the lanthanide. The studies presented are successful in arriving at well-defined and chemically reasonable substrate conformations. - V -TABLE OF CONTENTS Page GENERAL INTRODUCTION 1 CHAPTER I. STUDIES OF THE CHEMICAL SHIFT CHANGES IN BOTH PROTON AND CARBON-13 N.M.R. PRODUCED BY THE ADDITION OF PARAMAGNETIC LANTHANIDE CHELATE COMPLEXES 16 Introduction 16 Results and Discussion 18 A. Measurement of the ^"H Chemical Shift Changes of Carbohydrates Induced by Lanthanide Shift Reagents 18 B. Applications of Lanthanide Shift Reagents to 13 the Identification of C Resonances 35 C. Temperature Dependence of the Paramagnetic Induced Shift in 1H N.M.R 44 CHAPTER II. QUANTITATIVE INVESTIGATION OF THE LANTHANIDE SHIFT REAGENT-SUBSTRATE EQUILIBRIA: THE UNAMBIGUOUS EVALUATION OF THE BINDING CONSTANTS, BOUND CHEMICAL SHIFTS, AND STOICHIOMETRY 49 Introduction 49 Theory 52 I. Experiments in which [L]0 is Varied at Constant [S] 55 o II. Experiments in which [S] is Varied at Constant [L] 57 - vi -Page III. Stoichiometry 59 IV. Solvent Dependence 63 V. Temperature Dependence 65 Results and Discussion 68 A. Stoichiometry 74 B. Basicity of the Donor Group and the Importance of Steric Effects on L 79 C. Explanation for the Greater Effectiveness of Eu(fod)^ as Opposed to Eu(dpm)^ 81 D. Explanation for the Differing Magnitude of Induced Shifts for Different Ln(dpm)^ Complexes 83 E. Solvent Effects on Kg- and Ag-Values 85 F. General Applications 93 G. The Applicability of the Scatchard-Type Plot to the Analysis of the Concentration Dependence of the Shifts 108 CHAPTER III. DETERMINATION OF MOLECULAR CONFORMATION IN SOLUTION USING LANTHANIDE N.M.R. SHIFT REAGENTS: SIGNIFICANCE OF INTERNAL ROTATION 117 Introduction 117 Theory 125 Results and Discussion 135 GENERAL CONCLUSIONS » 163 - v i i -Page EXPERIMENTAL 165 A. Techniques and experimental methods, synthesis and/or purification of compounds, for Chapter I .. 166 B. Techniques and experimental methods, synthesis and/or purification of compounds not previously described in part A, for Chapters II and III 169 APPENDIX A. Calculation of r. and 6. from R, Q, and <j> 174 l I APPENDIX B. Computer program "COORD" used to calculate the cartesian co-ordinates for a l l atoms in the substrate molecule 176 APPENDIX C. Computer program used to determine complex 1 conformation for a rigidly locked complex 183 APPENDIX D. Computer program used to calculate complex conformation for free (or essentially free) internal rotation about the carbon-donor atom bond of the complex 187 REFERENCES 191 - v i i i -LIST OF TABLES Table Page CHAPTER I 2 3 4 5 Chemical shifts (x-values) for compounds 3_ and 4^  in deuterochloroform solution, showing values obtained by direct measurements and by corrected extrapolations to zero concentration of a shift-concentration plot for the addition of lanthanide reagents 5^ , J5, and ]_ .. 26 N.m.r. parameters for l,2:5,6-di-0-isopropylidene-a-D-glucofuranose 1 29 Ratios of the chemical shift changes of selected pairs of protons for compounds 1_ and 3_ in deutero-chlorof orm solution after the addition of lanthanide reagents 5_, J5, and 7_ 34 1 13 Summary of the H and C chemical shifts of 2,2-di-methyl-l-propanol j3 in chloroform solution showing the effect of added tris (dipivalomethanato)europium 5^ , thulium J5, or praseodymium 1_ 39 1 13 Ratios of the H and C chemical shift changes for compound 8^  in chloroform solution after the addition of lanthanide reagent 5^, 6., and ]_ 42 Temperature-dependent chemical shifts data of protons of 5-hydroxy-l,2,3,4,7,7-hexachloronorborn-2-ene JLl in deuterochlorof orm containing Eu(dpm)„, 5_ 45 CHAPTER II 7 71 - ix -Table Page 8 Calculated values of bound chemical shifts (A_) , B and binding constants ( K ) for complexes of organic substrates with Eu(dpm)^ in deuterochloroform solution 80 9 Calculated values of bound chemical shifts (A„), and binding constants ( K T > ) for complexes of organic substrates with different Ln(dpm)^ in deuterochloro-form solution 86 10 Calculated values of bound chemical shifts (A,,), ratios of AD and binding constants (K ) for complexes of 8 with Eu(dpm)^» Eu(fod)^, Pr(dpm)^ and Tm(dpm)^ in three different solvents 88 11 Calculated values of bound chemical shifts (A_) , ratios B of Ag and binding constants (K^) for complexes of 3,3-dimethyl-2-butanone, jL8_, with EuCfod)^ in three different solvents 91 12 Calculated values of bound chemical shifts (Ag), and binding constants (K^) for complexes of organic substrates with either Eu(dpm)^ or Eu(fod)^ • 94 CHAPTER III 13 Induced chemical shift ratios for association of four substrates with lanthanide n.m.r. shift reagents 137 14 Bond distances, bond angles and dihedral angles used to calculate a set of cartesian co-ordinates from COORD for 1,2 :5 ,6-di-C^-isopropylidene-a-D-glucof uranose. 139 - x -Table Page 15 Bond distances, bond angles and dihedral angles used to calculate a set of cartesian co-ordinates from COORD for aniline 146 16 Bond distances, bond angles and dihedral angles used to calculate a set of cartesian co-ordinates from COORD for 5-hydroxy-l,2,3,4,7,7-hexachloronorborn-2-ene 152 17 Induced chemical shift data for association of pyridine with Eu(dpm)„: three independent determinations 161 - xi -LIST OF FIGURES Figure Page CHAPTER I 1 The 1H n.m.r. spectra (100 MHz) of 1,2:5,6-di-0-isopropylidene-a-D-glucofuranose (1, 0.0842 g) in CDC13 (0.5 ml). A. The normal spectrum; B. The spectrum after the addition of Eu(dpm)_ (5_, 9.84 x -2 10 mol equiv); C. As for B but with the further addition of water (0.01 ml, 1.55 mol equiv per mol of 1) 20 2 Chemical shifts observed for a solution of 1 (0.0842 g) in CDC13 (0.6 ml) following the dropwise addition of a solution Eu(dpm)^ (5, 0.0312 g) in CDC13 (1 ml) 22 3 Plot of the chemical shift changes observed for a solution of JL (0.0897 g) in CDC13 (0.6 ml) induced by Tm(dpm)3,6^  23 4 Plot of the chemical shift changes observed for a solution of 1 (0.0964 g) in CHC13 (0.6 ml) induced by Pr(dpm)3, ]_ 24 5 The "Si n.m.r. spectrum (100 MHz) of 1,2:5,6-di-0-isopropylidene-a-D-glucofuranose (1, 0.0842 g) in CDC13 (0.5 ml). A. The normal spectrum; B. Computer simulation of normal spectrum by LA0CN3 27 6 Plot of the chemical shift changes observed for the H-3 and H-5 protons of 1_ induced by Eu(dpm)3 as a function of solvent 33 - x i i -Figure Page 1 13 7 Plot of the H and C chemical shift changes of 2,2-dimethyl-l-propanol, 8^ , in the presence of varying concentrations of Eu(dpm)^, _5, using CHCl^ as solvent 37 1 13 8 Plot of the H and C chemical shift changes of 2,2-dimethyl-l-propanol, j3, in the presence of varying concentrations of either PrCdpm)^,^, or TmCdpm)^ , using CHCl^ as solvent 38 9 Plot of the chemical shift changes versus inverse temperature for a solution of 5-hydroxy-l,2,3,4,7,7-hexachloronorborn-2-ene (11, 0.0951 g) in CDC1_ -2 (0.6 ml) with Eu(dpm) '(5, 9.4 x 10 M equiv) 47 CHAPTER II 10 The relationship between the terms <5 A 6 ^ B obs 6S a n d 6LS 5 4 11 Graphs of i n i t i a l substrate concentration [S] Q versus (1/6) for a hypothetical substrate of Ag = 2000 Hz in the presence of shift reagent of concentra-tion [L]Q = 0.006 M. For each graph, the binding is assumed to be either 1:1 with corresponding binding constant, K or 2:1 with binding constant, K. a (A) K = 32, Kg = 3.2; (B) K = 126, Kg = 12.6; (C) K = 501, K = 50.1; (D) K = 1000, K^  = 100 62 a d 12 Graph of [S] versus (1/<S) for the interaction of n-propylamine, 12_, (0.23 to 0.04 M) with Eu(dpm)3 (ca. 0.006 M) in deuterochloroform solution 69 - x i i i -Figure Page 13 Plot of induced chemical shift(6) versus ratio of the i n i t i a l concentrations of Eu(dpm)3, 5_, Il]0» to neo-pentanol, J3, I S ]q, in deuterochloroform solution 73 14 Plot of 6 versus JL] for the interaction of neo-Jo pentanol, j i , (whose concentration was fixed at the value stated for each line) with Eu(dpm)^ (ca. 0.02 to 0.005 M) in deuterochloroform solution. All shifts are for the H-l proton of neo-pentanol 75 15 Plot of 6 (induced chemical shift for the H-l proton) versus ratio of the in i t i a l concentration of Eu(fod)3, [L]o > to neo-pentanol, [S]Q, in CDCl^ solution ... 77 16 . Plot of [S] versus (1/6) for the interaction of neo-pentanol, (0.4 to 0.08 M) with Eu(fod)3 (ca. 0.006 M) in deuterochloroform solution 82 17 Plot of IS] versus (1/6) for the interaction of o neo-pentanol, j5, with three different lanthanide shift reagents (ca. 0.006 M). For Eu(dpm)3> 5_, and Tm(dpm), 6_, CDCl3 was used as solvent. For Pr(dpm)3> CHC13 was used as solvent. All shifts are for the H-l proton of neo-pentanol 84 18 Plot of [S]q versus (1/6) for the interaction of 1,2:3,5-di-0-methylene-a-D-glucofuranose (21, 0.02 to 0.102 M) with Eu(fod)3 (0.0059 M) in deutero-chloroform solution 98 - xiv -Figure Page 19 The 1H n.m.r. spectra (100 MHz) of N9Pg(NMe2)lg (27, 5.34 x 10~4 to 2.67 x 10~3 M) with Eu(fod) (ca. -4 6.0 x 10 M) in carbon tetrachloride solution. -3 A. The normal spectrum; B. 2.14 x 10 M 27, 6.1 x -4 x 10 M Eu(fod)^; C. The spectrum of the compound obtained by reacting 0.255 grams of Eu(fod)^ with 0.292 grams of 27 105 20 An exact S.catchard plot for the interaction of 18, (0.02 to 0.1 M) with Eu(fod)3 (ca. 0.008 M) in CC1. solution 114 4 CHAPTER III 21A Co-ordinate system for substrate-shift reagent complex. Origin is at donor atom 1, proceeding to atom 2 then defines the positive x-axis; atom 3 is then assigned a positive y-value in the x-y plane; z-direction then follows from right-hand convention. Q, <j> and R unambiguously define the position of the lanthanide relative to the substrate molecular frame . ... . 128 21B Co-ordinate system for substrate-shift reagent complex. Internal rotation of R about the x-axis consists of permitting a range of (f>-values, shown as the circle in the figure 130 22 A diagrammatic illustration of the weight distribution as a function of $ for three simple models of internal rotation 132 - X V -Figure Page 23 Contours of normalized variance ("R-value", agreement factor) between observed and calculated induced chemical shift ratios as a function of possible positions of the lanthanide atom relative to the donor atom of the substrate for JL. It has been assumed that there is no internal rotation about the bond from carbon to donor oxygen. A. 140 B 141 24A Contours of normalized variance as a function of lanthanide position for 1_. For the "static plot", there is no internal rotation about the carbon-donor bond. For the "narrow Gaussian", d>-values 2 are first weighted by the factor, (A//JT) expJ-A (<j>-2 <j) ) ]d<j>, and then integrated over a l l <j> (with A = /8) before comparing observed with calculated shift ratios 143 24B Contours of normalized variance as a function of lanthanide position for 1_. For the "wide Gaussian" <j>-values are first weighted by the factor, (A //rT) 2 2. exp[-A (<(•-<}>) ]d<j),and then integrated over a l l <j> (with A = 1) before comparing observed with calculated shift ratios. For the "free rotation" plot, <j>-values are averaged over a l l <{> from 0 to 2TT using unit weight factor 144 25 Contours of normalized variance as a function of lanthanide position for aniline. Internal rotation about the C-N bond is assumed to be completely free (unhindered) 147 - xv i -Figure Page 26 Contours of normalized variance as a function of lanthanide position for aniline. Top: fits based on experimental shifts for o, m and p protons, assuming no internal rotation about the C-N bond; Middle: fits based on experimental shifts for o, m and p protons assuming no internal rotation about the C-N bond; Bottom: fits based on experimental shifts for o, m and p protons, assuming rapid jumps between fixed <fi-values of 0° and 180° 148 27 Contours of normalized variance as a function of lanthanide position for 11. Internal rotation about the C-0 bond is assumed to be completely free (unhindered) 153 28 Contours of normalized variance as a function of lanthanide position for 11. Top: no internal rotation about C-0 bond; Middle: Gaussian j— 2 2 distribution in 4 , (A//ir) exp[-A (cb-d> ) ] with A = 1, o centered at A = 236°; Bottom: Gaussian of the To ' same width, but centered at (b = 248° 154 o - xvii -ACKNOWLEDGEMENTS I would like to take this opportunity to express my deep appreciation to Dr. L.D. Hall for his advice and constant encouragement throughout the course of this work. Special thanks are due to Dr. A.G. Marshall for his interest and valuable assistance on theoretical aspects, to Dr. P. Legzdins for his advice on inorganic aspects and to Mr. L.G. Werbelow for his assistance with the computer programming for the last section of this work. I acknowledge many helpful discussions with Mr. R.B. Malcolm and Dr. John R. Campbell. Finally, I would like to thank my wife for her understanding and help in the preparation of this thesis. / - 1 -GENERAL INTRODUCTION Proton nuclear magnetic resonance ("*"H n.m.r.) spectroscopy has achieved far reaching success when used for the study of small organic molecules in solution. However, one of the shortcomings' of H^ n.m.r. spectroscopy as a method for studying the structure of more complex organic molecules arises from the intrinsically low sensitivity of "^H chemical shifts to changes in chemical and stereochemical environment; as a result, i t often happens that a resonance of particular interest is obscured by the overlapping transitions of other resonances. Over the years, numerous methodologies and improved instrumentation have been developed to minimize the effects of this problem. These include: use ofhigher magnetic fields,^ spin decoupling and double resonance 2 3 4 experiments such as INDOR, deuterium substitution, solvent shifts, and the study of heteronuclei (spin 1/2 nuclei other than protons) < 19 2 31 13 5 present in the molecule (e.g. F, H, P, C). In addition to the above, as early as 1948,^ i t was recognized that the presence of any paramagnetic centre would influence the n.m.r. spectrum of a resonating nucleus. With respect to chemical applications, the most significant effects of the unpaired electrons in orbitals which have a finite existence at the magnetic nucleus are exhibited by - 2 -the changes in nuclear relaxation times,^ by nuclear spin polarization g which gives rise to the Overhauser effect, by chemical exchange spin 9 10 decouplings, and by large shifts in resonance positions. This latter effect, certainly the most common, is that which has been studied in the pages which follow. For not only is the addition of a , paramagnetic compound to the solution being studied likely to produce very large stereospecific chemical shifts over broader range of magnetic field strength (thereby resolving the complexity of overlapping transitions), but also i t may provide detailed geometrical information of the paramagnetic species as well as of the interacting substrate. Early studies in this area incorporated the paramagnetic properties of transition metal complexes''"^  (e.g. nickel(II) and cobalt(II) diacetyl-acetonates). Peak broadening effects, low solubility of paramagnetic species, and weak interaction with organic molecules have prevented the widespread use of these complexes to resolve overlapping n.m.r. transitions. The potential of paramagnetic lanthanide complexes as "chemicaL-shift" reagents has become the most important recent development in organic n.m.r. This field owes its beginning to Hinckley, who in 12 early 1969, performed experiments on a solution of cholesterol and the dipyridine adduct of tris(dipivalomethanato)europium(III), Eu(dpm)^• 2py, in carbon tetrachloride, with the result that the "'"H chemical shifts of the cholesterol protons were stereospecifically shifted without being significantly broadened. Our interest in this area was heightened by his paper and in the early months of 1970, we became fully engaged in the development of this novel technique as an aid to H^ spectral analysis of carbohydrates. - 3 -Many other laboratories also followed suit and as a result, in three years there appeared in excess of 300 papers in this area. This is ample indication that the era of shift reagents is here to stay and will soon, i f i t has not already, become a routine and integral part of organic n.m.r. spectroscopy. In spite of the enormous amount of attention afforded this area, it remains that a large number of the early, and even some of the more recent papers, have suffered from a serious lack of insight. Many have been entirely erroneous, a fact which has unfortunately distracted from the more than passing importance of this area. Our own i n i t i a l investigations suffered from somewhat similar limitations. Indeed, i t was the recognition of these limitations that led ultimately to the work described in Chapter II and III of this thesis. It is neither appropriate nor intended that this thesis should present a comprehensive review of this area as i t now exists. Rather it is hoped that the following summary will serve as a guide to some highlights which have developed over the past three years. Relevant papers will be discussed in greater detail in the text to follow. For those particularly interested, there are detailed reviews now available in the literature. Despite the diversity of the large number of existing applications pertaining to lanthanide shift reagents, a systematic approach to the area may s t i l l be achieved by the classification of the existing applications under the following three headings: (i) Inorganic, the chemical and physical properties of shift reagents, (ii) Qualitative, applications - 4 -to different classes of organic compounds, (i i i ) Physical, the nature and mechanism of the induced chemical shifts. (i) Inorganic The appropriateness of the paramagnetic, 8-dlketonate chelates of trivalent rare earth metals, of the following general formula, C^LnS^ (C = chelate, S = substrate) is a direct consequence of the variable co-ordination number of these rare earth elements. When n = 0 there are several free, acidic co-ordination sites available for the formation of stable adducts with a large number of substrates. Even complexes with n = 1 or 2, as is the case with Hinckley's reagent, which has a formal co-ordination number of 8, may s t i l l exhibit at least one free co-ordination site. D.PM. RO.D. In addition, the undesirable line broadening associated with para-magnetic complexes of transition metal ions, is not nearly as critical for complexes containing unpaired 4f electrons. This result can be - 5 -traced to their favourably short electron spin-lattice relaxation time, a property which renders them less effective for proton relaxation and hence n.m.r. line broadening. According to a systematic study of the relative proton resonance broadening abilities of the 13 various Ln(dpm)3 complexes by Horrocks, complexes of Eu(III) and Pr(III) are best suited (i.e. exhibit the sharpest signal). Other factors which render these lanthanide complexes more suitable as "chemical-shift" reagents than similar transition metal complexes, are the increased solubility and the absence of interfering absorptions in the usual range of the substrate spectra. Following Hinckley's initiative, Williams"^ demonstrated that the europium complex without the two moles of pyridine,which is commonly written Eu(dpm)3> and which had been first synthesized by Eisentraut in 1965,"^ produced shifts to lower field approximately four times larger in magnitude than those of Hinckley's dipyridine adduct. This was undoubtedly due to the lack of competition with pyridine for the available co-ordination sites. In addition interference resulting . from pyridine resonances in the region of interest for the substrate is removed. Subsequently Rondeau and Sievers"^ found that with the incorporation of the anion of 1,1,1,2,2,3,3-heptafluoro-7,7-dimethyl-4,5-octanedione (fod), an even superior n.m.r. shift reagent could be obtained with respect to both solubility and Lewis acidity. Presence of fluorocarbon on the B-diketonate ligand increases the solubility of the metal complex and, as we now recognize, the electron withdrawing fluorines increase the residual acidity of the cation, making i t a better co-ordination site for weak donors. The usefulness of Eu(fod)^ as a shift reagent is hampered only slightly by ligand resonances at 8-9 6 -T in the "^H n.m.r. spectrum of Eu(fod)3 plus substrate compared to 11-12 T for ligand resonances of Eu(dpm)^ plus substrate. In spite of the superiority of Eu(fod)3 as a "chemical-shift" reagent, there are situations where the use of the Eu(dpm)3 complex is preferable. One example of this occurs in the study of organic compounds which have more than one basic functional group capable of co-ordination to the lanthanide complex. In these cases, the weaker Lewis acid property of the Eu(dpm)^ complex allows it to react more selectively with the polybasic substrate. This results in less broadening of the peaks in the n.m.r. spectrum than that which occurs when Eu(fod).j is similarly employed. Workers in this area to date have incorporated, with some success, the complete range of lanthanide(III) metals with a variety of attached ligands. For the (dpm)^ and (fod)^ derivatives of praseodymium, neodymium, samarium, terbium, dysprosium, and holmium, upfield substrate ligand resonance shifts are obtained in organic solvents, while downfield 14 shifts are observed for erbium, thulium, and ytterbium. The acceptability of a shift reagent, however, depends not only on its ability to shift a substrate resonance but also on its line broadening effect which should be minimal. For example, shifts induced by 18 Yb(dpm)3 are ca. 4 times those for Eu(dpm)^ but the broadening is much larger with the result that a l l information derived from coupling constants is lost when this shift reagent is employed. In this respect, complexes of europium and praseodymium have been most widely used. Of 19 these, Eu(dpm)^ or Eu(fod)3 appears to be more useful than Pr(dpm)^ or Pr(fod)3 because the latter reagents tend to shift the already low - 7 -field resonances to a high field region which may already be complex, 20 thereby increasing the complexity of a n.m.r. spectrum. Several B-diketonates of rare-earths have now been prepared and tested for their suitability as shift reagents. Complexes of europium(III) with ligands such as acetylacetonate and dibenzoylmethanate have been found inadequate principally because of the hygroscopic nature of the 21 former and the low solubility of the latter. All applications discussed thus far and those which follow are for shift reagent-substrate associations in organic solvents. It should be noted that the applica-tion of the water soluble salts of the lanthanide(III) ions (e.g. EuCl3, Eu(N03)3'6D20, Eu(C104)3*6H20 ) to the studies of substrates in aqueous solutions has also been successful. The magnitude of the induced shift has been observed to depend not only on the metal, the ligand attached, the substrate functionality (see later), and various experimental conditions (see Experimental Chapters I and II), but also on the position of the hydrogen relative to the lanthanide in the substrate-shift reagent complex. In this connection, the structure of the lanthanide complex has important implications as will be appreciated later. (ii) Qualitative It is now appropriate to consider the dependence of the induced shift on the substrate functionality. This will be followed by a brief review of some of the many applications of this dependence to organic systems. It was soon realized that only substrates having a sufficiently polar and exposed donor atom could participate in complex formation - 8 -with the lanthanide shift reagents. Other laboratories were quick to realize that the magnitude of the induced shift depended on the basicity of this co-ordination site as well as on the previously discussed factors of metal, ligand and position of the hydrogen 21 relative to the lanthanide ion. Several systems containing suitable functional groups were investigated and the applicability of these lanthanide(III) complexes, which are Lewis acids, to form complexes with organic Lewis bases has now been shown for systems containing any one of the following functional groups; alcohols, amines, ketones, aldehydes, amides, phosphoryls, nitriles, phpsphines, nitro groups, sulfoxide ethers, ethers and esters. Shift reagents have been successfully used for the purpose of spect-ral analysis of and hence indirectly configurational assignment in a variety of molecular systems containing suitable donor groups of the sort already described. Included in the above are such classes of compounds as carbohydrates, steroids and terpenoids, ^  27 28 29 pesticides, polymers and organometallics. Shift reagents have also been used to determine the position of deuteration in deuterated 30 31 borneols, and optically active shift reagents have been used in many instances to determine enantiomeric purity. Interesting applications have also been reported in the n.m.r. of nuclei other than "hi, such 3L_ 23,32 . 14.. 33 . , ^ . _ _ 13_ 22a,34,35 as P, and N, and perhaps the most important C where, as a result of recent advances in n.m.r. instrumentation such as 13 Fourier Transform Spectroscopy,the observation of natural abundance C n.m.r. spectra of complex organic substances has become possible. The principal - 9 -problem remaining, which inhibits the generality of applications of 13 13 the F.T. technique to C n.m.r., is the assignment of individual C resonances. At present, these assignments are generally made on the 13 1 basis of either "off-resonance" C-( H) heteronuclear decoupling 36 experiments, by the internal consistency of the shifts of a series of closely related derivatives, or by studies of specifically deuterated derivatives. To this end, the application of lanthanide shift reagents has been shown to be an invaluable aid. (ii i ) Physical This third classification has as its origin two basic components: (i) the nature of the hyperfine interaction of the nuclei in para-magnetic complexes with the unpaired electronic spin - whether pseudo-contact (through space) and/or contact (through bond), (ii) a detailed analysis of the concentration dependence of the shifts. A discussion of the relevant theory necessary to the understanding of the first of these points follows shortly. As will be shown, i t is the pseudocontact interaction which contains the important geometrical dependence responsible for the stereospecific nature of the induced shifts. It is indeed significant, that right from the beginning 12 Hinckley recognized the potential of this aspect (which was well documented from earlier transition metal investigations) by showing the near linear slope of a, plot of induced shift versus the cubed 3 'tli reciprocal distance (1/r^ ) of the i proton of cholesterol from the co-ordination site. This provided important evidence for the predominance of the pseudocontact mechanism. Although Hinckley chose to neglect the equally important angular dependence of the pseudocontact equation, - 10 -he recognized its importance. Clearly before any structural information can be ascertained, one is faced with the difficult task of resolving the observed shift into its contact and pseudocontact components. To this end, subsequent experimenters have addressed themselves but unfortunately many early workers chose simply to neglect the already firmly established theory concerning the mechanism of such interactions previously developed by 37 McConnell. Thus, initially there appeared in the literature many reports which completely ignored the existence of a contact term and proceeded to equate the observed shift to where n = 1.6 38 through to 3! Before long, a large number of inconsistencies had , developed and then the way of fate followed another ill-conceived path. Rather than incorporate the correct existing theory, numerous investi-gators continued to use solely the 1/r" (n = 1.6 to 3) dependence. 39 40 This time any irregularities were equated to a contact interaction. ' More recently, our own work and that of others has shown,^ ^ ' ^ ^ by equating the shift to the product of the angular and distance dependence of the pseudocontact equation, that a contact interaction is indeed negligible for protons, i f present at a l l . This facet forms the basis of Chapter III where a more detailed account of these more recent applications will be discussed. 12 ' Hinckley was also first to recognize the concentration dependence of the induced shifts which indicated the labile nature of the lanthanide-cholesterol complex. However, prior to the quantitative investigation of this aspect as presented in Chapter II of this thesis, no detailed analysis existed. Qualitative investigations into the j - 11 -effects of substrate, ligand and metal variations on the induced shift relied upon the entirely erroneous representation first 44 45 46 proposed by Demarco. Following our publication in this area, ' numerous other papers have appeared delineating similar quantifica-47-51 tions. This area forms the foundation of Chapter II where a more detailed discussion will be found. In summary, the work described in the literature has demonstrated that the more or less routine use of lanthanide shift reagents to provide access to a set of chemical shifts and coupling constants, the latter of which provides a useful structural probe, is of great significance to the organic chemist. However, more detailed information with respect to substrate geometry is possible and can be realized only when a f u l l understanding of the chemical and physical processes involved in such interactions is attained. This need for a more quantitative investigation into the magnitude of chemical shift changes with respect to different lanthanide metals, solvent dependence, ligand dependence, substrate dependence, and temperature dependence has formed the basis on which the following thesis rests. It has proved convenient to subdivide the main body of this thesis into three separate Chapters which demonstrate in a sequential order the quantification of our insight into this area. In Chapter I we shall describe the experiments which were first performed (In 1970) and which had as their sole objective the development of understanding of the experimental procedure for using 1 13 lanthanide shift reagents to obtain optimally dispersed H and C spectra. These experiments uncovered the need for quantifying some - 12 -aspects of lanthanide shift reagents and this forms the core of Chapter II. Chapter II starts with the development of a theory for the molecular association. Use of this novel approach allowed an unambiguous determination of equilibrium constants, K^ , stoichiometry, n, and bound chemical shifts, A,,, for the lanthanide-substrate complex D of a range of model systems. Subsequently, the application of this knowledge gave rise to further understanding of the chemical aspects of lanthanide shift reagents and in so doing some of the limitations of the procedure adopted in Chapter I were uncovered. Finally in Chapter III we shall discuss some attempts to calculate absolute geometry using the correct values for bound chemical shift (A,,) as evaluated in Chapter II. D Before introducing the particular facets of this area that we chose to study, i t is appropriate to present a very brief summary of the salient features of the theory behind paramagnetic influences in 52 n.m.r.; this being quite thoroughly described in the literature. 37 More detailed treatment may be found in papers by McConnell and 53 54 Bleaney and in a review article by Webb. An electron spin in n.m.r. produces a characteristic chemical shift due to the very strong local magnetic fields resulting from hyperfine interactions. When we consider a paramagnetic ion in a solution with an isotropic hyperfine splitting 'a', the spin energy levels in a strong external field are given by the expression [1] = gftHS - gM3MHI + al S °N z N N z z z - 13 -The abbreviations used in this and following equations are as follows: ' g' and '3' are the electronic spectroscopic splitting factor and Bohr magneton; 'a' is the hyperfine interaction constant expressed in gauss; 'g^' and 'B^' are the nuclear 'g1 value and magneton respectively; 'H' is the applied magnetic field; '.S ' is the Z-component of the electron spin; 'I ' is the Z-component of the nuclear spin. The part of the energy which depends on the nuclear spin orientation is aS The quantity( —) in the above equation is refered to as 'H ' and represents the effective local field produced by the unpaired electron at the nucleus. For example a hyperfine splitting of 'a' = 84 Mc/s corresponds to a local field 'H ' of + 10,000 gauss, depending on the electron spin direction. | j2 When the electron is in the upper magnetic He energy level, there is a local field at the 1 _ a nucleus of +10,000 gauss and when the electron is in the lower level, a local field of -10,000 gauss. Thus when the electron undergoes a transition from one state to the other, the nucleus "thinks" that the magnetic field has changed by 20,000 gauss. The rate of these transitions, T^ T , for the electron must be 1 exceedingly fast for the nuclear resonance signals to be sharp enough to be observable. For the lanthanide(III) ions T^ < 10 seconds and consequently even at liquid helium temperatures E.S.R. measurements to - 14 -determine 'a' and 'g' values are not possible for these systems. In these situations where ^  » 'a» the nucleus sees only a time-1 averaged local field proportional to the mean value <S > of the electron z spin component. Also in the presence of a magnetic field the degeneracy of the electron spin states is removed. The a and 3 electron spin states now have significantly different populations with the effective a<S > z field H = — and the nuclear resonance signal shifts to high 6 **N N field by an amount AH = a<S >/g„B„ or to low field i f the i n i t i a l z N N hyperfine splitting 'a' is say -84 Mc/s. The above equation arising from the presence of unpaired spin at the resonating nucleus is that usually referred to as the contact interaction and will usually be written in the following form rn ^ 1 - _ a 'If. EBS(S+1) i J J H " ai yH 3kT The abbreviations used in equations [3] and [4] are as follows: 'AH' is the difference in resonance field of the nucleus i at applied field 'H1; 'y ' and 'y^' the magnetogyric ratios of the electron and proton, respectively; 'S1 the total spin quantum number; 'r^' is the separation between the unpaired electrons and the resonating nucleus; '9^' is the angle between this distance vector and the principal axis of symmetry of the complex; 'gjj' and 'gj^' are, respectively the parallel and perpendicular components of the electronic g-tensor with respect to this axis; other symbols have their usual significance. Another contributor, which can produce chemical shifts and is believed to be the major i f not sole contributor when the paramagnetic substance is a lanthanide(III) ion, is the pseudocontact hyperfine - 15 -interaction. This results from the combined interaction between the dipolar hyperfine coupling and an anisotropic g factor with the nuclear moment. The equation for this shift depends on the symmetry of the g-tensor and takes its simplest form for dissolved complexes with axially symmetric g-tensors (i.e. gx = g^ ^  gz)-A Hi -62S(S+1) " " A - " + , r. 1 The importance of the geometric dependence of the pseudocontact shift, Eq.[4],will be rigorously evaluated in Chapter III. For the moment, i t is clear that the magnitude of shifts for nuclei in the same complex will vary, perhaps even the sign, since the term 2 (3cos 6^-1) changes sign for angles of 6 ^ 54°44'. In summary, contact shifts provide information concerning the electron spin derealization from the metal atom to the ligand, whereas the pseudocontact shifts are stereospecific and contain important geometrical information. Some justification for the use of Eq.[4],which pertains to complexes of axial symmetry only, will be presented in Chapter III. No attempt has been or will be made to analyze shift data with respect to the more complex equation derived for the general use of g ? g i g . - 16 -CHAPTER I STUDIES OF THE CHEMICAL SHIFT CHANGES IN BOTH PROTON AND CARBON-13 N.M.R. PRODUCED BY THE ADDITION OF PARAMAGNETIC LANTHANIDE CHELATE COMPLEXES Introduction Our systematic approach to the complete understanding of the nature of lanthanide-substrate interactions and subsequently to the determin-ation of molecular geometry, began in 1970 as a result of the application of the lanthanide shift reagents to monosaccharide derivatives, an area in which no previous data were available. The sole objective in this investigation was to develop the necessary insight as to the optimal experimental procedure for using lanthanide shift reagents to obtain optimally dispersed "4i spectra of this important class of molecules. Such systems have previously been extensively studied by this laboratory and suitable systems were available in varying degrees of purity. From a practical point of view, these systems were conforma-tionally relatively rigid and possessed one site likely to provide the major point for association with the lanthanide shift reagent. The importance of the above conditions will become apparent later. Also, the spectra of monosaccharide derivatives are not unusually complicated - 17 -by the overlapping of different transitions. This results in l i t t l e ambiguity in assigning individual resonances, thus minimizing any errors resulting from incorrect assignment of transitions. This latter characteristic was necessary because previously, workers had studied organic systems having a single "chelating" substituent, usually a hydroxyl group. The potentially polyfunctional monosaccharide on the other hand, could not be presumed a priori to follow the previously well established linear dependence of shift versus added lanthanide. 13 The applicability of lanthanide shift reagents to C n.m.r. 13 spectroscopy as a means of assigning Individual C resonances will also be discussed. As a result of instrumental limitations at U.B.C. at the time this research was initiated, it was not easy to study the 13 C spectra of such interesting molecules as monosaccharides. The conclusions are, nevertheless, general. In the following discussion, the optimal conditions under which to perform these particular experiments (i.e., to obtain the maximum shift with the least amount of line broadening) have been qualitatively assessed. In this respect, we have investigated the dependence of the magnitude of the induced shifts on variations in the rare earth metal for complexes with tris(dipivaloylmethane), the solvent system and the temperature at which the experiments were performed. It will be shown that the simplistic rationales concerning the relationship between the magnitudes of the induced shifts and the geometry of the substrate can in some instances be entirely misleading. In addition, an incisive experiment to distinguish between the contact as opposed to the pseudo-contact mechanism will be presented. - 18 -These investigations were responsible for introducing the need to quantify some aspects of lanthanide shift reagents, whereupon Chapter II originated. The results presented in Chapter II will reveal many of the limitations of the procedure presented in this chapter, nevertheless, qualitatively the conclusions drawn from this present study are unchanged. Thus the results presented here have useful significance for a large number of present applications seeking 1 13 only optimally dispersed H and/or C spectra with s t i l l measurable coupling constants, the aim of many organic chemists. Results and Discussion A. Measurement of the "hi Chemical Shift Changes of Carbohydrates  Induced by Lanthanide Shift Reagents Initial studies using the lanthanide paramagnetic shift reagents involved the use of four derivatives of the 1,2:5,6-di-0-isopropylidene-a-D-hexofuranose system as the model substrate molecules. Instrumental Me Me 3 R = CCH, II O 1 R = H 2.R = H AR = CCH, II O - 19 -in this particular choice was the fact that a l l but one, 4., were available from previous studies in our laboratory and required only final purification. In addition, these derivatives have the necessary property that they a l l have reasonably well defined geometries and possess one group, either a hydroxyl or acetoxyl group, most likely to provide the major association site for the lanthanide reagent. Lanthanide shift reagents were synthesized for the tris(dipivalomethanato) derivatives of three typical lanthanide metals; europium _5 , thulium 6_ , 16 and praseodymium 7_ following the standard literature procedures. In a l l experiments, freshly sublimed lanthanide reagents and carefully dried solvents and substrates were used. It was essential to remove al l traces of water. Water if present would "compete" many times more effectively for the lanthanide shift reagent than would the substrate, thereby reducing the resulting shift for an equivalent amount of lanthanide and possibly causing considerable line-broadening. A comparison between the spectra shown in Fig. 1A and B, typifies the effect of lanthanide reagent (in this case the europium reagent 5) on the "^H spectrum of 1' The outcome of adding water to this system is shown in Fig. 1C; clearly the added water has almost entirely eliminated the induced shift; from Fig. 1A, T„ , = 4.080, T„ „ = 5.489 and from H— X , ri— Z Fig. 1C, T R_ 1 = 4.060 and xH_2 = 5.463. This exemplifies the fact that water associates more strongly with _5 than does the carbohydrate derivative 1_. Preliminary experiments also established that the rather small quantities (<0.15 mol equiv; <25 mg; <3.5xl0 mol) of lanthanide reagent needed to produce interesting chemical shift changes, were most - 20 -Figure 1. 4.0 5.0 7.0 80 9.0 The H n.m.r. spectra (100 MHz) of l,2:5,6-di-0-isopropylidene-a-D-glucofuranose (1, 0.0842 g) in CDC13 (0.5 ml). Tetramethylsilane~was used for the internal field-frequency lock. A. The normal spectrum. B. The spectrum after the addition of Eu(dpm)3 (_5, 9.84x10"^ mol equiv). C. As for B but with the further addition of water (0.01 ml, 1.55 mol equiv per mol of 1). A diagrammatic representation of the first-order assignment is given above the spectrum shown in B. - 21 -conveniently obtained by the addition of volume aliquots of freshly prepared stock solution of the reagent. This procedure also provided an automatic access to two important sets of data. These were, (i) plots of the magnitude of induced shifts as a function of the amount of added reagent and (ii) the spectrum of the compound having the optimal disper-sion of chemical shifts and hence the maximum number of measurable coupling constants. This latter aspect is clearly illustrated in Fig, 1, which shows spectra of l,2:5,6-di-0_-isopropylidene-a-D-glucofuranose 1 . -2 The spectrum in Fig. IB shows the effect of 9.84x10 mol equiv of added europium _5; a l l seven ring-proton resonances are clearly resolved. A routine series of spectra was then measured in which aliquots of each of the lanthanide reagents _5, 6^, and 1_ were added to each of the four sugars 1_, _2, _3, and 4^ , using deuterochlorof orm solutions throughout. The plots shown in Figs. 2, 3, and 4 are characteristic of those found for each of the lanthanide reagents interacting with each of the four sugars. They indicate that there is a linear relationship between the magnitude of an induced shift and the amount of added lanthanide reagent, at least up to ca. 0.15 mol equiv. The linearity of these plots implies that on the n.m.r. time scale, the exchange between the "free" and "complexed" lanthanide reagent must be in the fast exchange limit. Besides providing a convenient means for indicating the progress of an experiment and for obtaining the spectrum having the optimal dispersion of chemical shifts, this linear relationship provides for the important recovery of the chemical shift data. Thus, extra-polation of a shift-concentration plot back to zero concentration of the 300-1 Figure 2. Chemical shifts observed for a solution of 1 (0.0842 g) in CDCI3 (0.6 ml) following the dropwise addition of a solution of Eu(dpm)3 (5_, 0.0312 g) in CDCI3 (1 ml). The dotted sections of the plots shown for the H-4, -3, and -5 resonances apply over the region where assignments were considered to be insufficiently accurate to be included here. Tetramethylsilane was used for the Internal field-frequency lock. - 23 C O N C . O F T M ( D P M ) , ( M O L E % ) x 1 0 ' 01 UJ D J $ h LL I 00 J < y U J i o 600 500-2 3 _1_ A _L_ 5 6 _ J _ 7 8 _l 9 i 10 A 400-3 0 0 200-Figure 3. Plot of the chemical shift changes observed for a solution of 1 (0.0897 g) in CDCl3 (0.6 ml) induced by Tm(dpm)3, 6. The chemical shifts of the two H-6 resonances remained essentially the same throughout the experiment. The chemical shift of the H-5 resonance ran roughly parallel with that of H-4; i t could not be measured with sufficient accuracy to justify its inclusion here. Tetramethyl-silane was used for the internal field-frequency lock. AOO-30CH 1 1 1 1 \ 1 1 1 1 \ 1 O 1 2 3 4 5 6 7 8 9 10 11 C O N C . O F P r ( D P M ) 3 ( M O L E % ) x 1 0 2 Figure 4. Plot of the chemical shift changes observed for a solution of• _1 (0.09 64 g) in CHCI3) (0.6 ml) induced by Pr(dpm)3, 2- T h e H"3 resonance moves at approximately the same rate as the H-4 resonance; that is at a rate less than that of H-5. CHCI3 was used for the internal field-frequency lock. - 25 -added lanthanide gives the "normal" shift of that particular proton. This useful procedure can, however, be subject to sizable experimental error, and this is illustrated in Fig. 3 for the thulium reagent 6_. Here there appears a "lag" during the addition of the first 0.01 mdl equiv of 6j a lag which is identical for a l l protons in the substrate molecule. These observations are consistent with a small amount of water s t i l l present in the carbohydrate sample, which complexes preferentially with the thulium reagent. In accord with this suggestion the lag was decreased by further drying of the carbohydrate samples. The final magnitude of the error induced by this effect, which is greatly amplified the larger the slope, can fortunately be compensated for. This is accomplished simply by moving the y-axis to the right by the amount proportional to the lag - a quantity which can be measured provided that the normal chemical shift of one proton is directly measurable. The excellent agreement obtained between normal and extrapolations of shift-concentration plots when applying this correction factor is shown for the data listed in Table 1. These corrected extrapolated chemical shift values and coupling constants as measured from the first order spectrum achieved by the addition of the lanthanide shift reagent can now be used to simulate the original complex spectrum using LA0CN3. Fig. 5B illustrates this treatment for the highly complex portion of the spectrum of 1. Input parameters are those corrected extrapolated chemical shift values listed in Table 1 for 1_, and coupling constants from the first order spectral - 26 -Table 1. Chemical shifts (T-values) for compounds 1^, _3 and k_ in deuterochloroform solution, showing values obtained by direct f measurements and by corrected extrapolations to zero concen-tration of a shift-concentration plot for the addition of lanthanide reagents _5, 6_ and 7. Chemical shifts Compound Proton Corrected extrapolated values Direct T (Eu) o x (Tm) o values H-l 4.075 4.075 4.075 4.075 H-2 5.485 5.440 5.480 5.488 1 H-3 5.710 5.800 5.700 ca.5.7 H-4 5.930 6.020 5.920 ca.5.9 H-5 5.670 * 5.700 5.669 H-l 4.152 4.152 4.152 4.152 , 3 H-2 5.527 5.522 5.543 5.552 H-3 4.770 4.775 4.820 4.765 H-l 4.223 4.223 4.223 4.223 4 H-2 5.245 5.230 5.222 5.233 H-3 5.165 5.140 5.160 5.143 Indeterminate In a l l cases, the correction factor was calculated from the 'normal' shift of H-l. Note: Compound 1_ n a s n o t been included because the shifts of a representative range of protons could not be determined with sufficient accuracy to justify its inclusion here. 4.0 4 . 5 5.0 5.5 6 . 0 r Figure 5. The H n.m.r. spectrum (100 MHz) of l,2:5,6-di-0-isopropylidene-a-D-glucofuranose (1, .--0.0842. g) in CDC 13 (0.5 ml). A. The normal spectrum; B. Computer simulation of normal spectrum by LA0CN3. - 28 -* analysis of Fig. IB. The excellent agreement between Figs. 5A and B is proof of the reliability of this technique and, more important, indicates that for the concentration range studied, complexing with EuCdpm)^ _5 sdoes not alter the geometry of the substrate which would be displayed by a change in the measured coupling constants from Fig. IB. Thus coupling constants measured in this way can be related t to a Karplus-type curve and this provides important geometrical information concerning the substrate -molecule. True coupling constants for jL are listed in Table 2. For the compounds studied in this series, the thulium reagent _6 always produces larger changes in chemical shifts than would an equivalent amount of the europium reagent. Insofar as the shifts induced by europium are already very large, there seems l i t t l e advantage at this time in using the thulium reagent except possibly for conformationally labile systems. Furthermore, the fact that for any particular amount of induced shift, 6^  causes significantly more line 13 broadening than 5_, (as has been shown elsewhere ) dictates in favor of 5_. There may be occasions when the shift to high field induced by the praseodymium reagent 1_ is advantageous, but this was certainly not the case for the monosaccharide derivatives _l-4_ of this study. Several observations made during the course of this study provided _ The calculated number of transitions for this complexed seven spin system exceeded the storage capabilities of LA0CN3. It was necessary therefore, to analyze this region of the spectrum first for 5 spins then for 2 spins. This then, is responsible for the slight difference noticeable in the region of H-3, ca. 5.7 T. t This is the well known dependence of the magnitude of the coupling constant between vicinal hydrogens (J^c^) o n t n e dihedral angle (<f>) between the projected C-H bonds. Table 2. N.m.r. parameters for l,2:5,6-di-0-isopropylidene-a-p-glucofuranose 1_. Chemical shifts (x-values) H-l H-2 H-3 H-4 H-5 U-6± H-62 4.08* 5.49* 5.69 5.95 5.68 5.85 6.01 Coupling constants (Hz) H-l,H-2 H-3,H-4 H-4,H-5 H-4,H-61 * 3.7 2.3 7.7 -0.2 H-5,H-61 H-5,H-62 H-61,H-62 6.1 5.2 -8.6 Measured in deuterochloroform solution. First order numbers only. - 30 -some interesting insights, and caused considerable skepticism against some of the simplistic rationalizations which have been implied elsewhere. Chapters II and III are a direct result of the need for a more complete method of analysis of the situation, which allows for a quantitative explanation of these and other observations. The following discussion will serve to demonstrate this need. Prior to our work i t had been shown that, for simple aliphatic : derivatives, i t was the protons which are nearest in terms of bond separation to the functional group predominantly engaged in complexing 15 21 with the lanthanide, which undergo the largest shifts. ' It would seem naive to anticipate that this same behaviour should necessarily pertain to more complex molecules, particularly rigid cyclic systems. For i f the shifts induced by lanthanide reagents arise via the pseudo-contact mechanism, as has generally been assumed, then as well as a distance dependence, an angular dependence must also be included in calculations of the induced shift-changes.• From equation [4] in the Introduction, i t will be necessary to calculate the complete factor 2 3cos 9^-1 < 3- > for each proton. Clearly the angular term will be a r. I most important part, especially for those protons nearest to the donor group, because i f 9^ > 54.4° this whole variable even changes sign. This function may be even more complicated i f the complex does not 12 55 possess axial symmetry as has been suggested. ' This will be discussed in greater detail in Chapter III. The results for l,2:5,6-di-0-isopropylidene-a-D-glucofuranose 1 indicate the complication which can arise for cyclic systems. From the - 31 -many studies using aliphatic derivatives, one might have assumed that the C-3 hydroxyl group would be the principal donor group and therefore the H-3 resonance should undergo the largest shift. This is not the case. As seen in Fig. 1 H-5 shifts 1.35 times as fast as the H-3 resonance. The use of the praseodymium reagent _7 with 1_ has a similar effect; the shift of H-5 is greater than H-3. Interestingly, the other three compounds 2^, _3 and 4_ do behave in a "normal" fashion with _5 and 7_, with H-3 undergoing the largest shift. Further complexity arises with the observation that when 1 is studied with the thulium reagent jS, H-3 does shift the most. There are several possible reasons for this unusual difference in behaviour of 1 with _5 and 1_ than with 6^. These are, in increasing order of likelihood: (i) i t could be that the geometry of J. is uniquely suitable for forming a second donor bond with the europium reagent _5 and the praseodymium reagent _7 but not with the thulium reagent 6^ , providing even further complexity in the symmetry of the complex and therefore the angular dependence; (ii) perhaps the angle 9 implicit 2 in the cos 0^ term of the equation for the pseudocontact interaction with the axial complexes is different for _5 and 7_, than i t is for 6_; ( i i i ) the angle 6^ is the same for a l l three lanthanides but the thulium reagent j) has some degree of contact contribution which is known to have the greatest effect on the protons nearest the donor site. Only by detailed computer study of the geometry term in the pseudocontact equation will the above inequality between the metals be solved. Interesting, in its own right, is the large value of J, _ = 7.7 Hz for 1^  implying that H-5 is "transoid" with respect to H-4 and is hence - 32 -located quite near to the C-3 hydroxyl group. Nevertheless, based on the simplistic arguments applied elsewhere, the above unusual behaviour would certainly not have been expected. A further observation is that the magnitudes of induced shifts appear to be significantly solvent dependent. For example the shift-changes of the D-gluco derivative 1 induced by europium 5_ have been measured for both chloroform (or deuterochloroform) and carbon tetra-chloride solutions. As shown by the slopes of the lines for H-3 and H-5 in Fig. 6, the shift induced by a certain amount of europium 5_ is approximately twice as large in a carbon tetrachloride solution (heavy lines) as i t is for the same absolute concentration of 1_ studied in a chloroform solution. This eventuality could result from a difference ft in bound chemical shift (AB) between the two solvents; a larger B equilibrium binding constant (K_) in CC1. ; or from changes in both A_ and Kg. This point will receive further treatment in Chapter II. 18 In a preliminary communication, Williams and coworkers have commented that, "the shift ratios of protons in any given substrate remain the same whichever lanthanide is used". That our chemical shift changes appear to be in very poor accord with this suggestion is demonstrated by the data summarized in Table 3. Noteworthy is the similarity of the ratios for 3-0-acetyl-l, 2: 5,6-di-0-isopropylidene-a-D-glucofuranose 3_ with the europium 5_ and praseodymium _7 reagent. * A,, is defined as the chemical shift which would be observed for the B substrate resonances when the substrate is rigidly bound to the lanthanide shift reagent. CONC. of Eu(DPM)3 (MOLE%)xl0 2 6 0 0 5 5 0 -5 0 0 -4 5 C H Figure 6. Plot of the chemical shift changes observed for the H-3 and H-5 protons of 1 induced by Eu(dpm>3 as a function of solvent. Light lines indicate the chemical shift changes observed for a solution of _1 (0.0842 g) in CDCI3. Heavy lines indicate the chemical shift changes observed for a solution of 1 (0.0817 g) in CCI4. Tetramethylsilane was used for the internal field-frequency lock in both cases. - 34 -Table 3. Ratios of the chemical shift changes of selected pairs of protons for compounds 1^  and 3_ in deuterochlorof orm solution after the addition of lanthanide reagents .5, 6^  and _7. Compound Protons Numerical value of ratio considered Eii 5 Pr 1_ Tm 6 1 H-l/H-2 0.82 0.84 0.65 H-l/H-3 0.35 0.47 0.29 3 H-l/H-2 0.62 0.59 0.41 H-l/H-3 0.35 0.37 0.23 - 35 -These . ratios are identical, within experimental error and yet significantly different from those determined for the thulium reagent 6^  whereas for the D-gluco derivative 1, this distinction is even more complicated. If one could rest assured that a l l lanthanide shift reagents bound in the same manner and form, then from the variance in these ratios one must concede the presence of a contact shift in addition to the acknowledged pseudocontact shift. However, as will be shown later, the contact contribution must be negligible, i f present at a l l . Therefore until studies have been performed to determine reliable values for the bound chemical shift (A ), the binding constant (K ) and A stoichiometry (n) any such conclusion as the above is without grounds. Thus these ratios stand alone as strong critics of the simplistic rationalizations that are so often implied. B. Applications of Lanthanide Shift Reagents to the Identification 1 3 of C Resonances As commented earlier this study was initiated before the availability 1 13 at U.B.C. of a Fourier Transform accessory; thus a H-( C) INDOR spectro-13 meter was used. The C chemical shifts were measured for the model substrate 2,2-dimethyl-l-propanol _8 in the presence of varying concentra-* Interaction between lanthanide shift reagent and substrate can be represented as follows: kl L + nS ^ LSn where L denotes lanthanide, S denotes k ^ substrate and the binding constant for this process [LS ] j£ — 1 1  B _ [L][S]n - 36 -tions of the tris(dipivalomethanato) derivatives of europium 5_, thulium 6^ , praseodymium 1_, and gadolinium 9_. These measurements also provided the '''H shift changes automatically. Due to instrumental limitations, the substrate concentration was maintained constant during a l l experiments at a value of 2.27 M and the lanthanide concentration was varied from ca. 0.15 to 0.075 M. This procedure was carried out by first preparing a standard stock solution (5 mis) of 2.27 M neo-pentanol 8^ , then using 1 ml of this solution to dissolve ca. 0.100 g of lanthanide reagent. 0.5 ml of this latter solution was then placed in a n.m.r. tube. Chemical shift measurements were then -made on this sample and the experiment continued by successive additions of aliquots (0.05 ml) of the standard 2.27 M stock solution. The resulting decrease in molar concentration of lanthanide reagent was monitored as a decrease in the induced shift. * 1 13 [ L ]o Plots of the changes in H and C shifts versus , -. for three.of l b Jo the four metals studied are shown in Fig. 7 and Fig. 8. The data are summarized in Table 4. From the Figures, i t is quite clear that for 1 13 both H and the C resonance a direct relationship exists between the observed shift and the amount of added europium reagent _5 and praseo-dymium reagent _7, up to ca. 0.15 M added lanthanide. The same is also true for the thulium reagent j> up to ca. 0.05 M. 13 From the standpoint of C spectral assignments several points are 13 1 noteworthy. It is encouraging to note that C shifts, like the H counterpart, were sufficiently sensitive to added lanthanide for this [L] = total lanthanide shift reagent concentration; [S] = total o ° o substrate concentration. [ E U ( D P M ) 3 ] " 3 7 " [ substrate ] .02 .04 .06 .08 I I L_ L_ - 6 . 0 J  1 13 Figure 7. Plot of the H and C chemical shift changes of 2,2-dimethyl-l-propanol, 8^ , in the presence of varying concentrations of Eu(dpm)3, _5, using CHCI3 as solvent. Tetramethylsilane was used for the internal field-frequency lock. Tm(DPM)3 Figure 8. 1 13 Plot of the H and C chemical shift changes of 2,2-dimethyl-l-propanol, 8^ , in the presence of varying concentrations of either Pr(dpm)3, 2, or Tm(dpm>3, §.> using CHCI3 as solvent. CHCI3 was used for the internal field-frequency lock for measurements with ]_> and tetramethylsilane for those with 6. - 39 -Table 4. Summary of the H and C chemical shifts of 2,2-dimethyl-l-propanol j8 in chloroform solution showing the effect of added tris (dipivalomethanato)europium 5_, thulium 6^ , or praseodymium ]_. Solution Chemical shifts studied Proton ** resonances C resonances CH3 CH2 " C „3 UCH2 Normal -0.90 -3.27 -26.26 -73.59 With added 5+ -1.63 -5.03 -27.38 -77.60 With added ,tt b -2.37 -7.26 -28.27 -80.00 With added f 0.08 -0.81 ca.-24.90 -68.99 The solutions a l l contained ca. 20% (w/v) of 8_ in chloroform solution. Measurements were made at a probe temperature of ca. 35°C. t t t Values for 0.05 mol equiv of added lanthanide, interpolated from the shift concentration plots. Values for 0.02 mol equiv of added thulium reagent. 6-values based on tetramethylsilane as an internal reference: error + 0.02 p.p.m. Values in p.p.m. relative to tetramethylsilane calculated for a magnetic field at which the protons of tetramethylsilane would resonate at precisely 100 MHz; for details see reference 2 , error + 0.08 p.p.m. - 40 -approach to have some generality. Also, the carbon nearest the donor function of the organic substrate (C-l in this case) undergoes a significantly larger shift than the more remote one. In this regard however, the angular dependence of the pseudocontact equation as well as the distance dependence must be considered, especially when studying cyclic organic substrates. This is clearly demonstrated by the work 34a of Briggs and coworkers, for borneol 10. Both C-l and C-3 are lO adjacent to the hydroxyl donor group, yet their Agu values as 26a calculated by Demarco's method are -14.0 and -21.8 p.p.m. respectively. 13 Clearly then, C spectral assignments can be greatly facilitated with the proper use of the pseudocontact relationship. Subsequent extra-polations of suitable shift versus concentration plots can be used to determine the "normal" chemical shift values of individual resonances. Again with regard to spectral assignments i t is noteworthy that whereas both europium 5_ and thulium 6^  induce shifts to lower field with a Tm:Eu shift ratio of ca. 5.0, the praseodymium reagent 1_ produces high-field shifts with a corresponding Pr:Eu shift ratio of A£ u represents the difference in chemical shift between the free substrate and that for 1 mole of substrate bound to 1 mole of shift reagent. - 41 -ca. 1.5. These shift ratios definitely dictate in favour of 6^  as the preferred shift reagent. However, degenerate transitions are not 13 1 nearly as common in C spectra as in H spectra and therefore the superior shifting ability of 6_ is unnecessary and undesired in view of the increased broadening of resonances produced with this reagent. 1 13 In Table 5 are summarized the H and C shift ratios for the three lanthanides studied. It is important to note that for this acyclic system, the proton shift ratios with _5, b_ and _7 are to within experi-mental error identical. These results further support the presumption, for lanthanide shift reagents, of an exclusively pseudocontact contribu-tion to the observed proton shifts. On the other hand, the large 13 variance observed for the C shift ratios may be indicative of a contact contribution, in addition to the pseudocontact contribution, to the observed shift mechanism. Recently Cushley,34^ and Willcott"^ 13 have demonstrated a dominant contact contribution in the C spectra for those carbons closest to the point of co-ordination with the lanthanide. These results will receive further discussion in Chapter III. If a contact contribution was responsible for this difference in 13 C shift ratios, then a different mechanism of electron spin delocaliza-13 tion into C orbitals would be indicated. This conclusion, resulting from not only our data but from that of others, demonstrated a need to be able to differentiate between the contributing mechanisms for induced shift. To that end, the following experiment was performed. The experiment is based on previous studies by Kluiber and Horrocks"^3 and by Yonezawa, Morishima, and Ohmori"^ of main group - 42 -Table 5. Ratios of the H and C compound 8_ in chloroform lanthanide reagent J5, 6_, chemical shift changes for solution after the addition of and 7. Nuclei considered Numerical value of ratio  Eu 5 Pr 7 Tm 6 1 C H3 H - 0.40 0.41 0.38 13 C H3 C - 0.18 0.25 0.36 - 43 -transition metals. Combining equations [3] and [4] from the Introduction one can write equation [5] which relates the observed chemical shift induced by a paramagnetic species in terms of both the contact and pseudocontact contributions. Any species having a spherically symmetric charge cloud (S-state) also has an isotropic g-value, that is m /AHv _ -ai(V . gfiS(S+l) +. , (g,, - g^QcosV-l) [ 5 ] ^ i (VT ~ l k T 2(3^,+4gL)- [- 3 • ] N r. l g| I = g^ . Substitution of this equality into equation [5] results in the cancellation of the second term which is the pseudocontact term and leads to equation [3] which now describes the contact contribution. m A - a ± i l s l SBS(S+1) 1 J 1 H;i (yN) 3kT Gadoliniumj in Gd(dpm)3> is in the +3 valence state and thus has a half-filled f-shell: i t follows, then, that its orbital angular momentum, L, is zero and hence that i t has an isotropic g-value. Consequently any shift induced by Gd(dpm)3 must arise from the contact mechanism. If we now assume that the complex formed between a particular substrate molecule and Gd(dpm)3 has the same geometry and distribution of unpaired electron spin as that of other Ln(dpm)^ complexes then the contact-shift of Gd(dpm)^ should give an estimate of the contribution which the contact mechanism makes for the other lanthanide shift reagents. Thus, in this indirect fashion, i t is possible to separate the shift contributions of the contact and pseudocontact mechanisms. The abbreviations used in the equations [5] and [3] are as listed in the introduction with Z = B2S(S+l)/45 kT. - 44 -An experiment with Gd(dpm)3 9_ and neo-pentanol 8 was performed following the same procedure adopted for the other experiments described previously and over the same concentration range. No detectable proton shift-change could be observed although the resonances of H-l and H-3 were severely broadened which prohibited the detection 13 of the C resonance via the INDOR technique. Consequently i t follows that i f the assumptions of the above approach are correct then the contact mechanism makes very l i t t l e contribution i f any, to the proton shifts induced by Ln(dpm)3 reagents, at least for non-aromatic substrates. C. Temperature Dependence of the Paramagnetic Induced Shift in 1H N.M.R. As part of this qualitative evaluation of the lanthanide shift reagents, the temperature dependence of lanthanide induced chemical shift changes was investigated: as the temperature is reduced the magnitude of the shift increases. This behaviour, with decreasing temperature, is due to the large difference in population of the a and 3 electron spin states and as a result, the local field H^  increases. It is therefore possible to increase the "effectiveness" of a lanthanide reagent by decreasing the temperature at which the measurements are made. This result may prove to be extremely useful where the limited solubility of the lanthanide complex is inadequate. A chlorinated bicycloheptenol 11 was used as a model system in this study and the measurements are summarized in Table 6. For H-5 _2 the shift induced at -47.5°C by 9.4 x 10 mol equiv of 5_ is 2.5 times - 45 -Table 6. Temperature-dependent chemical shifts data of protons of ft* 5-hydroxy-l,2,3,4,7,7-hexachloronorborn-2-ene 11_ in f deuterochlorof orm containing Eu(dpm)„ 5_. T (°C) H-6 H-6' H-5 -47.5 7.170 6.790 3.950 -38.0 7.230 6.840 4.150 -18.5 7.385 6.910 4.400 0.3 7.495 6.953 4.560 21.0 7.575 6.983 4.668 33.0 7.615 6.998 4.720 tt Ref 8.028 7.155 5.238 T-values. ftft 0.0951 g in-0.6 ml. t -2 9.4 x 10 M equiv. tt 11 in CDC13 at 33°C. - 46 -that produced by the same amount of reagent at 33°C. Figure 9 represents these, data in the form of a plot of the induced shift versus inverse temperature. The observed non-linear response, in contrast 26b 58 to a linear response fortuitously obtained elsewhere, ' is as * 53 expected from theoretical grounds. No further experimental work in this area will be presented for it is hoped that with the above results and the relevant theory, (see Chapter II), the f u l l potential of this area can be realized. One particularly important application would be in the use of shift reagent and temperature to raise the effective coalescence temperature of systems whose low barrier to inversion gives rise to a n.m.r. coalescence temperature too low for most normal spectrometers. Only just recently has the literature contained a report of the successful application of the above technique.^ In summary then, the preceding successful investigation of the "''H 13 spectra for a series of carbohydrate derivatives and the C spectra of neo-pentanol interacting with a series of Ln(dpm)^ complexes does nevertheless indicate the need for a more quantitative approach. We have demonstrated that the tris(dipivalomethanato)lanthanide(III) complexes do indeed produce useful chemical shift changes in the "'"H n.m.r. spectra of potentially polyfunctional carbohydrate derivatives; that these shift changes are dependent on solvent and metal used; that 13 the induced shifts are very dependent on temperature; the C spectra A For a complete discussion of the theory involved, including a discussion of other investigations into this area, see Chapter II, Theory Section V. - 47 -I2QO IO.O OH 1 1 1 1 1 1 1 1 0.30 0.32 0 . 3 4 0 3 6 0.38 0.40 0.42 0 . 4 4 0.46 ^XIOW) Figure 9. Plot of the chemical shift changes versus inverse temperature for a solution of 5-hydroxy-l>2>3,4>7>7-hexachloronorborn-2-ene (11, 0.0951 g) in CDC13 (0.6 ml) with Eu(dpm)3 (5, 9.4xl0-2 M equiv). Tetramethylsilane was used for the internal field-frequency lock. - 48 -is shifted to the same proportion (on a p.p.m. basis) as the "*"H spectra, 13 with perhaps a somewhat different mechanism involved for C; that the common assumption as to which proton is likely to undergo the largest change in shift based only on the — | — dependence can lead to ri erroneous results. These and other points form the basis on which Chapters II and III have been developed. - 49 -CHAPTER II QUANTITATIVE INVESTIGATION OF THE LANTHANIDE SHIFT REAGENT-SUBSTRATE EQUILIBRIA: THE UNAMBIGUOUS EVALUATION, OF THE BINDING CONSTANTS, BOUND CHEMICAL SHIFTS, AND STOICHIOMETRY Introduction In spite of the successful use of lanthanide shift reagents to 1 13 obtain optimally dispersed H and C spectra, a number of inconsisten-cies had developed in our own work and that of others, inconsistencies which originated most likely from the neglect to analyze with any degree of accuracy, the existing equilibrium. This was the incentive behind the detailed analysis to be presented in this chapter. The problem of the determination of formation constants and other constants for weak intermolecular complexes in solution has received considerable attention during the past several years, particularly for the investigation of enzyme-inhibitor interactions, an area where n.m.r. has proved to be very useful. Realizing the many similarities between these lanthanide-substrate interactions and enzyme-inhibitor interactions (e.g. limited solubility of both lanthanide complex and enzyme), a method of approach similar to that for enzyme interactions was adopted. The following detailed analysis of the equilibrium process which occurs when a lanthanide shift reagent combines with a substrate molecule having - 50 -a suitable donor function rests on the interpretation of the resulting experiments in terms of the following three parameters: (i) the equilibrium constant, K_,, which is important since i t provides Inf anna-tion concerning the stability of a complex; (ii) the bound chemical shift, A „ , which is required before any determinations of molecular structure can succeed; ( i i i ) the stoichiometry of the complex, n, also important for determination of molecular geometry. No account has been taken of the activity coefficients which may vary disproportionately with the change in substrate or lanthanide concentration or of the possibility of multiple equilibria of which some of the more likely are listed below. L + S —=* LS L + 2S ^ LS2 2L + S ^ L2S 2L - L2 L2 + S ^ L2S L2 + 2 S ;± L2S2 The possibility of all the above competing equilibria could undoubtedly discourage interested investigators. However, by placing certain restrictions on the range of concentrations of the reactants, i t is possible to force the system to adopt certain preferred equilibria or at least minimize to a significant extent the number of competing equilibria. This was the approach chosen and which will be presented - 51 -in the following text. Some attempts have been made to analyze the concentration dependence of the observed chemical shifts by the least-squares f i t of the parameters to a two-step equilibrium mechanism. This type of treatment can result in confusion in that a numerical solution can always be obtained but i t may not be a chemically sensible one. It suffices to point out that the number of experimentally measurable parameters remains constant, while the number of unknown parameters increases by a factor of two for each competing equilibrium. The most important result of this detailed analysis is the unequivocal determination of the "bound" chemical shift for each proton of an organic substrate (S) bound to a lanthanide shift reagent (L), a parameter which cannot be observed experimentally. When reliable bound chemical shiftshave been determined for such complexes, it should be possible to establish with some confidence the conformation of the complex and hence the organic moiety it s e l f , as will be shown in Chapter III. Thus a need for a f u l l quantitative analysis of the chemical equilibria operating between the lanthanide shift reagent and the substrate molecule is essential for the f u l l potential of this technique to be realized. Then, use of the correctly determined value of bound chemical shift, A,,, justifies the f u l l computerized treatment for molecular geometry (Chapter III). In the course of this study, i t became obvious that the desired bound chemical shift, A , of a substrate while i t is bound to the lanthanide, may be obtained from either of the following methods of investigation: (i) measuring the induced shift,6 , for several solutions having the same [S] but differing [L] or, (ii) measuring 6 for solutions - 52 -having constant but varying [S]o« As a consequence of the theory, it will be evident that for method ( i ) , the slope of a plot of observed shift versus [L] /[S] , as employed by the majority of investigators, O O N yields an empirical number which can differ greatly from the actual A , and that the error can even be different for different protons in the same.molecule. Thus, the theory to follow is intended to enable the reader to clearly distinguish between these two methods on the basis of a general and accurate evaluation of A_, K , and n. Predictions based on this theory are then subjected to rigorous experimental testing which permits for the first time the quantification of the effects of metal and ligand variation, basicity of the donor group and solvent on the magnitude of the induced shift. Theory The first step in analyzing the chemical shifts for a one step binding process, (in which L denotes lanthanide, S denotes ligand or kl [1] L + S — ^ LS substrate, and LS is the 1:1 lanthanide-substrate complex whose chemical shift we would like to obtain) is to establish whether the exchange 13 rates are fast or slow on the n.m.r. time scale. There are two simple limits, (a) and (b): (a) If k 1 , kn [L] » (<5 - <5 ) , the fast-exchange limit, then there will be a single resonance centered at - 53 -[2] 6 obs where 6 and 6 are the respective chemical shifts for S and LS, and f and f are the respective concentration fractions O J-iO of S at the two sites. But f = 1 - f , so an "induced chemical shift", 6, may be defined as [4] or simply 6 = fL gAB where A,, is the chemical shift for the LS complex relative to a the chemical shift for free S. The relationship of these terms is shown in Fig. 10. (b) If, on the other hand, k k..[L] « A,,, the slow-exchange — i 1 D limit, then resonances are expected at <5g and and even i f the LS sites were so dilute that the 6 resonance could not be detected, the 6„ resonance would s t i l l be independent of f Q Experimentally, then, observation of a single resonance whose chemical shift varies linearly with the fraction of substrate present as complex is direct evidence that the fast-exchange limit applies. Using this criterion, i t was found that the fast-exchange limit was valid for a l l data reported, with the exception of the interaction between lanthanide shift reagent and a series of dimethylaminocyclophosphonitriles, where the slow-exchange limit was found to apply. [3] 6 = 6 obs 6S = fLS(6LS " V - 54 -Free substrate Equilibrium mixture Pure complex r e f e r e n c e s i g n a l Figure 10. The relationship between the terms 6, AB, 6 , 6 and 6 ; see equations [3] and [4]. - 55 -I. Experiments in which [L]G is Varied at Constant [S]Q This was the method in general use at the time our research in this area was initiated. No theoretical justification for this method of approach had been presented and that which follows will demonstrate the limitations inherent in this manner of data reduction. Let [L] and [ S ] be the i n i t i a l concentrations of lanthanide and o o substrate - see Experimental section for mixing procedure. Then rsi £ - ^ ^B _ [is] , 1 J ° " [LS] + [ S ] [ S ]q nB Next, let the binding constant for the process, [1], be K : rfi1 „ _ [LS] _ [LS] 1 J B [L][S] - ([L]o - [LS])([S]Q - [LS]) It is now necessary to solve Eq. [6] for [LS] and then substitute for [LS] in Eq. [5], so as to determine the desired quantity A_ in terms D of the measured parameters [L]0> [S]0> and 6". In order to avoid solving the quadratic equation, [6], and to minimize the occurrence of multiple equilibria, i t is convenient to simply restrict the experiments to the range, 17] [S] » [L] , then [S] » [LS] o o o thus guaranteeing that ( [ S ] Q - [ L S ] ) - [ S ] q in Eq. [6]. Using [7] to solve [6] for [ L S ] , and substituting for [ L S ] in [5] gives, - 56 -KB[L]o AB t 8 ] 6 = 1 + K [SI a o Equation [8] is the principal result of this section. The immediate question now becomes, what will happen i f one plots 6 versus [ L ] Q / [ S ] O ? The answer is clear for two simple limits: (a) K_.[S] >> 1, i.e., strong binding or high substrate ii o concentration. In this limit, Eq. [8] reduces to 19] 6 = A_[L] /[S] D O O so that a plot of 6 versus [L]Q/[S]o will be a straight line through the origin, with slope, A „ . D (b) K^tS] « 1, i.e., weak binding or low substrate concentra-JJ o tion. In this limit, Eq. [8] reduces to [10j 6 = KBAB [S]Q ( i ^ ) . o In other words, a plot of <5 versus [ L ] O / [ S ] q will give a straight line but the slope is now proportional to [S] o Results (a) and (b) from Eq. [8] suggest that in carrying out several sets of experiments (each set at a different [S]Q level), then for low [ S ] Q the slope of a plot of 6 versus [ L ] Q / [ S ] O will be proportional to [S]o, while for large [S]Q the slope will simply be A^ independent of [ S ]q. Therefore, only at high substrate concentrations is i t permissible to take the slope of a plot of 6 versus [ L ] / [ S ]q as A^. - 57 -This conclusion is of quite practical significance, as will be shown in the Results section. II. Experiments in which [S]q is Varied at Constant [Ll^ Since i t is now clear that there is no simple way to extract AD from a single plot of 6 versus [L ]O/ [ S ]q at constant [S]Q, one is led to seek out some other simple experiment which will yield the bound 2 chemical shift. Returning to Eq. [6], suppose that only the [LS] 61 term is neglected; then VL ]oAB [11] 6 = i + K I S ] —+ K [L] * w h i c h m ay b e re-grouped to give [12] [S]Q = [L]QAb(1/6) - ((1/KB) + [L]o). Equation [12] gives the important fact that a plot of [S]q versus (1/6) gives a straight line whose slope is [L] A^ and whose y-intercept is o B -((1/IO + [L] ). Such a plot thus yields both An and K unambiguously. B o B D However, as pointed out by Dahlquist and Raftery for analogous 61 enzyme kinetics experiments, the approximations, (1/K^) >_ f^] and 6 « A,., are necessary to reach Eq. [12]. The safest procedure is B therefore to solve the full quadratic equation [6] according to the 6 2 following computerized procedure first suggested by Sykes. First, guess a value for and use this value to compute [LS] from Eq. [6]; this gives [LS] expressed as a function of [L]Q a n u < [^]Q. Next perform experiments in which [L] is fixed and [S] is varied. Use the - 58 -expression for [LS] to compute [LS] for each of the experimental values. Next, plot 6 versus [LS]/[S] to obtain A„ from Eq. [5]. This o JJ plot (since the wrong value of was probably guessed in the first place) will usually give a curve rather than a straight line. Thus, as a criterion of how well K^ , was chosen, let the computer calculate a least mean square slope for the plot and also the standard deviation for the slope. This whole procedure is now repeated for say, 100 values of K„ spanning three powers of ten in magnitude, and the standard deviation of the slope is plotted as a function of K^ . The correct value of BL, is then taken as the one which gives the smallest standard deviation in the plots of 6* versus [LS]/[S] Q. For practical purposes, we have found that for low [S]q concentra-tions (see Discussion) the graphical treatment based on Eq. [12] gives reasonable agreement with the f u l l computer treatment outlined above, and may often be preferable, inasmuch as precise values for K from a the computer treatment seem to require quite accurate shift measurements. All values of K_ and A_ reported in this text were taken from low-concentration experiments in which [S]q was varied at constant [1]0» In principle, one might hope to extract K and A from experiments in which [1]0 is varied at constant [S]Q, based on the slopes of plots of 6 versus I L ] Q according to Eq. [8]. There are three reasons why this procedure is impractical. First, the slope of such a plot depends on [ S ]q, so one would have to carry out several series of experiments at different [S]Q values, necessitating many more experimental measurements than a single "run" in which I S ]q is plotted versus (1/6). Second, when [L] is changed, substantial changes in the bulk magnetic - 59 -susceptibility of the solution are introduced, and even an internal standard may not compensate properly for them. Third, at high [L]D concentrations, the possibility for self-association of [L] is 63 increased. III. Stoichiometry In this section, the implications of a one-step binding process, [13] L + 2S 2 are discussed, a reasonable assumption i f the binding constant of this complex is large and/or the substrate molecule S is present in large excess. The actual binding process might involve several steps; in writing 113] , i t is simply assumed that there is a single step which is associated with the large change in chemical shift between "free" and "bound" substrate. It is only this step which will affect n.m.r. 13 measurements. It is easy to imagine multi-step binding phenomena which will not satisfy Eq. [13] even on an n.m.r. basis - such phenomena are not treated here, because i t will not be possible in general to obtain separate binding parameters for even a two-step process, when the n.m.r. data f a l l in the fast-exchange limit. For the one-step 2:1 binding model, [13], the criterion for fast exchange is readily shown to be the same as for the case of 1:1 binding; thus an observed proportionality between 6 and f is direct evidence Lb 2 that the fast-exchange limit is satisfied. The equilibrium binding constant for process [13] is - 60 -[LSJ [LS ] [14] K = l [ L ] [ S ] 2 ( [ L I - [ L S ] ) ( [ S ] - 2 [ L S „ ] ) 2 o l o 2 and i t follows that [LS ] [LS ] [15] 6 = [S] + [LS ] B [S] - [LSJ "B 2 o 2 since [S] = [S]Q - 2[LS2], Equation [15] applies i f we assume that both S molecules have the same chemical shift when bound to the lanthanide. It is now possible to solve [15] for [LS^] and then substitute for [LS,J in Eq. [14] as in Section II, resulting in the cubic equation [16] for [16] 4ILSJ3 - 4([L] + [S] )[LSJ2 + (| + 4[L] rsi l o o Z K o o + [ S ] O 2 ) [ L S 2 ] - [ L ] O [ S ] Q 2 = 0 the exact solution. In order to avoid solving the cubic equation, [16], experiments are again restricted to the range [ S ] Q >> [ L ] Q J SO that 3 2 6 « A_, and since [LS_] < [L] then [LS„] « [S] [LS0] and equation B Z — O L o Z [16] can be expressed in the quadratic form [17]. [17] 4[S]Q[LS2]2 - (|+ 4[L]Q[S]o + [S]2) [LSJ + [L]o[S]2 = 0 If now, one makes the further approximation 4[L]q << [S]Q, then 2 4 [ L ] Q [ S ] O << [ S ] Q and equation [17] can be expressed in the following form - 61 -[18] [S]2- - f [L]o[S]o + (£) - 0 [It may, be noted that Eq. [18] has the same form as Eq. [12] i f one makes the correspondence, K [ S ]q = Kg? the [L]Q term in Eq. [12] is usually negligible.] Now i f one can restrict experiments to the range where 4[L]q<< [S] a simple criterion for stoichiometry is available. One need simply specify II] » Ag, and K, and then use Eq. [18] to compute a set of 6-values from a given range of [S]o~values; the values may then be used to construct a plot of [S] versus (1/6) as shown in Fig. H « This figure shows the result for several choices of Kg which span the range of Kg-values actually determined in the present experiments. To facilitate comparison with the result for 1:1 binding, a plot of [S] versus (1/6) for 1:1 binding is also shown; to make the comparison as direct as possible, values of K = 0.1 K were chosen since typical experimental [S]Q-values were about 0.1 M. The plots clearly show that for either large Kg (strong binding) or large [ S ]q, one cannot distinguish between 1:1 binding and 2:1 binding from a plot of this type. On the other hand, when Kg is small enough to be measurable, there are readily observable differences between 1:1 and 2:1 binding. Since a l l IS] versus (1/6) plots (vide infra) are linear, i t is evident * at once that the binding is either strong or 1:1 or both. If the experimental extrapolations to (1/6) = 0 give a y-intercept which is more negative than - [ L ] , then a straight-line experimental plot is In only one instance was a non-linear behaviour in a plot of [ S ] Q versus (1/6) observed (see Results). - 62 -.28 .36 Figure 11. Graphs of i n i t i a l substrate concentration [S]Q versus (1/6) for a hypothetical substrate of Ag = 2000 Hz in the presence of shift reagent of concentration [L]Q = 0.006 M. For each graph, the binding is assumed to be either 1:1 with corresponding binding constant, Kg or 2:1 with binding constant, K . (A) K = 32, Kg = 3.2; (B) K = 126, Kg = 12.6; (C) K = 501, Kg = 50.1; (D) K = 1000, Kw = 100. - 63 -definitive proof that the binding is 1:1 rather than 2:1. When K„ is large (strong binding), there are no well-controlled D measures of stoichiometry. However, some information may be obtained from (high-concentration) experiments in which 6 is determined as a function of at constant and the data are displayed in a plot of 6 versus [ L ]O/ [ S ]q. If either Kg or I S ]q were infinitely large, such a plot would simply be a straight line from the origin to the end-point, 6 = A„ at [L] /[S] = 1. For smaller [S] , there r g o o o will no longer be a sharp end-point and one will observe a family of curves which converge for large [S]q (see Results). Experimentally, then, one need construct several such plots at increasing [ S ]Q concentra-tion until the lines begin to converge; extrapolation of the limiting line to 6 = A,, (where A_ has been determined reliably from low-concentration data according to the method of Part II of this section) A will then give an x-intercept of (1/n). In conclusion, the most critical test for 1:1 stoichiometry is the linearity of a plot of [ S ]Q versus (1/6), where the range of [S]q values should cover an order of magnitude in concentration, and include the lowest accessible concentrations for best results. IV. Solvent Dependence Whenever a diluting solvent, A, is used, there is the possibility A In principle, one might hope to obtain Kg in strong-binding situations by fitting the 6 versus I L ]Q/ [ S ]o curve of the preceding paragraph. In the Discussion i t is shown that this method may not work, even i f an independently determined Ag is used for the f i t . - 64 -of solvent competition for one or more components in the complex. Detailed theoretical treatment of competitive solvent binding to 64 lanthanide only, has been presented elswhere. [19] L + A and ' 2 ° ] KA - -£m From a very qualitative sense, the practical significance of solvent effects has already been demonstrated in Chapter I, Fig. 6, however, the following brief discussion is necessary to the understanding of the more complete investigation of this effect (see text). Even though the appropriate binding constant for [19] is small (of the order of 0.2 liter mole 1 for CHC13, acting as a suitable donor), the large concentration of solvent (ca. 12 M) may cause a significant change in the apparent binding constant for the complex LS. For example, for solvent binding to lanthanide only, [20], then the concentration of L available to complex with S will be reduced. It can be shown that this can be related in terms of the appropriate binding constants in the following manner. [21] K„, . = K , ..(1 + K T[A]) 1 B(apparent) B(real) AL J K values reported in the text are uncorrected for such competition B and perhaps should be more correctly referred to as L , v B(apparent) - 65 -^B(app )* It is important to note that the above consideration does not predict a change in A values obtained for the same substrate with the same lanthanide in different solvents. It may also be assumed that K_, ' , = K„ . . for the CC1, solution. B(real) B(app.) 4 To what extent the above theoretical treatment is confirmed will be discussed in greater detail (see text). It is sufficient, at this point to say, that any observed discrepancies can most likely be attributed to complications arising from either: possible dimerization 6 3 of Ln(dpm)3 or Ln(fod)^ complexes in solvents of differing polarities; the possibility of solvent-substrate interaction for which no account has been made. V. Temperature Dependence Although no further use was made of the temperature dependence of the chemical shift changes, i t does seem appropriate at this stage, in view of the results presented at the end of Chapter I, to present the theory and perspective necessary for the proper analysis of such an effect. Numerous other groups have investigated the temperature dependence but a l l have suffered from an incomplete allowance for the processes involved. Other researchers have investigated the temperature dependence of * For convenience only, we use the term Kg to denote the binding constant throughout the text. ** An example of such an interaction is the well-known benzene-ketone interaction. - 66 -the lanthanide induced chemical shift changes and have found a linear . dependence for a plot of the induced shift versus inverse tempera-26b 58 ture. ' They conclude that this Curie behaviour is as expected on a theoretical basis. In fact, this resultant linear dependence is a mere coincidence of the temperature range investigated and the value of AH for L + S —*• LS. For the temperature dependence of the chemical shift to be a straight line would mean that a single type of chemical complex is under observation and that i t would be very unlikely for there to exist any equilibrium between different configura-tions requiring rupturing of lanthanide-substrate bond. That this is certainly not the situation in the above investigations and our own is evident by the linear dependence of induced shift versus lanthanide to substrate ratio. Thus in addition to the inverse temperature dependence of the pseudocontact equation (Chapter I, Eq. [4]), there exists the additional temperature dependence of the equilibrium (dlnKB/d(^) = -f-). Beaute et a l . , ^ observing a similar behaviour to that of Fig. 9, Chapter I, attempted to combine the two temperature dependencies. He concluded that a plot of change in chemical shift versus l / / f would yield a straight line. However, this apparent temperature dependence is purely coincidental and has no theoretical basis. More recently 66 Ritchey et al. have attempted to evaluate the changes in chemical shift as a function of temperature. In so doing, a plot of 6 versus y^j— was prepared from the data collected at three different temperatures. l b Jo ft AH0 refers to the standard enthalpy. - 67 -For the temperature range employed, the slope of each of these lines was constant and decreased with increase in temperature. However, in view of Eq. [ 8 ] , the above resultant linear dependence is indicative that one is in the limit K B [ S ] Q » 1 where Eq. [ 9 ] applies. In general, this limit, K [S] » 1 , will not apply, particularly since ° [ L ]o K D = f (T). In such situations the slope of a plot of 6 versus j-xi— B [SJo will be a function of Ag, K ^ , and T. Thus a study of the temperature dependence of A becomes impossible. A more general approach which suffers no limitations would be to perform the experiment as outlined in Section II for several different temperatures and then to construct the apprppriate [S]Q versus 1/6 plot at each temperature. Such a representation allows one to determine unambiguously the changes in A,, with temperature and also permits an evaluation of K at each D D temperature. Just recently, following a complete re-evaluation of the pseudo-53 contact equation, Bleaney has arrived at a temperature dependence for Eu(III) somewhat > ~^ but < ~ . This result alters but in no way affects the accuracy of the above approach to the study of the temperature effect. - 68 -Results and Discussion The method believed to be best suited for the general and accurate evaluation of AD and K,, will be discussed first with suitable examples, B B followed by a demonstration that the method currently used to determine Ag from the slope of a plot of 5 versus [ L ] Q / [ S ] o can result in large errors in AD and moreover that these errors can vary even among different protons in the same molecule. Thereafter, using only the method as outlined in Section II of the Theory, lanthanide-substrate interactions will be analyzed in an attempt to explain each of the specific behaviours, characteristic of this interaction. A. Stoichiometry B. Basicity of the donor group and the importance of steric effects on K B C. Explanation for the greater effectiveness of Eu(fod).j as opposed to Eu(dpm)^ D. Explanation for the differing magnitude of induced shifts for different Ln(dpm)^ complexes E. Solvent effects on K_- and A -values F. General applications Finally, in Section G, the applicability of a Scatchard-type plot to the analysis of the interaction will be evaluated. Solutions of n-propylamine, 12_, and of neo-pentanol, _8, each with Eu(dpm)3 were prepared according to the procedure outlined in the Experimental Section as Method 2. The chemical shifts of these solutions were then measured, and the results plotted on a graph of [S]Q versus (1/6); the plot for n-propylamine is shown in Fig. 12, The. values of K - 69 -re 12. Graph of I S ]D -versus (1/6) for the interaction of n-propylamine, 12, (0.23 to 0.04 M) with Eu(dpm)3 (ca. 0.006 M) In deuterochloroform solution. Tetramethylsilane was used as the internal-reference signal for the field-frequency lock. The separate lines are for protons Hj, H2, and H3 of n-propylamine. The precision of the Kg evaluation is indicated by the close convergence of the three lines to the same y-Intercept. - 70 -and A„ were obtained from these plots following the relationship given D in Eq. [12] ; the numerical values for these parameters are shown in the first four columns of Table 7. It is expected that the same value should be obtained for regardless of which proton is used for its determination. This may be confirmed experimentally by noting that the plots for protons H-l, H-2, and H-3, in Fig. 12, a l l intercept the y-axis at the same point. It may also be noted that the A -values obtained by this method vary inversely with distance from the co-ordination * site, as expected for a pseudocontact shift. Similar results were obtained for neo-pentanol, and the values of AD and K for that substrate are also summarized in Table 7. Again, B B the high internal consistency between the evaluations of K based on B different proton resonances is evident. The experimental data obtained for the interaction of 8^  and jL2_ with Eu(dpm)^ were then analyzed by the computer-based method outlined in Section II of the Theory. The values of K„ and An calculated in B D this way are compared in Table 7 with the values obtained by the more approximate graphical method. The excellent agreement between the two sets of values indicates that the conditions which are implicit in the graphical analysis are satisfied in these experiments. It is now useful to consider the evaluation of A from plots of B 6 versus [ L ] O / [ S ] q according to Method 1 of the Experimental Section 44 to show why the slope of such a plot should not be taken as AD. a * It must be remembered that an angular dependence must also be included in the calculation of induced shift-changes. This dependence will be treated in greater detail in Chapter III. Table 7. Calculated values of bound chemical shifts (A,,), binding constants (K ), and stoichiometry for D B complexes of organic substrates with either Eu(dpm)„ or Eu(fod)_. Substrate Eu(dpm)3 Eu(fod)3 i Graph Computer Graph b Computer Stoichiometry Graph Graph KB Computer^ * Stoichiometry0 H-l 12.8 11.0 32.1 40.2 1.00 + 0.06 19.0 ->100 >100 0.7 + 0.1 n-propylamine H-2 7.7 6.5 32.9 43.1 12.7 >100 >100 H-3 4.1 3.7 37.8 44.6 6.6 >100 >100 neo-pentanol ^ ^  H-3 19.7 7.6 18.7 7.0 9.7 9.8 10.1 10.5 0.94 + 0.06 20.8 8.3 >100 >100 >100 >100 0.9 + 0.1 3 Values of A^  (parts per B million) and Kg (liter mole derived from a least-squares f i t of a plot of [S] versus (1/6) ; precision of either result is + 10%. Values of A,, and K,, derived (from the same raw data) by a more exact formula , based on an iterative computer program (see text); precision of either result is + 10%. These values should be regarded with some skepticism (see text). - 72 -As shown in Fig. 13 the slope of such a plot can vary markedly with the absolute concentration of substrate in a set of experiments with 67 18 different [S]Q-values. Both Uebel and Williams have reported similar behaviour. This variation in slope with concentration is related to the strength of binding of substrate to lanthanide and is readily accounted for by reference to the two possible limiting cases of Eq. [8] of Section I of the Theory. For interaction of Eu(dpm)3 with 8^  and 12, the limiting condition, Kg[S]Q « 1 pertains up to an [S]Q level of at least ca. 0.04 M, so that Eq. [8] reduces to Eq. [10] rather than to the anticipated Eq. [9]. Only for the highest rieo-pentanol concentration of 0.6 M, for which KB[S]Q = 5.8, is the desired limit of KBt S ]Q » 1 effectively reached, since at this concentration the A -value of 20.5 p.p.m. is within experimental error of the true value of 19.7 p.p.m. (derived from the H-l proton resonance by the method of Section II of the Theory). It is thus neither correct, nor does i t suffice to report values of A,, for different substrates - even i f the molarity of a given substrate is kept constant - unless experimental evidence shows that the molarity of the substrate involved is large enough to satisfy the limit, K B [ S ] Q » 1, so that Eq. [8] reduces to Eq. [9]. However, Eq. [9] is no longer a function of K and thus even under these optimum conditions, K B B cannot be determined. Furthermore, at high concentrations of lanthanide which would be necessitated at high substrate concentrations, bulk susceptibility changes become substantial, and i t is not clear that even an internal standard will properly compensate for them. One issue of continuing concern was the need in Chapter I, to apply - 73 -0 0.10 0.20 0.30 0.40 0.50 cy [SQ] Figure 13. Plot of induced chemical shift (6) versus ratio of the i n i t i a l concentrations of Eu(dpm)3, 5_, [L]D, to neo-pentanol, J3, [S]0, in deuterochloroform solution. Tetramethylsilane was used for the internal field-frequency lock. Points on a given line represent experiments in which the concentration of Eu(dpm)3 was varied, keeping the rieo-pentanol concentration fixed at the value listed for that line. - 74 -a small correction factor in order to obtain the correct normal chemical shift for protons on a given substrate. The magnitude of the required correction factor varied with respect to the precautions taken to exclude moisture in the i n i t i a l preparations. Thus i t would seem that in part,the magnitude of the required correction factor was an indication of the purity of the lanthanide reagent used. However, even when the most rigorously anhydrous conditions were employed, discrepancies, though minimal, persisted as will be shown. It follows from the Theory section that a plot of 6 versus [ L ] Q for any particular fixed concentration of [S]Q, Eq. [ 8 ] , should intercept the x-axis at the origin i f the lanthanide reagent is "pure". The results for just such experiments performed according to Method 1 of the Experimental are shown in Fig. 14, However, this figure reveals a finite x-lntercept, which is unaccounted for by Eq. [ 8 ] . This behaviour is now known to be indicative of the change in absolute concentration of lanthanide as a result of solvent binding to lanthanide. Solvent used for the present experiments was deuterochloroform which as will be shown in Section E of this discussion, can participate in binding to the lanthanide. This result is consistent with the preceding discussion regarding the importance of the absolute concentration of the substrate and for that matter for any experiments which contain other suitable donors in addition to the substrate of interest. A. Stoichiometry Establishing the stoichiometry for the combination of a substrate with a lanthanide shift reagent is a prerequisite before any attempt - 75 -500.0 400.0 300.0 8 (Hz) 2000 100.0 0.0 0.0 Sn=0.60 20.0 Figure 14. 10.0 15.0 [L0] (mM) Plot of <5 versus {Lj0 for the interaction of neo-pentanol, j3, (whose concentration was fixed at the value stated for each line) with Eu(dpm)3 (ca. 0.02 to 0.005 M) in deuterochloroform solution. Tetramethylsilane was used for the internal field-frequency lock. All shifts are for the H-l proton of neo-pentanol. The finite ix-intercept of the lines Is a result of a change in the absolute concentration of Eu(dpm)3« 25.0 - 76 -can be made to f i t calculated to observed A^-values, to obtain molecular 15 geometry. The reason for this will become clear in the following chapter; for now i t is sufficient to point out that the angular dependence of the pseudocontact equation is dependent on the orienta-tion of the principal magnetic axis relative to the bound organic substrate. Prior to this study, the stoichiometry was unknown, although 17 13 Rondeau and Sievers' experiments with EuCfod)^, left the impression that the leveling-off of a graph of 6 versus [ L ] O / [ S ] O at a mole ratio of approximately 1:1 might be taken to indicate a 1:1 stoichiometry. In the Theory section, i t was shown that such a conclusion is warranted only for cases where Kg and I S ]q are large; Fig. 15 Illustrates several such plots determined at different [S]Q levels, for the interaction of neo-pentanol with EuCfod)^. In this case, the limiting line (the left most points in Fig.15) extrapolated to the known A„-value gives a corresponding L / S ratio of 0.9:1, or JS about 1:1. However, the data points correspond to different [L] concentrations, and when [L]Q is changed there will be large changes in the bulk magnetic susceptibility of the solution, and these changes may not be compensated correctly even by an internal standard. Indeed, the poor internal consistency of the results is clearly eyident in the dotted line of Fig. 15. This line was obtained by using the middle data point in the [S]Q = 0.1 M data set to compute K^ ; this value of K^  was then used to obtain the dotted line by using Eq. [5] and the f u l l quadratic form of Eq. [6]. It is evident that the dotted line gives a poor f i t to the remaining data points in the [ S ] = 0.1 M set. Since S (Hz) 1000.0 = 0.61 M = 0.20M = 0.10 M • s 0 =0.053M 1.5 2.0 3.5 Figure 15. Plot of 6 (induced chemical shift for the H-l proton) versus tatio of the i n i t i a l concentration of Eu(fod)3, [L]0, to neo-pentanol, IS] 0, in CDCI3 solution with tetramethylsilane as the internal reference. The solid lines represent experiments in which TL] 0 w a s varied while keeping IS]Q constant at the value listed for that curve. The dotted line (see text) is a theoretical f i t to the TS] 0 => 0.1 M curve, based on a known "value for Ag and with-Kg magnitude chosen to f i t the middle data point of that curve exactly. - 78 -it is now obvious that experiments in which [L]Q is varied can give inconsistent results, i t is not surprising that for the interaction of n-propylamine with Eu(fod).j, the stoichiometry deduced from similar experiments is not even integral. In conclusion, when the binding is strong (large IC), these experiments do not reliably predict B stoichiometry. For the weaker binding of 8^  or V2_ to Eu(dpm)3, the outlook is much improved. As argued in Section III of the Theory, the linearity of a plot of [S]q versus (1/6) is direct proof of 1:1 binding (compare Figs. 11 and 12). Since the range of choices of K illustrated in Fig. 11 B brackets the observed K^-values (see Table 7) for binding of or 12. to Eu(dpm)3, there can be no doubt that the binding is 1:1 in each of these two cases. For the interaction of norcamphor, jL4_, with Eu(fod)^ in carbon tetrachloride, the binding is sufficiently weak to allow for an accurate determination of K (ca. 22.5 liter mole "S from a plot of [S] versus a — o (1/6). The linearity of this plot is direct proof of 1:1 binding. However, a similar plot for the above interaction in deuterochloroform produces a curve resembling that for 2:1 in Fig. U and when these same 2 data were plotted in terms of the variables [S]Q versus [S] (1/6), a linear plot was obtained. This is proof that 2:1 binding is occurring in deuterochloroform and that the limiting conditions, 4[L] « [Si o o 68 applies. For a l l other studies reported here where K_ could be B accurately determined, 1:1 binding was observed. Practically speaking, then, when the binding is weak (K_ < 100 liter mole ^ ) , i t is possible to obtain reliable, consistent values for - 79 -A_, IC, and solution stoichiometry; when the binding is strong (K__> 100 liter mole ^ ) , Ag may s t i l l be determined accurately, a lower bound for Kg can be proposed, but the stoichiometry may be indicated only approximately. B. Basicity of the Donor Group and the Importance of Steric Effects on_KB From Table 7, it will be noted that the binding constant for n-propylamine is significantly larger (stronger binding) than that for neo-pentanol - for association with either Eu(dpm)3 or Eu(fod)^. For Eu(dpm)„ where accurate determination of K is possible, the amine binds j B 3.5 times as strongly as the alcohol. This suggests that for a given shift reagent, the characteristic induced shift magnitudes, in the order -NR^  > -OH > ^ C=0 > -0- > -C02R > -CN discussed by Williams,21 may be correlated primarily with variations in the binding constants for substrates with different donor functionalities. In Table 8 are listed the values for K and A„ as determined by B B Method 2 of the Experimental, for a series of amines and alcohols. The values for K„ clearly indicate a dependence on the basicity of the B donor group as well as a steric dependence (see below). An indication of the steric effect on K 1s is shown in the values B for this parameter for n-propanol 15, and neo-pentanol J?, (Table 8). The greater steric hinderance in neo-pentanol is reflected in a K^  value which is ca. 0.5 that for n-propanol. The more basic character of amines is reflected in the overall larger K -values for these substrates as compared with the alcohols. Again even within a series - 80 -Table 8. Calculated values of bound chemical shifts (A,,), and binding B constants (K ) for complexes of organic substrates with B Eu(dpm)„ in deuterochloroform solution. Substrate AB/p.p.m.a K 11 mol _ 1 a B H-l 12.8 32.1 n-propylamine H-2 7.7 32.9 H-3 4.1 37.8 o 14.9 19.0 aniline m 3.1 22.0 P 3.7 20.0 o 23.8 74.0 pyridine m 7.8 80.0 P 7.4 74.0 H-l 13.9 19.0 n-propanol H-2 8.1 19.5 H-3 5.0 17.9 neo-pentanol H-l 19.7 9.7 H-3 7.6 9.8 Values of A B a n d *B from least-squares f i t of a plot of [S] versus o (1/6); prec ision of values + 10%. The linearity of the [Si versus o (1/6) plot for each of the above substrates implies 1:1 binding. - 81 -of amines, K -values determined in this manner indicate the change in basicity as displayed in the four-fold increase in K0 between aniline, 16, and pyridine, 17. From these results, i t would appear that this parameter, K , is sufficiently sensitive to chemical and stereochemical B environment and thus may be useful as a means of determining the potential reactivity at various donor sites. A more detailed evaluation of Kg dependencies can be found in Section F. C. Explanation for the Greater Effectiveness of Eu(fod)j as Opposed  to Eu(dpm)^ Attention was next directed to the interaction of 8_ and 12, with Eu(fod),j. Again using the form of data reduction as outlined in Section II of the Theory, attempts were made to process the experimental data by both the graphical and computer-based methods. With either treatment, it was possible to obtain A_ accurately, but K was too B B large to be measured. Fig. 16 shows why. A_ is taken from the slopes of B the lines in Fig. 16 and is readily determined. However, the y-intercept depends on (l/lO , and when K_, is large, the y-intercept is so close B B to zero that K„ cannot be determined with any confidence; in this case n * only a lower limit for Kg may be deduced. It should be appreciated that the graphical method is an approximation which is not expected to be valid when K„ is large. The computer-based method involves no approximations, but simply becomes numerically insensitive when the limit, (1/Kg) > fS]Q, is not satisfied. For the _ This limitation, intrinsic in our form of data reduction has been criticized and forms the basis for the discussion presented in Section G. As will be shown, Fourier Transform spectroscopy may perhaps offer the only possible solution to this problem. 0.50n 0.40 0.30-( / ) ' o 0.20 0 . 1 0 O.IO ( 4 ) X 1 0 2 ( Hz"1) Figure 16. Plot of IS] versus (1/6) for the interaction of neo-pentanol, 8, (0.4 to 0 . 0§ M) with Eu(fod)3 (ca. 0.006 M) in deuterochloroform solution. Tetramethylsilane was used for the internal field-frequency lock. The separate lines are for protons H-^  and H3 of neo-pentanol; the different slopes of the two lines are due to the different values of Ag for the two respective protons. - 83 --2 -1 Eu(fod)_ experiments just mentioned, (1/K ) < 10 mole liter , 3 D while [S] Q = 0.1 mole liter \ so that even the computer method will yield only a lower limit for Kg. Similar experiments with n-propylamine and Eu(fod)3 also gave precise linear plots. Again i t was possible to obtain the A^-values graphically to yield the data listed in Table 7, but again Kg was too large to be measured; a l l that can be stated with certainty is that K_, is at least 100 liter mole \ When this study was initiated, i t was already known that for any particular substrate, EuCfod)^ produced larger induced shifts than did EuCdpm)^ on a weight-weight basis. From the data listed in Table 7, i t is clear that the principal source of this enhanced effectiveness is the roughly ten-fold increase in binding constant, Kg, since the bound chemical shifts are nearly the same for a given substrate. D. Explanation for the Differing Magnitude of Induced Shifts for  Different Ln(dpm)^ Complexes In contrast to the above, the differing effectiveness of various LnCdpm)^ complexes can be accounted for by the differences in Ag-values rather than K -values. This may be confirmed experimentally by noting that the plots for neo-pentanol interacting with EuCdpm)^, PrCdpm)^ and TmCdpm)^  in deuterochloroform solution, Fig. 17, a l l intersect the y-axis at the same point and thus have a common value of K whereas the slopes, therefore A , vary markedly. The numerical - 84 -• L 0=Tm(DPM) 3 A [ _ 0 = Pr (DPM) 3 •1 = EuCDPML O «3 0.6 0.8 1.0 1.2 1.4 1.6 (1) x 102 (Hz1) Figure 17. Plot of l S j0 versus (l / f i ) for the interaction of neo-pentanol, 8^ , with three different lanthanide shift reagents (ca. 0.006 M). For Eu(dpm)3, 5_, and Tm(dpm)3, J3, CDCI3 was used as solvent with tetramethylsilane for the internal field-frequency lock. For Pr(dpm)3, _7, CHCI3 was used as solvent and for the internal field-frequency lock. All shifts are for the H-l proton of neo-pentanol. The precision of the Kg evaluation is indicated by the close convergence of a l l lines to the same y-intercept. - 85 -values for these parameters are shown in Table 9 along with the values of K_ and An determined from a similar study with n-propylamine. For D a both substrates, K -values are found to remain constant while A^-values B D vary noticeably within a series of Ln(dpm)3 complexes. Similar, though not as distinct behaviour has also been observed for the interaction of 8^  with different Ln(dpm)3 complexes in solvents other than deuterochloroform, (e.g. carbon tetrachloride and deuterobenzene, vide infra). E, Solvent Effects on K - and A -Values J5 B For completeness in the investigation of the binding of substrates to lanthanide shift reagents in solution, the effects of typical solvents on the values determined for K and A_ were examined. Quantitative B B investigations into this aspect of the interaction are not without complications,,as is customary in any study of weak complexes, for not only is there the possibility of solvent binding to the shift 6 33. b reagent ' (binding in this context has the sense of solvent existing in the solvation sphere of the metal), but also solvent binding to substrate. In addition, there is the possibility of dimerization of 63a shift reagents in different solvents. Solvent shifts in n.m.r. have long been the subject of lengthy investigations with perhaps one of the more common uses being to induce differential shifts which may often allow hidden resonances to become observable. Benzene-ketone: 4b interactions are typical of this "solvent-induced shift" effect. In the following discussion, a l l solvent effects will be analyzed with regard only to solvent competing with substrate for the shift Table 9. Calculated values of bound chemical shifts (A,,) , a and binding constants (K„) D for complexes of organic substrates with different Ln(dpm)3 in deuterochloroform solution. Substrate EuCdpm)^ Pr(dpm)3b Tm(dpm)3 Ag/p.p.m. KB/1 mol 1 Ag/p.p.m. K„/l mol - 1 Ag/p.p.m. K_/l mol 1 ft H-l 12.8 32.1 46.8 ^32.3 71.7 25.4 n-propylamine H-2 7.7 32.9 30.8 22.0 39.5 26.6 H-3 4.1 37.8 15.6 25.0 21.6 27.3 H-l 19.7 9.7 25.3 10.6 150.1 10.0 neo-pentanol H-3 7.6 9.8 9.7 11.2 59.5 9.4 Values of A,, and o Kg from least-squares f i t of a plot of [S] versus (1/6); o precision of values + 10%. CHC13 was used as solvent and to provide a reference signal for the field-frequency lock; other metal solvent was CDC1„ with tetramethylsilane as the internal reference. - 87 -reagent. The deficiencies and discrepancies which result are then * discussed with respect to competing solvent-substrate interactions which have not been allowed for in Section IV of the Theory. In Section IV of the Theory, i t was shown that i f solvent binds to the shift reagent, the apparent K computed by our method would be smaller than the which would be observed in a totally inert solvent but no change would be expected in A^-values. It should be pointed out B that this in no way invalidates the fact that our reported K -values correctly measure the binding constant for the stated substrates to the stated shift reagent in the stated solvent. In Table 10 are listed values for KD, A_ and the ratios of A 's 15 15 15 for neo-pentanol interacting with Eu(dpm)3> Eu(fod)3> Pr(dpm)3 and : TmCdpm)^  in three different solvents. For Eu(dpm>3 the Kg-values are found to decrease in the order CC1. > C,D, > CDC1-, exactly the order 4 6 6 3 one might expect from a chemical point of view with regards to either solvent-substrate interaction or solvent-lanthanide interaction or both. The fact that the A -values for H-l and H-3 are not identical B within experimental error in a l l three solvents as theory predicts is not as clear but may be due to solvent-substrate interactions since binding of solvents CDCl^ and C^ D^  to substrate may be of the same order of magnitude as the interaction of these solvents with Eu(dpm)y On the other hand, this difference in A -values may reflect the tendency 15 of Eu(dpm)3 to dimerize (vide infra) to differing extents in solvents of varying polarity. In this connection, dimerization would be expected * Different substrates will be solvated to various degrees in different solvents and the extent to which a substrate is solvated should undoubtedly affect its ability to interact with the lanthanide shift reagent. Table 1Q. Calculated values of bound chemical shifts(Ag), ratios of Ag and binding constants (1 for complexes of j} with Eu(dpm)^, EuCfbd)^, PrCdpm)^, and Tm(dpm)^  in three different solvents. Substrate Eu(dpm)„ Eu(fod) Pr(dpm) Tm(dpm), Solvent * * Ratio Ag Kg Ratio Ag Kg Ratio * AB * Ratio H-l 19.7 9.7 2.59 20.8 >100 2.51 25.3** 10.6 2.61 150.1 10.0 2.53 CDC13 H-3 7.6 9.8 8.3 9.7 11.2 59.5 9.4 H-l 25.3 36.9 2.46 21.8 >200 2.43 43.4 37.0 2.47 115.9 >200 2.66 CC1, — _ 4 H-3 10.3 34.0 9.0 " 17.6 35.0 43.6 H-l 22.5 31.7 2.53 20.7 >100 2.52 40.3 10.7 2.52 172.6 22.4 2.68 C,D, 6 6 H-3 8.9 30.0 8.2 " 16.0 10.5 64.5 22.9 Values of A (p.p.m.) and K (1 mol ) derived from a least-squares f i t of a plot of [S] vs. (1/6) D D O ** preci i n of either result is + 10%. CHCl^ was used as solvent and to provide a lock signal; some TMS was added to provide a chemical shift reference. For a l l the other cases., TMS was used to provide a lock signal. - 89 -to be least probable in a donor sol-vent such as CDCl^. Even without shift reagent, the chemical shifts of H-l and H-3 are not identical in the different solvents, indicating the effect of polarity or solvation of substrate on the measured chemical shift. It is not unreasonable then to expect that the complex LS would also show a notable variation in chemical shift with solvent. Analogous ordering of K^-values has been observed for neo-pentanol interacting with Tm(dpm)3 and Pr(dpm)3 (with the exception of the value of Kg determined for the latter in benzene) in these three solvents. However, the Ag-values determined for these particular rare earth complexes in the three solvents are found to differ even more signifi-cantly than for Eu(dpm).j. This result, as previously stated, was not predicted from theoretical consideration and can only be rationalized as above. Noteworthy are the ratios of bound chemical shifts shown in Table 10 which are constant to within experimental error for each metal * in a l l three solvents. This must imply that the associated adducts have essentially the same shape and stoichiometry throughout, which thus favours the explanation of differing degrees of solvation in the three solvents and not that of dimerization or contact shifts. The extent of solvation would be expected to be most important in The value of these ratios for the Ln(dpm)^ complexes in a particular solvent (across the table) allows one to speculate as to the possible contribution of a contact shift and/or the shape of the complex. From such a comparison i t would seem that Tm(dpm)3 behaves perhaps somewhat differently in CCl^ and C^ D^ , either as a result of a contact contribution or more likely from a change in the shape of the complex. - 90 -CDCl^ as is indicated by the nearly constant Kg-values shown in Table 9 for this solvent system. This ordering of K^-values, which appears to reflect the extent of solvation, occurs to a somewhat lesser degree in benzene and even less so in CCl^ where the large value for IL, withTm(dpm) (Table 10) would seem to indicate a dependence on the B 3 ionic radius of the lanthanide which decreases across the row, in spite of the very bulky $-diketonate ligands attached. This finding is also in accord with the above ratios. For a similar analysis, but this time using Eu(fod)3, a comparison of the K -values in the three solvents is not possible because of the D inaccuracies involved when K_ > 100. However, the values of An determined n —" / o from these experiments are identical within experimental error as are the ratios. In view of the range in A -values observed for Eu(dpm)„, B J this result would seem to indicate the diminishing importance of solvent-substrate interaction (solvation), as a result of the much greater interaction of Eu(fod)^ with both substrate and solvent. In an attempt to better understand the influence of different solvents with Euffod)^, the interaction between the ketone, jL8_, and Eu(fod)0 was studied with the assumption that now the K -values would be in a range (< 100 liter mole "*"), where accurate determination was possible. The result was not as anticipated, as shown for the values of K_ (> 100 liter mole"1), listed in Table 11. B Even though a comparison of Kg's is not possible as was the original intent, this study did provide a bonus with regards to the stoichiometry and/or the shape of the complex in the three solvents . - 91 -Table 11. Calculated values of bound chemical shifts (A._), ratios of n Ag and binding constants (Kg) for complexes of 2,2-dimethyl-3-butanone, 18, with Eu(fod) in,three different solvents. Substrate * Eu(fod)3 * Ratio Solvent CH3 11.56 >100 1.74 CDC13 (CH3)3C 6.65 I I u 0 CH3 16.12 >ioo 1.96 CC1. 4 (CH ) C (CH3)3C 8.21 I I ' 18 0 CH3 14.90 >100 1.95 C6°6 (CH-KC 3 3II 7.64 It 0 Values of A15(p.p.m.) and K (1 mol ) derived from a least-squares f i t of a plot of [S] vs. (1/6); precision of either result is + 10%. i - 92 -as depicted in the values for the ratio of the bound chemical shifts. This ratio is found to differ significantly in CDCl^ from that for CCl^ or benzene. If, of the above possibilities, one chooses to regard this as indicative of a change in stoichiometry, then this result is in accord with the change in stoichiometry observed for the ketone 68 (norcamphor) with a similar change in solvent from CCl^ to CDCl^. This rather unusual behaviour - possible change in stoichiometry -which has only been observed for ketones in the polar solvent CDCl^, may perhaps be related to the planar arrangement of the two lone pairs 69 on the oxygen. Evans has recently reported a situation where the stoichiometry for the interaction of dimethyl sulphoxide with Eu(fod)3 in CD2CI2 can be directly determined as 2:1. Thus, in view of the similarity between a l l three systems - polar solvent, EuCfod)^, and planar arrangement of the two lone pairs on the oxygen - it does not seem unreasonable to conclude that the change in observed shift ratios, Table 11, is in fact indicative of a change in stoichiometry of the lanthanide substrate complex. In summary, i t would appear that for quantitative investigation into the interaction of different shift reagents with suitable substrates, the solvent of choice would be CDCl^, at least with regards to alcohols and amines. This solvent would then allow the investigator to * As stated in Section III of the Theory, accurate determination of the stoichiometry is not possible when K > 100 liter mole 1 and thus B 1 from the present investigation, a plot of [S]q versus (1/6) for CDCl^ would yield a straight line. Analysis of the data on the basis of 2:1 binding, which also yields a staight line, resulted in different values for A- but as before the ratio for CDC10 (1.70) differed significantly from that for CCl^ and CgDg (1.89). - 93 -quantitatively compare values of K and A„ for different lanthanide shift reagents. However, for the eventual determination of substrate geometry utilizing ratios of A's, the solvent of choice for ketones * would appear to be CCl^. On the more practical side, those investigators concerned solely with the magnitude of the induced shift for spectral simplification, CCl^ would be the solvent of choice. F. General Applications In Sections A to E of this discussion, we have described in detail the nature of lanthanide-substrate interactions. We shall now attempt to demonstrate the relevance of these detailed investigations to other areas of chemistry. In Chapter I, we described the usefulness of 1 13 these reagents for obtaining optimally dispersed H and C spectra and in Chapter III we shall present what is perhaps the most important aspect of this area - the potential of lanthanide shift-reagents to the determination of substrate geometry. However, in addition to the above, there is a great deal more fundamental chemical insight to be gained from a quantitative understanding of the lanthanide-substrate equilibrium. The following discussion describes some of these more general aspects; i t will be noted that many of the sections contain a discussion of experiments s t i l l in progress. i (i) An organic problem The following Table 12, an extension of Table 8, lists the values of The significance of this statement will be appreciated in Chapter III. For now, it suffices to mention the importance of the symmetry of the complex for geometry determination. - 94 -Table 12. Calculated values of bound chemical shifts (AT,), and binding constants (Kg) f °r complexes of organic substrates with either Eu(dpm)3 or Eu(fod)3. Substrate Ag/p.p.m. KB/1 mol -1 H-l 4.46 32.7 H-2 6.06 31.0 H-3 15.70 29.0 H-4 8.61 __§ H-5 22.14 30.0 H-l 2.97 69.8 H-2 7.41 65.2 H-3 13.10 79.0 H-4 4.91 __§ H-5 6.34 __§ H-l __§ >100 H-2 4.62 n H-3 12.80 t i H-4 8.57 i t H-5 14.37 I I H-l 9.64 >100 H-2 a 9.41 I I H-2 e 15.95 I I H-3 6.67 I I H-4 2.33 I I H-5 __§ H-6 a 3.39 >100 H-6 e 6.61 I I hC-H 2.47 I I OMe 5.59 I I Shift reagent 19 M e . , 0 — C H2 Me 3 °AMe Me Mev-O—CH2 Me-Me R = CCH3 O M evO - C H , M e ^ O RO Me Me R = CCH3 II O O H O M e Eu(dpm). Eu(fod). Eu(fod). Eu(fod). - 95 -Table 12.(continued) Substrate Ar./p.p.m. KB/1 mol -1 H-l 2.29 >75 H-2 a 9.93 I I H-2 e 8.17 i t H-3 13.66 I I H-4 ca. 6.3 I I H-5 2.58 I I H-6 a ca. 9.4 I I H-6 e 5.41 I I iC-H S3 3.98 I I OMe 1.33 I I H-l 3.00 >100 H-2 2.60 t i H-3 3.67 I I H-4 7.83 i t H-5 14.21 I I H-7 6.84 I I H-8 5.84 I I H-9 1.32 I I H-10 1.60 I I CH3 11.56 >100 »>3C 6.65 1 1 H-l 12.16 >100 H-2 2.04 I I H-3 1.79 I t H-4 1.49 I I H-5 1.55 I t H-6 1.88 I t H-7 8.21 I I Shift reagent OMe 21 C H 2 O H 18 O II ( C H 3 ) 3 C - C H : 22 t t Eu(fod). Eu(fod). Eu(fod). Eu(fod). - 96 -Table 12. (continued) Substrate Ag/p.p.tn. V 1 mol -1 Shift reagent 14 H-l H-2 H-3 H-4 23.54 24.09 21.37 7.79 22.3 22.7 23.7 22.3 Eu(fod). Solvent was carbon tetrachloride with tetramethylsilane for lock. Solvent was deuterochloroform with tetramethylsilane for lock. Solvent was deuterobenzene with tetramethylsilane for lock. This value could not be determined with sufficient accuracy to justify its inclusion here. - 97 -A ' s and K 's determined for a larger variety of organic substrates. B B Fig. 18 shows a plot of [S]q versus (1/6) for 21 and is typical of the consistency observed in similar plots for the other compounds listed in Table 12. Several of the molecules listed are carbohydrates and most of these exist in a locked conformation, a necessary prerequisite to geometry investigations to be discussed in Chapter III. In the discussion which follows, the importance of being able to determine accurate values for K and A,, will be analyzed with respect to the B B important chemical and configurational implications implicit in these parameters. In many instances the values of A,, can be rationalized in terms B of the distance dependence of the pseudocontact equation alone. However, the significance of the angular term in the pseudocontact equation, the importance of which is amplified for those protons closest to the donor site, is often unmistakable as is seen in the values of A„ B determined for H-3 and H-5 of 1 and similarly for the values of A — B for H-3 and H-5 of _4. In a l l other examples tabulated, distance alone is 'sufficient' for a configurational assignment to be made. The importance of this latter observation, which will be demonstrated for compounds 19_ and _20_, is significant to the practising organic chemist. Assignment of the configuration at C-3 for furanose and pyranose sugar rings is often possible only with great difficulty and even then a large amount of uncertainty remains. Methods currently used to make such assignments include n.m.r., o.r.d., c.d. and chemical derivatization. In many instances, even employing a l l the above methods does not - 98 -t Figure 18. Plot of [S]Q versus (1/6) for the interaction of l,2:3,5-di-0-methylene-a-D-glucofuranose (21, 0.02 to 0.102 M) with Eu(fod)3 (0.0059 M) in deuterochloroform solution. Tetramethylsilane was used for the internal field-frequency lock. The precision of this plot is indicated by the close convergence of a l l lines to the same y-intercept. - 99 -unequivocally confirm the stereochemistry at C-3. We proposed to investigate the applicability of lanthanide shift reagents as a viable means for making such an assignment. Compounds chosen for this investigation were, methyl 4,6-0-benzylidene-2-deoxy-q-D-ribo-hexopyranoside '_19_ and methyl 4,6-0-benzylidene-2-deoxy-q-D-arabino-hexopyranoside 20. These molecules were suitable as models for such an investigation because they possessed one group, a hydroxyl, likely to provide the major association site for the lanthanide reagent and configurational assignment could be confirmed in advance from the value of the H-3, H-4 splitting. Comparison of the Ag-values for equivalent protons in 19_ and 20, Table 12,show substantial variations which, with the aid of a molecular model, appear to correlate well with the distance dependence of the pseudocontact equation. Most noticeable are the differences between Ag-values for H-2e> H-3 and OMe in compounds 19 and _20_. These values, significantly different as they are, agree on a first order basis considering distance alone, x^ith the known stereochemistry at C-3. The magnitude of the A^-values also re\Teal the steric effect on the position of co-ordination of the lanthanide shift reagent. This dependence has been demonstrated previously in Section B and will be discussed in a quantitative manner in Chapter III. It would appear, therefore, that the use of lanthanide shift reagents as a method for assigning configuration at C-3 for cyclic forms of sugars may prove to As will be discussed in Chapter III, the angular dependence of the pseudocontact equation must never be neglected i f one is seeking to calculate the absolute geometry; however, for many configurational assignments distance alone often suffices. - 100 -be a very attractive alternate technique. The value of Kg = 31 liter mole 1 determined for the interaction of 1^  with Eu(dpm)3 in carbon tetrachloride compares favourably with that determined for the similarly sterically hindered rieo-pentanol (Kg =» 35.5 liter -mole interacting with Eu(dpm)^ in carbon tetrachloride. Such a comparison provides important evidence as to the reliability of the Kg-values determined in this way. Quantitative comparison of Kg-values determined for analogous interactions with Eu(fod)3 is usually not possible for reasons which have been previously discussed. However, i t is interesting to examine the K -values determined for the B interaction of compounds 18, 22, and 14 with Eu(fod).j. The dependence of the K -value on the basicity of the donor group has previously been discussed (Section B). Thus, i t was anticipated that for a ketone interacting with Eu(fod)„, the K -value might be J B sufficiently less than that found for similar interactions with alcohols (K > 100 liter mole ^ ) , thereby allowing for an accurate evaluation of Kg. This was the case for compound 3.4 but not with 18_ or 22. The reason for the small value of K = 22.5 liter mole 1 with 14 is u — undoubtedly due to the steric hinderance at the point of co-ordination of the lanthanide for this substrate, an effect which would be much less significant for compounds 18_ or 22 as reflected in a value of Kg > 100 liter mole 1 for these substrates. Also noteworthy was the observation of a single resonance for the H-l protons of 22 with and without shift reagent. This indicates that Eu(fod)3 binds to this ketone in such a way as not to alter the existing symmetry. This would seem to Imply that the lanthanide must bind in such a manner as to bisect the angle - 101 -between these protons or alternatively, spends half of its time on each of the carbonyl lone pairs. (ii) An inorganic problem As part of another program, Paddock and Wingfield (Department of Chemistry, U.B.C) had prepared a series of dimethylaminocyclophospho-nitriles I^P^NMe^g 23, N^^NMe^Q 24, N6P6(NMe2)12 25, N?P? (NMe£)^ 26, NoPo(NMe0)1Q 27] ranging in ring size from 4(P-N) to 9(P-N) units. "^H n.m.r. proved unsuccessful as a means of characterizing these compounds for they a l l exhibited only a single resonance which was broadened (ca. 8.0 Hz) by the coupling to phosphorus. More recently, several complexes containing phosphonitrilic ring systems and transition metal ions have been prepared and detailed studies of the bonding and structure of such complexes have relied solely upon X-ray investigations which have been carried out on only a few of these molecules.^^a'^ The present investigation of the interaction of Eu(fod)3 with the phosphonitrilic systems 23-27 (following Method 2 of the Experi-mental) , was undertaken to measure the K,, values for this series in anticipation that a systematic variation in K_, would be observed D corresponding perhaps to the differing basicities resulting from ring size. If successful, this study would then permit a better understanding of the differing abilities of these compounds to form complexes with transition metal ions. The experiments which followed produced results which were totally unexpected although interesting in their own right. The following several points are noteworthy from this investigation: (i) in spite of the bulkiness of these substrates, 23-27, and their polyfunctional - X02 -donor qualities, a l l were observed to interact with EuCfod)^, (ii) for a l l except N^P^(NMe2)g, chemical exchange is slow - a separate peak was observed for both the free and complexed substrate, (i i i ) bonding with Eu(fod)3 occurs via the ring nitrogens - except perhaps for N^ P^  (NM^) ^ - as is most always the case for transition metal complexes, (iv) for compounds 24, 25 and 26 a two-step binding process was observed, (v) for N^P^(NMe2)^g, the stoichiometry can be trivally deduced as 1:1. The implications of the above points with regards to the chemical properties of the phosphonitriles must await the final analysis of the result for the interaction of Eu(fod). with N„P„(NMe_), and N0P0(NMe„),,, J J J Z o o o L io currently in progress. In the meantime, i t is interesting to speculate into this aspect but more important are these results as they pertain to the chemical nature of the interaction with Eu(fod)3> For N^P^NM^^, only one resonance is observed in the n.m.r. spectrum and for this compound '6' is a function of the concentration of Eu(fod).j. Thus in contrast to the rest of the series, the fast exchange limit applies. This is in accord with previous findings for complexes with transition metal ions where the stability of the complex was found to increase with ring size. This result is likely a consequence This implies that the induced shift is no longer a function of lanthanide concentration. This is the first reported case of slow exchange between lanthanide shift reagent and substrate at room temperature. Evans^9 has reported the only other similar occurrence for the interaction of Eu(fod)3 with dimethyl sulphoxide where slow exchange was found to occur at -80°C. ** Synthesis of this compound is currently in progress. - 103 -of the larger steric effect for the smaller ring systems. Performing the experiments as outlined in Method 2 of the Experimental allows one to calculate a bound chemical shift, AD = 0.4 p.p.m., and a B Kg > 100 liter mole"1. It is interesting to note that this calculated value of A- = 0.4 B p.p.m. is of the order of that observed directly for compounds 24-27, where the slow exchange limit was found to apply; A„ as measured from the spectra for compounds 24-27 ranges from ca. 1.0 p.p.m. to 1.5 p.p.m. This provides important proof as to the reliability of Method 2 of the Experimental for determining A- when the fast exchange limit applies. Bonding of EuCfod)^ to the ring nitrogens can be confirmed in two ways. (i) For a l l those cases where the chemical exchange was slow -with the exception of N^P^(NMe2), where more than one peak is observed for the complexed substrate - only one peak for the complexed substrate was observed. The equivalence of al l the methyl groups could only result i f the bonding occurred with the ring nitrogens. (ii) The magnitude of the bound chemical shift, ca. 0.5-1.5 p.p.m., which is a function of the angle and distance of Eu(III) from the protons, is small when compared with say the a protons of n-propylamine, (Table 8)-For the concentration range of substrate employed, the shifted resonance for compounds NcPc(NMe„)1 , N,P£(NMe0)10 and N.,P-, (NMe„).. . .) j 2 11) D O 2 12 II 2 14 appears to be somewhat dependent on lanthanide concentration even though a separate peak for free substrate exists - proof the slow exchange limit applies. This can only be explained in terms of a two-step binding process, with the first step being in the slow exchange limit - 104 -* and the second a fast exchange process. Thus, i t is not possible to deduce a stoichiometry directly from the relative intensities of the resonances for these three substrates. For NgPg^NM^^ig t n e situation is not as complexe , Fig. 19. Here only two resonances are observed, Fig. 19B, one for the free (7.42T) and the other for the bound substrate (6.52T) (Resonance at 9.04T for the Eu(fod)^ protons is not shown). The resonance for the complexed substrate is not a function of the lanthanide concentration for this compound. Fig. 19C shows the observed spectrum for the compound obtained from reacting 0.255 grams of Eu(fod)3 with 0.292 grams of NgPg(NMe2)^g (see Experimental for conditions used). The resonance at 6.52 T is that of the Me's of _2_7 and that at 9.11 x for the protons of Eu(fod)g. This is the first report of a stable complex of Eu(fod)3 with a substrate of this size and the resulting n.m.r. confirms the assignment of the n.m.r. spectrum shown in Fig. 19B. From the relative areas of the two peaks, Fig. 19C, it was found that each mole of shift reagent complexed 1.0 + 0.1 mole of 2_7, corresponding to a co-ordination number of 7 for the europium ion. The above results are not only noteworthy from the point of view of providing important evidence as to the nature of lanthanide-substrate interactions as has been discussed, but have the potential of providing important information with regard to the chemical nature of these inorganic systems. * The chemical shift of the resonance for the free substrate in the presence of shift reagents is identical with the resonance observed in the absence of shift reagent. This result is proof that the first step is in the slow exchange limit. ** 71 Selbin has reported the preparation and properties of other 7 co-ordinate Eu(III) complexes. - 105 -6.52 9 . 1 1 r -6 - r 7 9 8 r IO B 7.42 7 7.42 6 I 7 Figure 19. spectra (100 MHz) of NQPg (NMe?)-;^  (27.* 5-3 4 x 1 0 • 10-4 M ) -4 The H n.m.r 2.67 x 10-3 M) with Eu(fod) (ca. 6.0 x ~ ) in carbon tetra-chloride solution. Tetramechylsilane was used for the internal field-frequency lock. A. The normal snectrum B. 2.14 x 10"3 M 27, 6.1 x 10-4 M Eu(fod)3. C. The spectrum of the comoound obtained by reacting 0.255 grams of Eu(fod)3 with 0.292 grams of 27. to - 106 -(i i i ) A liquid crystal study As part of a preliminary investigation in conjunction with R.B. Malcolm of this laboratory, the suitability of paramagnetic lanthanide shift reagents to liquid crystal n.m.r. was investigated. The theory required to understand and interpret the liquid crystalline n.m.r. spectra has been fully developed elsewhere and will 72 73 not be discussed in this thesis. ' For those who are unfamiliar with this form of n.m.r., i t suffices to point out that in the liquid crystalline spectra, both the dipolar couplings and the normal J couplings from isotropic n.m.r. studies are observable. Analysis of the resulting liquid crystalline spectrum, which will therefore be many times more complex than the isotropic spectrum, has then been shown to provide a very sensitive means for determining the absolute geometry of the substrate in the liq-uid crystalline phase. No previous reports existed on the applicability of lanthanide shift reagents to this area. It was our primary concern to determine whether these reagents would be effective in spreading out the complex liquid crystalline spectra. Pyridine was chosen as the model substrate and its liquid crystal spectrum measured in the liquid crystalline solvent, N-(p-ethoxybenzylidene)-P-n-butylaniline (EBBA) in the presence of EuCdpm)^. For [L]o/[S]o = 0.1, the following shift was observed for the protons of pyridine; o = 260.0 Hz m = 82.5 Hz p = 74.5 Hz - 107 -It is important to note that the magnitude of these shifts is ca. 1.5 times larger than for similar I L ]Q/ [ S ]o ratio of pyridine and Eu(dpm) in CDCl^. It is also noteworthy that the ratios of these induced shifts are identical to those found in the latter solution. No interpretation of the above results will be presented at this time but await the completion of a more detailed investigation which is currently in progress by R.B.M. In addition, the generality of this method as a means of dispersing complex liquid crystal n.m.r. spectra cannot be commented on prior to a further more complete investigation of liquid crystalline solvents, temperature, and lanthanide. From the point of view of furthering the understanding of the nature of substrate-shift reagent interactions, this area may have a great deal of potential. The following points indicate some of the more promising aspects further investigations may follow. (i) Studies of the mechanism of binding in the nematic phase - this would entail calculating values for K and A,,. (ii) The possibility of using the magnitude of the induced shifts in this phase as an independent means of solving the controversy between the mechanism of the induced shift -contact versus pseudocontact. ( i i i ) Geometry determinations based on liquid crystalline data determined in the presence of lanthanide shift reagent may provide important independent proof as to the accuracy of geometry determination resulting from lanthanide shift reagent studies in isotropic solutions. _ The implications of this statement are not yet fully understood. - 108 -In summary, the solid theoretical basis has allowed for a detailed and in most cases quantitative explanation of many of the characteristic behaviours exhibited by lanthanide-substrate interactions. In some areas, as that of solvent effects, more experiments are required before i t will be possible to arrive at any firm conclusions and in this connection X-ray studies of 6, 7 and 8 co-ordinate lanthanide complexes may be useful. G. The Applicability of a Scatchard-type Plot to the Analysis of the  Concentration Dependence of the Shifts It will have been noticed throughout the preceding discussion that we have not discussed numerical values for K when this parameter B is > 100 liter mole 1 (strong binding) as is most often the case when Eu(fod)3 is employed as the shift reagent. We have commented that both our graphical and computer methods were inadequate for K,, values in this region although values for Ag could s t i l l be accurately evaluated (vide infra). In addition to the above recognized limitation of our method of analysis, some contention has originated regarding the use of Eq. [12] with its necessary approximations.^4 It has been suggested that the use of this equation may not always provide an accurate method for the evaluation of K and A,, and that i t is seldom B B a rigorous test for 1:1 complex formation. This objection is based on the assumption that in order to test for 1:1 complex formation, i t is necessary to vary the concentration of a l l interacting reagents over as wide a range as possible and then to solve for the full quadratic form of Eq. [6]. - 109 -The method proposed as a possible solution to the above points is that of a Scatchard plot. This plotting procedure has enjoyed considerable success in areas other than lanthanide-substrate interactions^"* and has sometime ago been the subject of a critical appraisal by Deranleau.^ The following discussion is intended to provide an explanation as to why we chose not to use this method for our data representation. We shall show that although i t is possible in principle, and perhaps experimentally to use the Scatchard plot to obtain a numerical evaluation of K when > 100 liter mole 1 in practice any such evaluation is likely of l i t t l e chemical significance. We will also show that a Benesi-Hildebrand plot is always the best source of A^. It is for that reason that we have left this discussion to the end. Let us start the discussion by reviewing the salient features of the Scatchard plotting method. Deranleau has concluded that, "obtention [sic] of roughly 75% of the data comprising the complete saturation curve seems necessary before the model can be considered proven by any single equilibrium technique". Representation of the resultant data by a Scatchard plot then provides for the most accurate evaluation of K B and solution stoichiometry, n. In addition to the above requirement, it is important to note that Deranleau's treatment had been derived for the situation, (with [S]Q >> [L] ), where [L] and [LS] are the measured quantities, (i.e. measurements are made on the dilute component). However, this is not the situation that would pertain to any lanthanide The following discussion is an evaluation of a Scatchard plot only as i t pertains to the lanthanide-substrate interaction performed according to Method 2 of the Experimental. - 110 -experiments described thus far. In these investigations [S] and [LS] are the measured parameters. The importance of this difference between the two treatments is the basis on which rests the entire following discussion. Representation of our data for the concentration dependence of the shifts (determined in the manner as outlined by Method 2 of the Experimental), in the form of a Scatchard plot corresponds to a plot of 6/(At)-6)[L] versus 6[S] /A^JL] . The slope of this plot is equal B O O B O to -K , the y-intercept = K , and the x-intercept is 1.0. B B Combining Eq. 15] and 16] and making no approximations, one can write the following expression, which is the form required for a Scatchard plot as discussed above, (i.e. when the measured quantities are [S] and [LS]). To the same level of approximation our own Eq. [12] can be expressed as follows; 123] [S] (1 - ~ ) = IL] AB(j) - ((~) + [LI ) •o A„ o B 6 K o It is obvious that either of these methods for data representation requires a knowledge, in advance, of the value for A,,. However this B ' value can seldom be measured experimentally (vide infra). Thus, for A This method imposes the restriction that IS] >> Il]0» thus forcing the systems to behave as a one step binding process. Also the concentration of lanthanide is kept low,. < 0.006 M, which significantly lowers the possibility of dimerization of lanthanide.^"* - I l l -either approach to yield itself to analysis, i t is necessary to impose the restriction that 6 << A.,. Eq. [22] now takes the form proposed D by Deranleau,^ and Eq. [23] becomes Eq. [12]. Interestingly, a Scatchard plot of our data in the form proposed by Deranleau, 6 / [ L ]q versus 5 [ S ] O / [ L ] q (from Eq. [24]) produces a linear dependence only when 6 « A- and yields AT, from the x-intercept and O D -Kg from the slope. However, because we impose the restriction that I S ]q >> l L ]Q and the fact that we are measuring [S] and [LS], the data points on such a plot will always f a l l in the region of the plot * where the errors are a maximum. Thus, A -values determined from B these plots will be extremely imprecise. This is not the case i f experiments are performed according to those discussed by Deranleau (i.e. [L] and [LS] are the measured quantities). For these experiments, the analogous limitation which is concomitant in Deranleau's treatment namely, [S]Q » [L]Q» n o w permits one to obtain data points throughout the entire saturation curve and thus A., can be accurately determined. B This method, however, only applies when 6 « AT. and thus, would not be B applicable for cases of strong binding (i.e. K > 100 liter mole ^ ) . B On the other hand, to the same degree of approximation and for the same data as above, a plot of the form [S ]q versus (1/6) (from Eq. [12]) will yield an accurate value for A . This result is in accord with jthe B For a fu l l error analysis of the plotting routines discussed here, the reader is referred to the paper by Deranleau.76 - 112 -minimum errors for the region of this plot where these same data points f a l l . ^ Additional proof of the accuracy of the value of A„ determined from the slope of this [ S ] Q versus (1/6) was shown in the agreement between A„ and K values determined in this way and those determined from a computer f i t of the f u l l quadratic function (Table 7 ) . From the preceding discussion, i t seems reasonable to conclude that in view of the method in which present lanthanide experiments are performed, a plot of the form [S]q versus (1/6) is most likely the best method for determining Ag, Kg and n, (at least for Kg < 100 liter mole•^). It is also important to note that Scatchard plots, of the form proposed by Deranleau, will not be successful as a means for determining K,, when this parameter is > 100 liter mole \ D There remains only one possible significance to using the Scatchard plotting procedure - to obtain a numerical value for K when this B parameter is > 100 liter mole 1 as is frequently the case only with Eu(fod)0. [When K„ > 100 liter mole \ the y-intercept from a plot J B of [ S ] O versus (1/6) is obviously near zero, thus providing a very poor measure of Kgj the Ag value determined in this way is nevertheless correct as previously discussed.] In these situations, i t is no longer possible to construct a Scatchard plot of the form proposed by Deranleau because the restriction 6 « A,,, implicit in Deranleaufs treatment, will no longer apply. One must therefore construct the exact Scatchard plot from Eq. [ 2 2 ] , To do so, i t is necessary that be known in advance. For the interaction with Eu(fod)3, there are only two possible methods which may be employed to yield, in advance, a value for Ag. They are as follows; (i) from a plot of [S]q versus (1/6) - 113 -where [S] >> [ L ] and (ii) from a plot of 6 versus [ L ] /[Si where o o o o high enough [L ]Q/ [ S ] ratios have been reached such that a constant value of 6 was obtained. Some practical limitations of this latter method will be discussed f i r s t , followed by an example of an exact Scatchard plot using the A „ values determined by both the above methods. Using the Ln(fod)3 complexes, a constant value of § can be obtained in plots of 6 versus [ L ] Q / [ S ] o . However, the large molar ratio of Ln(fod)3 needed to reach this saturation point, particularly for weak donors, may produce large changes in the bulk magnetic susceptibility of the solution, increasing the likelihood of the internal standard binding to [ L ] Q at large concentrations of [ L ] q . In addition, when the concentrations of a l l interacting reagents are varied over the wide range required for Deranleau1s treatment, the greater will be the importance of multi-step equilibria, (e.g. lanthanide dimerization), with the number of unknowns increasing by a factor of two for each additional equilibrium, while the number of observable parameters remains constant. An evaluation of the exact Scatchard plot using A -values determined —*—-—- B by method (ii) will now be discussed. For the interaction of Eu(fod)^ with 3,3-dimethyl-2-butanone in CC1., the value of A determined from 4 B the leveling off of a plot of 6" versus [ L ] Q / [ S ] was 11.0 p.p.m. for the C-4 protons. Using this value to construct the exact Scatchard plot produces the curve as indicated in Fig. 20. The K,, value determined from the y-intercept of this plot would be unrealistic as this plot can not be made to intersect the x-axis at 1.0 as required by Eq. [22]. On - 114 -S [ S ] 0 / A B [ L ] O Figure 20. An exact Scatchard plot (Eq. [22]) for the interaction of 18, (0.02 to 0.1 M) with Eu(fod)3 (ca. 0.008 M) in CCI4 solution. Dotted line represents the plot obtained using a value of = 11.0 p.p.m. (see text). Solid line represents a similar nlot but with AB = 16.12 p.p.m. (see text). Error bars on this plot are approximately those shown in ref. 76. - 115 -the other hand, a similar plot was constructed using the same data * as above, but this time using the value of A,, = 16.12 p.p.m. as determined from a plot of IS] versus (1/6). This plot is also indicated in Fig. 20. The straight line which can now be drawn through the data points, intersects the x-axis at 1.0 as required and yields a value for K - 105 liter mole 1. It would appear therefore, that this B second choice of A„ is somewhat more precise, producing an x-intercept B ** of 1.0 and a numerical value for K . However, in view of the B imprecision in this region of the saturation curve, l i t t l e significance should be applied to this parameter. In conclusion, for the method used to perform the present experi-ments, i t does not appear advantageous to use even the exact Scatchard-type plots for the particular situations where > 100 liter mole 1 and where some estimate of this parameter is desired. From the nature of the plot using A_ = 11.0 p.p.m., Fig. 20, the discrepancies B (possibly of lanthanide dimerization or other multiple equilibria) inherent at high [L] /[S] ratios appear to be significant. Thus, i t would seem that data reduction using Eq. [12] suffices both in ease and accuracy of parameters determined. If for any reason, one wishes to characterize the reactivity at a suitable donor site for a series of 6-values used to construct these Scatchard plots were determined from experiments performed according to Method 2 of the Experimental. ft* In Fig. 20, an indication of the magnitude of the errors, in this region of the plot, has been shown for the data using Ag = 16.12 p.p.m. only. It is important to recall that the necessary restriction [S]Q >> [L]Q will always restrict the data to this region of the plot when the measured quantities are [S] and [LS]. - 116 -related compounds by comparing K -values, then clearly the preferred shift reagent would be EuCdpm)^ where Kg values will most likely always be. < 100 liter mole In principle i t may be possible to extend the range where accurate determinations of K are possible by using a Fourier Transform spectrometer which will enable one to drop the substrate concentration by a factor of up to 100 (while maintaining a very low concentration of lanthanide to exclude possible dimerization), and s t i l l observe the n.m.r. spectrum. - 117 -CHAPTER III DETERMINATION OF MOLECULAR CONFORMATION IN SOLUTION USING LANTHANIDE N.M.R. SHIFT REAGENTS: SIGNIFICANCE OF INTERNAL ROTATION Introduction In the General Introduction, reference was made to the potential use of lanthanide shift reagents for the determination of substrate geometry in solution. This potential use was first realized for the 12 present series of lanthanide shift reagents by Hinckley. It has since provided the motivation for most reported applications of these reagents, including our own. Before discussing our own contribution to this particular aspect of lanthanide shift reagents, i t is appropriate to discuss at somewhat greater lengths the historical sequence of events which has led to the present state of affairs with regards to the applicability of this approach for conformational determinations. In so doing, i t will become apparent that the determination of molecular conformations from experimentally derived bound chemical shifts (A ) or ratios of bound chemical shifts is generally, a highly under-determined problem and becomes tractable only when several preliminary conditions are satisfied. Before continuing on this quantitative approach , i t should - 118 -be stressed that i f the only purpose for using lanthanide shift reagents is to aid in assigning n.m.r. spectra (Chapter I), i t matters l i t t l e what reagents are used or how the experiment is conducted. However, for conformational conclusions, the situation is not as simple as will be shown. The following equation is a repeat of Eq. [4] Chapter I, and is * restated here for convenience. AH ' -32S(S+1) (3cos 2 e.-l) "TF = 45kT 1 x (3g|| + 4g j L)(g | | - g±) r. 1 The stereospecific nature of the Induced shifts and thus the potential use of these shifts to determine absolute substrate geometry is a 2 3 ** direct consequence of the quantity [(3cos 8^ - l ) / r ^ ] ; a l l other terms in the above equation being constant for different protons on the same substrate. * 37 This equation is of the form stated by McConnell, which only quite recently has been restated in a somewhat different form by Bleaney.^3 The significant difference between the two forms is that the new theory accounts for the shifts in solution from the anisotropy in the susceptibility rather than ascribing the pseudocontact shifts to anisotropic ' g' factors. In terms of practical applications, both expressions contain the same quantity relating the induced shift to substrate geometry. For this reason, I will not restate the equation as proposed by Bleaney. Differences do occur however, in the predicted temperature dependence between the two equations. Thus, in any temperature studies, i t will be necessary to adopt this new expression. ** r^ is the separation between the unpaired electron and the resonating nucleus and 0^ is the angle between this distance vector and the principle magnetic axis of the complex. - 119 -In writing the above equation, we have already made ore very important approximation - specifically that the complex has axial (n-fold, n > 3) symmetry (see Discussion). For a complex with C^v or symmetry, the quantity relating the magnitude of the induced shift to substrate geometry is so complex as to make its use, we feel, technically impractical. This in no way justifies using the rather firmly adopted equation as stated above but, as will become apparent at the end of this discussion, for this technique to have any use at a l l , i t is necessary to compromise between rigor and practical utility at this and other stages of the analysis. The reader may find this approach totally unacceptable. Nonetheless, even the most elementary analyses (vide infra) have already produced chemically significant information. Quite simply, the optimal procedure is dictated by the information desired and excellent fits have been obtained using only the 2 3 quantity [ (3cos 0^ - l)/r J . Crystal structures have now been reported for a number of lanthanide n.m.r. shift reagents^ including both the seven and eight co-ordinate 55 78 complex with the most frequently used shift reagent - Eu(dpm).j. ' None were found to even approximate axial (n > 2) symmetry. This result would seem to distract significantly from the credibility of using just 2 3 the quantity [(3cos 8 ^ - l)/r^] as the geometry factor. However, in view of some of the excellent results obtained using only the above * The general equation for gx f g^ ^ gz can undoubtedly be solved, but in addition to the unknowns r. and 6., one would need to know the i l above three 'g'-values and an additional angle. - 120 -i 22b 79 quantity, particularly R.J.P. Williams' work with mononucleotides, ' it is conceivable that the above X-ray results may not apply to the complexes in solution. Some justification for this 'belief on our own part stems from the fact that the steric-directing effect of the f orbitals is negligible when compared to that of the d orbitals. As a consequence, according to Moeller, "neither the co-ordination sphere of the cation nor the geometry of the complex can be readily predicted in solution. Since the bonding forces involving the lanthanide cations are primarily electrostatic, solvent forces play an important role in determining co-ordination geometry. Thus, only rarely can i t be assumed that the molecular structure found in a crystal'will be the same in a 80 solution of the substance in question." So far, discussion has been,limited, perhaps somewhat prematurely, to the equation for the pseudocontact mechanism as being the one solely responsible for the observed induced shifts. In the General Introduction, it was argued that a paramagnetic complex may contribute to the induced chemical shift by two distinct mechanisms - contact and pseudocontact. In many instances, i t has been assumed that a l l perturbations of proton resonances were attributable to the pseudocontact mechanism. Such an assumption stems from the fact that it is difficult to envisage a direct experiment which would permit an unequivocal determination between these two mechanisms in a l l situations. In Chapter I, the results * This assumption has been based on the fact that the 4f electron shell is well screened. Therefore, there is l i t t l e likelihood of overlap between the unpaired electron density on the lanthanide and the ligand electrons such as would be required for the 'through bond' contact mechanism. - 121 -from an experiment with GdCdpm)^, implied the absence of a contact contribution to the induced shift. Another approach to this problem has been to compare the experimentally induced chemical shifts (or shift ratios) with those calculated on the basis of a pseudocontact /rj] - foi 34a,41-43 2 3 interaction - [(3cos 6^ - l)/r^] - for a rigid substrate whose geometry is already well established Interpretation of the pseudocontact model for n.m.r. shift reagents by comparing the experimentally observed induced chemical shifts with those calculated for the lanthanide-substrate complex 2 3 using the quantity I(3cos 9^ - l ) / r ^ ] , is the basis of existing conformational studies. This technique is usually performed in the following manner. One guesses the most likely configuration for the substrate (preferably of rigid stereochemistry) and then uses this configuration to compute the expected ratios for a l l pairs of ** protons and for many different orientations of the lanthanide metal. For each orientation of the lanthanide complex, a l l calculated A_ ratios are compared with experimental ratios and the agreement is noted. If no agreement is found for a l l reasonable orientations of the lanthanide complex, then this whole process is repeated for a number of possible substrate configurations and the correct configuration is taken to be the one which gives the best agreement between calculated * 1 No induced H chemical shifts were observed for neo-pentanol interacting with Gd(dpm)3 where a contact shift, i f present in any of the lanthanide complexes, would be most likely. ** A typical starting point for positioning of the lanthanide metal in this regression is that of least steric hinderance with Ln-donor bond distances and angles from related X-ray studies. - 122 -and observed AT, ratios. The success (and ease) of such an approach is dependent on the analytical methods used to treat the experimental data. As a result, it is not surprising that there have been many attempts to correlate the induced shifts with those calculated, only —3 *38 with the distance variable (r^ ), assuming a constant angle term. Such an unwarranted neglect of the angular dependence can never be 41 42 justified as we will show. Many of the recent applications ' have used a computer to calculate the entire quantity \(3cos^Q . - l)/r^] and have, for rigid substrates with known conformations, achieved notable success over the conventional method of measuring angles and distances from a Dreiding model. The excellent correlations from a number of these studies have served to further confirm the predominance of the pseudocontact mechanism at least for protons. These results also substantiate results from similar investigations on substrates of unknown conformation. However, in spite of the apparent success achieved while employing the above technique, inconsistencies have developed and often without justification, these inconsistencies are attributed 39 40 to the existence of a contact contribution to the induced shifts. ' We have even further optimized this existing procedure in such a way that accurate determinations of substrate-lanthanide complex (and thus substrate) conformation are possible without the necessity of incorporating a contact contribution. Our approach to the use of lanthanide shift reagents to obtain In order to correct for the inconsistencies which originated, other orders of the distance variable were tried (from r.1*^ to r 3^38c,e,81 I l For C-13, Cushley and Willcott have both observed a contact contribu-tion to the induced s h i f t .3^ f ,5 6 - 123 -molecular geometry from the pseudocontact type contribution to the induced chemical shifts has as its basis the following two distinct aspects: (i) Experimental determination of reliable values for the bound chemical shifts, A for each proton involved; (ii) Proper 2 3 use of the [(3cos 9^ - l)/r^] dependence in (see Theory). When, as in the present instance, the ultimate goal is molecular conformation, the experiment should be designed to yield A_ and * stoichiometry while suppressing the complication of intermediate steps in formation of the complex. Such was the reason and justification behind the detailed theoretical treatment presented and tested in Chapter II, which provides a simple and direct way to obtain accurate A -values, stoichiometry, n, and binding constant, K , for the substrate-Is ii shift reagent complex. All previous determinations of molecular geometry using the lanthanide shift reagents (from the angle- and distance-dependence of bound chemical shifts, A D ) , have treated the substrate-shift reagent D complex as rigid. However, if there is appreciable flexibility at the site of attachment to the lanthanide or elsewhere in the complex (certainly a possibility i f there are minimal intramolecular steric interactions at the point of attachment), then the substrate is permitted to sample many orientations during its residence on the shift reagent. In these circumstances, i t is necessary to first average over a l l available The importance of knowing the stoichiometry is related to the previous discussion regarding the symmetry of the complex in solution. It suffices to point out that i t may be reasonable to assume effective axial symmetry only for a 1:1 complex. Aft For particular examples of this see references 34a, 41, 42 and 43. - 124 -conformations before comparing observed and calculated A^'s or ratios of A 's as will be shown in the Theory which follows. For the time being, this condition can be stated quite explicitly as follows: <[(3cos2ei - D/rJ]> ± [ O c o s2^ ^ - l)/<r >3], where <> indicates a weighted average over a l l possible configurations, A variety of new models for free or hindered internal rotation are proposed and tested on three organic substrates which are rigid except perhaps at the point of attachment to the lanthanide. Moreover, examples are provided which show that "good" fits between observed and calculated shift ratios are not in themselves proof for the predominance of that conformation. However, the use of several models for internal rotation, interpreted by means of contour plots of " f i t s " as a function of geometry of the complex, can provide a means for sorting out the correct from the spurious calculated conformations. In addition, a rather unique experiment, unique in the sense that no geometry was chosen for the substrate in advance, will be discussed. While present treatments were successful in arriving at well-defined and chemically reasonable substrate conformations, the inter-pretation rests on the fulfilment of a number of requirements (some of which have already been discussed), which will be stated below. - 125 -Theory As stated previously the determination of molecular conformation from experimentally derived bound chemical shifts (Ag) is a highly under-determined problem. The analysis becomes tractable only when 82 83 several preliminary requirements are satisfied. ' (1) The A_-values themselves are obtained in the most direct and reliable way (Chapter II). (2) Ag is wholly pseudocontact in origin, as seems to be the 13 case for proton shifts induced by Eu or Pr shift reagents. This 13 assumption does not appear to be valid for C shifts from either of these shift reagents. Yb(dpm)3 has been found to give the least amount 13 56 of contact contribution in C shifts, <5%. (3) The geometry of the substrate bound in the complex is the same as tfiat of free substrate in solution. (4) Only a single stoichiometric species exists in solution in equilibrium with uncomplexed substrate. (5) Only a single geometric isomer of this complex species is present. (6) The substrate ligand exists in a single conformation or an appropriate averaging over internal motions is carried out. (7) The effective electronic g-tensor is axially symmetric, with principal magnetic axis along the Eu-donor atom bond. Without this assumption,the problem is too under-determined to solve. Determination of stoichiometry for the complex thus becomes important, since the g-tensor principle axis will most easily be located in a 1:1 adduct. Since the g-tensor in the solid can deviate markedly from axial symmetry, - 126 -we require sufficient internal rotational motion about the Eu-donor atom bond to ensure effectively axial symmetry for the complex in solution. This motion need merely be fast compared to AD, which seems highly likely in view of the rather long Eu-donor bond distances observed by X-ray diffraction. 84 Realizing the importance of this latter requirement, Roberts has recently proposed a method of analysis which does not assume in advance that the Eu-donor atom bond of the complex is collinear with the principal magnetic axis. This treatment requires that the induced shifts be compared with those calculated using 2 angles and 1 distance to define the position of the metal atom, (vide infra) and an additional two angles to define the orientation of the magnetic axis, a total of 5 unknown geometric parameters. His results are significant in that they confirm the assumption that the principal magnetic axis of alcohol-lanthanide complexes are essentially collinear with the Ln-donor atom bond. The validity of this result i s , however, questionable for the following reasons: (i) their treatment rests on the assumption that the complex is rigid at the point of attachment to the lanthanide (vide infra), (ii) i f the complex does not possess axial symmetry, then is proportional to 2 3 2 3 [ (3cos 9^ - l)/r J + [sin 8^ cos2$_^/rJ and must be evaluated as such. * For non-axial magnetic symmetry, the induced shift is of the form, 2 3 2 3 A_ = const[3cos 9. - l)/r.] + const'[sin 9 . cos2<!>. /r. ] B l iJ i i i For fast internal rotation, averaging of cos2$ over 2TT makes the second term go to zero, leaving the desired Eq. [4], Chapter I. - 127 -In addition to the above requirements, i t has been suggested that: "(i) A variety of lanthanide shift reagents must be employed in each study and the ratio of shifts at different proton sites then compared for the different lanthanides. If these ratios are independent of the lanthanide cation then the shifts have their origin in dipolar coupling (pseudocontact) and, (ii) the observed shifts must be corrected by , observing shifts due to complex formation with diamagnetic lanthanides, 3+ 3+ La and Lu ." In Chapters I and II we have presented the results for studies using a variety of lanthanide shift reagents and these results alone indicate that at least as far as proton shifts are concerned, complexes, either (dpm)^ or (fod)^, with Eu(III) are the most appropriate for conformational investigations. With regards to the second point, the experiments discussed in this text are a l l performed in the region ISJ » [L] with the maximum concentration of IL] ca. = 0.006 M. o o o — At these low lanthanide concentrations,- the Internal standard is satisfactory in correcting for bulk susceptibility effects and there is no need to make use of corrections possible by using diamagnetic lanthanides. With these requirements, Fig. 21A defines the starting point for determination of molecular geometry. This right-handed co-ordinate system has been designed to facilitate computer fits of shift data. The donor atom (atom //l). defines the origin; proceeding from atom #1 to #2 defines the positive x-direction; atom #3 is then assigned a positive y-value in the x-y plane. Q, (j) and R unambiguously fix the position of the lanthanide atom relative to the molecular frame. Since the molecules of present interest are rigid except at the Figure 21A. Co-ordinate system for substrate-shift reagent complex. R is the lanthanide-donor atom bond direction vector; |R'| = |R|sin£2. Origin is at donor atom 1, proceeding to atom 2 then defines the positive x-axis; atom 3 is then assigned a positive y-value in the x-y plane; z-direction then follows from right-hand convention. Q, <f> and R unambiguously define the position of the lanthanide relative to the substrate molecular frame. - 129 -point of attachment to the lanthanide, a "determination" of the conforma-tion of the complex consists of finding the "best" values of R, 0, and (J) (if a unique <j> exists), given the conformation of the substrate molecule its e l f . Appendix A gives a rapid method for obtaining the desired parameters, r^ and 8^ for the i'th proton, from (guessed) values of the Eu-donor atom bond distance, R, the polar (fj) and azimuthal (cfj) angles which locate the Eu-donor bond axis relative to the molecular frame, and the co-ordinates of a l l atoms in the substrate, (Fig. 21B). Assuming a perfectly rigid complex, one could proceed as follows. First put into the geometry program the cartesian co-ordinates for the * protons of the substrate molecule as well as the corresponding shift ratios, then estimate a starting location for the lanthanide atom 2 3 (i.e., choose values for R, and cj) ) and compute [ (3cos 8^ - l)/r^] for each proton of the substrate; then calculate the normalized variance (the "R-value")^"'" between ratios of this quantity and observed * * * shift ratios for a l l possible independent pairs of protons. / AH1 AH1 2 nrrj — , where W. is a weight 1N2 3 . i AH. obs factor. 3Tl j 2 A modified version of the computer program COORD which is listed in Appendix B was used to calculate cartesian co-ordinates for a l l atoms in the substrate. Input data to COORD were bond lengths, bond angles and dihedral angles taken from X-ray studies of related compounds. The computer programs used to perform these geometry calculations are listed in Appendix C and D. An "R-value" of 0.04 or less for the present calculations corresponds to agreement well within experimental error for each of the experimental "bound" shift ratios. - 130 -A z Figure 21B. Co-ordinate system for substrate-shift reagent complex, r. is the distance vector from the lanthanide atom to the i'th proton of the substrate;' 8^ is the angle between R and r^. Internal rotation of R about the x-axis consists of permitting a range of <j>-values, shown as the circle in the figure. - 131 -Repeat the procedure many times for different values of R, and <$> then choose the most probable conformation as that which gives the best " f i t " (smallest normalized variance, smallest "R-value") to the observed shift ratios. The difficulty with this treatment is that i t is quite possible to obtain correct shift ratios from incorrect absolute shifts, so that sometimes the best " f i t s " are obtained at chemically unreasonable values of R and R (see Results). The source of the difficulty lies in attempting to f i t the observed shifts to those computed for individual conformations - this procedure will at best Indicate the average values of <r > and <0.>. i i However, the observed quantity is AR 3cos29.- 1 [1] Ag a< ^ > 4 ri where the brackets denote an average over all possible bound conformations during the residence of a substrate at a shift reagent. Whenever rapid internal rotations are present, i t is necessary to average the 2 3 entire quantity, [(3cos 0^ - l)/r^] on account of the inequality just written, before comparing observed and calculated shift ratios, and any analysis based on a best single conformation should not be expected to succeed. The three simplest models for internal rotation are free rotation, no rotation, and jumps between the minima of an n-fold potential. Fig. 22 may be used to visualize what is meant by these three models. The remainder of this discussion concerns application of these three models to the internal motions in selected molecules 2 3cos <9.> I <r .> x 1 27T - 132 -Free rotation Eq.C 2 ] Triple Gaussian (A= 2 ) Eq. C 4 ] Figure 22. A diagrammatic illustration of the weight distribution as a function of <f> for three simple models of internal rotation. - 133 -which are expected to f a l l into these categories. Free rotation about the atom #1 - atom #2 axis is readily 2 3 simulated by multiplying the quantity [ (3cos 6^ - l)/r^] by a normalized unit weight factor. 12] P(<j>)d<f> = (l/2TT)d(j), followed by integration over a l l <(> from 0 to 2TT, where this operation is carried out before comparing observed with calculated shift ratios. The same procedure may be used for the opposite limit of a rigidly  locked complex by use of the weight factor, I3J P(4>)d<|).--- 6((j) - (j>o)d(j> , where <j> is the (fixed) azimuthal angle in the Dirac 6-function. Since no real molecule will be perfectly rigid, i t is desirable to relax the distribution, 13] , to span some specified angular range in <j) in the vicinity of $ - we have for convenience chosen a Gaussian weight factor. [4] P(4))dcf) = (A//u) exp[-A2(<}) - <j>o)2]dc{> . In Eq. 14], a large value of A corresponds to a narrow distribution of 1/2 possible angles; the values of A = (8) or A = 1 in the next section correspond to rms widths of about 14° or 40° about 4>q, respectively. _ The normalization implied in Eq. [4] corresponds to an infinite domain in <J>, whereas the physical domain of integration is only from cp = <p — I T to <f>0 + ir. Thus it Is correct to compute induced shift ratios for any given A, but one should not compare absolute shifts computed from different choices for A. - 134 -Finally, the possibility of rapid random jumps between n equally likely values of <j> may be simulated by use of the periodic weight function, [5] P(<f>)d<j> = (l/TT)cos2I(n/2)((J) - y)]d<fr, where y is the <j)-distance between $ = 0 and the nearest potential minimum in (j,. Random jumps may also be simulated by 5-function distributions, [6] P(<J>)d<J> = a6(<|» - <J> ) + b6((j) - <|) ) + . ..+f6(4> - <f> )d<J> , where a,b,...,f represent the probability of finding the complex with $-value <f)^ , fy^t •••> $ t respectively. Numerical integration (when necessary) was carried out by low-order Gauss-Legendre quadrature (i.e., 6, 8, or 10 point) and in most cases checked against higher order formulas to verify its validity. The Appendix contains a complete listing of the computer programs used in the analysis of complex conformation according to the above models. Only the programs for completely free rotation and that for a rigidly locked complex are listed. The programs used with a Gaussian weight factor are similar to that for free rotation,requiring only a change in weight function from Eq. [4]. - 135 -Results and Discussion Determinations of molecular geometry from chemical shift ratios appear to be best illustrated by contour plots of the type shown in Figs. 23-28. The contours are simply paths of constant normalized variance ("R-value", agreement factor) between observed and calculated shift ratios, as a function of possible positions of the lanthanide-donor atom distance (R) , the angle (£2) between the europium-donor bond and the bond between atom #2 and the donor atom, and the azimuthal angle (<J>) shown in Fig. 21A. A small normalized variance (< 0.04) thus indicates very good agreement between observed and calculated shift ratios. The first substrate considered was the monofunctional donor, l,2:5,6-di-0_-isopropylidene-a-D-glucofuranose 1. Me. O — C H 2 M e ' i D Me * Only those protons directly bonded to the rigid furanose ring were Rigid in the sense that the lsopropylldene ring substituent prevents the furanose ring from adopting a l l but a few possible conformers in the pseudorotation cycle. For the purpose of this present study, a single rigid conformer has been assumed. - 136 -used to derive the complex geometry. The co-ordinates for these protons can be accurately defined whereas use of the other protons would necessitate a much more detailed analysis which allowed for internal rotation within the substrate itself. This particular molecule was chosen to represent the model where there was unlikely to be any rotation about the C^-donor atom bond as a result of the intramolecular steric hinderance. This was only an intuitive assumption based on visual inspection of a Dreiding model of JL and will be tested by comparing the results from a l l three models for internal rotation. Table 13 lists the values of the shift ratios which were used to determine the geometry of the furanose ring. These ratios are calculated from the appropriate A -values listed in Table 12, Chapter II. The stoichiometry for this complex can be accurately determined to be 1:1. Several attempts were made to f i t the observed shift ratios to those calculated, with the assumption that there was no internal rotation about the C^-donor atom bond, for several reasonable conformations of the furanose ring. All conformations tested had bond lengths and bond angles in accord with X-ray and neutron diffraction data for related 86 furanose ring systems. A number of different values for the dihedral angles, which were estimated from X-ray data and n.m.r. coupling constant data, were tested (e.g. the near zero coupling for H-2, H-3 is indicative (Karplus) of a H C C H dihedral angle near 90°). - 137 -Table 13. Induced chemical shift ratios for association of four substrates with lanthanide n.m.r. shift reagents. Substrate A -ratios J3 Shift Reagent Solvent Aniline, 16 o/m=4.79 o/p=4.00 Eu(dpm)3 CDC13 Pyridine, 17 o/m=3.05 o/p=3.22 Eu(dpm)3 CDC13 1,2:5,6-di-O-isopropyl'-. H-3/H-2=2. 59 idene-a-D-glucofuranose, . ~ lc H-3/H-1-3.52 H-3/H-4=1.82 Eu(dpm)3 CDC13 5-hydroxy-l,2,3,4,7,7- H-5/H-6(exo)=1.40 hexachloronorborn-2-ene, lib H-5/H-6(endo)=2.90 Eu(fod). CC1, Shift ratios were determined from bound chemical shifts which were obtained from plots of [S]c versus (1/6), as explained in Chapter II. For 16, 17, and 1, binding was unequivocally shown to be 1:1. For binding of 11_ to Eu(fod)3, the binding was too strong to measure, and the listed shift ratios correspond to the induced shifts for an [L]0/[S] ratio of 0.3. The shift ratios for 11 are in good agreement with those in ref. 44 for the unsubstituted alcohol. The H-5 proton was not used in the analysis because of the possibility of internal rotation about the C-4 - C-5 bond which would complicate the analysis. - 138 -The conformation which finally allowed for a successful geometric f i t to be obtained has bond lengths, bond angles, and dihedral angles as shown in Table 14. This conformation is signified as from the pseudo-3 rotation cycle and differs only very slightly from the conformer arrived at from high resolution n.m.r. studies. It should be emphasized that, although a l l likely conformations were investigated, this method does not test whether the conformation used is the best possible one, only that this conformation is preferred over other proposed conformations. The data in Table 14 are then input to the program COORD which produces a set of cartesian co-ordinates for the atoms shown with oxygen at the origin. These cartesian co-ordinates for the protons, H-l, H-2, H-3 and H-4 as well as the corresponding shift ratios (Table 13) are then put into the appropriate geometry program. Fig. 23A,B shows the contours which are obtained, under the assumption that there is no internal rotation about the carbon-donor bond. Two features are evident. First, for some choices of <f>, there are no "good" fits (i.e. having normalized variance, R, smaller than 0.04). Second, among the range of ^-values for which good fits are obtained, some <f>-values lead to unreasonably short europium-oxygen bond distances. Based on these results, i f JL is rigid with respect to internal rotation about the carbon-donor bond, then the most o likely position of the europium is R = 2.2 A, Q = 1 1 4°, and <f> = 1 1 6°. It is significant that these parameters appear to correspond with an The numbering scheme here is as shown on the structure, i t is not numbered in the conventional manner. For the purpose of these geometry calculations, atom #1 is always the donor atom. - 139 -Table 14. Bond, distances, bond angles and dihedral angles used to calculate a set of cartesian co-ordinates from COORD for 1,2:5,6-di-O-isopropylidene-a-D-glucofuranose. Numbering scheme is as shown below with atom #1, the oxygen of the hydroxyl group. 1-2 Bond Distance = 1.40 A; 2-3 Bond Distance = 1.523 A; 123 Bond Angle = 115.7°. Atoms Bond Distances(A) Bond Angle(deg.) Dihedral Angle (deg.) A B C D CD BCD ABCD 12 3 4 2 3 4 5 3 4 5 6 12 3 8 3 4 5 9 4 5 6 10 5 6 2 7 1.450 1.427 1.523 1.083 1.083 1.083 1.083 105.8 109.3 105.8 109.0 109.0 109.0 109.0 105.0 15.0 345.0 210.0 225.0 240.0 150.0 Dihedral angle of CD relative to AB, measured clockwise along the direction B to C. - 140 -~1 I 1 1 1 1 1 1 1— 1.84 2.00 2.16 2.32 2.48 R(&) "1 1 1 1 1 I 1 1 1 1 1 1.84 2.00 2.16 2.32 2.48 R(&) ure 23A. Contours of normalized variance ("R-value" agreement factor) between observed and calculated induced chemical shift ratios as a function of possible positions of the lanthanide atom relative to the donor atom of the substrate for jL. It has been assumed that there is no internal rotation about the bond from carbon to donor oxygen. - 141 -ure 23B. Contours of normalized variance ("R-value" agreement factor) between observed and calculated induced chemical shift ratios as a function of possible positions of the lanfhanide atom relative to the donor atom of the substrate for 1_, It has been assumed that there is no internal rotation about the bond from carbon to donor oxygen. - 142 -orientation of Eu(dpm)^:1 which has the metal in a sterically favourable position. The position of the metal is also in accord with the observed shift for H-5 being greater than H-3. Fig. 24A,B shows the effect of varying degrees of internal motion on the agreement between observed and calculated ratios for 1^. Beginning (as in Fig. 23) with a static molecular frame, we now allow for a Gaussian distribution of (((-values, centered at the most likely (f>-value of 116° , with a root-mean-square width of either 14° ("narrow Gaussian" in Fig. 24A) or 40° ("wide Gaussian" in Fig. 24B). It is clear that this greater latitude in internal rotational position produces less reasonable f i t s , with respect both to agreement with experiment (normalized variance) and also intuition (too-short values for Eu-0 bond distance). In fact, the contour plot for the assumption of completely free internal rotation about the carbon-donor bond (Fig. 24B) shows that free rotation is simply not possible in this complex. Thus we have demonstrated that the l:Eu(dpm)3 complex is relatively rigid and thus the geometry of the complex may be determined with confidence. The above model (that of a rigid complex) can hardly be expected to hold for a substrate such as aniline, 3-6_, where there should be l i t t l e preference for the shift reagent to be rigidly attached at any one value of (j>. This presumption is reasonable in view of the rather large bond distance for europium-nitrogen bonds. X-ray determinations o of this distance put i t in the range of ca. 2.65 A. Table 13 lists the values of the shift ratios which were used to - 143 -gure 24A. Contours of normalized variance as a function of lanthanide position for 1. For the "static plot", there is no internal rotation about the carbon-donor bond. For the "narrow Gaussian"., <j>-values are first weighted by the factor, (A/ /rr) exp I-A2 Q) 2] d<f>, and then integrated over al l $ (with A = /W) b efore comparing observed with calculated shift ratios (see Theory). - 144 -R(S) Figure 24B. Contours of normalized variance as a function of lanthanide ' position for 3^. For the "wide Gaussian", ^-values are first weighted by the factor, (A/Vrr) exp[-A2(<)>-<)>0)2]d<f>, and then integrated over a l l <f> (with A = 1) before comparing observed with calculated shift ratios (see Theory). For the "free rotation" plot, <}>-values are averaged over a l l <fi from 0 to 2TT using unit weight factor. - 145 -determine the geometry of the 16:Eu(dpm)3 complex. These ratios are calculated from the appropriate Ag-values listed in Table 8, Chapter I I . The stoichiometry for this complex can be accurately determined to be 1:1. Table 15 lists the bond lengths, bond angles, and dihedral angles which are in accord with X-ray and microwave data for related compounds and which wereused as input to COOPJ) to calculate a set of cartesian co-ordinates for 16. The cartesian co-ordinates and the observed shift ratios for the o, m and p protons were then put into the appropriate geometry program. Fig. 25 shows the contours which were obtained for this substrate, 16, under the assumption of completely free internal rotation about the o C-N bond; "good" fits were obtained. The value of 2.55 A for the Eu-N bond distance (R) and 111.0° for the Eu-N-C bond angle (Q) computed in o this way compares favourably to typical X-ray values of about 2.65 A for R. This "good" f i t obtained under the assumption of free internal rotation will now be compared to the fits obtained when other models for internal motion for aniline were examined. The results for these other models are shown in Fig. 26 and are a particularly incisive illustration of the danger of literal interpreta-tion of shift reagent results. As for the case of free internal rotation discussed above, three protons (o, m and p) formed the basis for the calculation^ but now under the assumption that there was no internal rotation about the C-N bond. Excellent fits were obtained in - 146 -Table 15. Bond distances, bond angles and dihedral angles used to calculate a set of cartesian co-ordinates from COORD for aniline. Numbering scheme is as shown below with atom ill, the N donor atom. 1 0 — 5 \ // » \ 6 / / \ / / • N 1\ 11 12 1-2 Bond Distance = 1.37 A; 2-3 Bond Distance = 1.40 A; 123 Bond Angle = 123.0°. Atoms 0 Bond Distance(A) Bond Angle(deg.) * Dihedral Angle (deg.) A B C D CD BCD ABCD 1 2 3 4 1.40 125.0 180.0 2 3 4 5 1.39 119.0 0.0 3 4 5 6 1.39 117.0 0.0 4 5 6 7 1.39 125.0 0.0 7 2 3 8 1.07 120.0 180.0 2 3 4 9 1.07 120.0 180.0 3 4 5 10 1.07 122.0 180.0 4 5 6 11 1.07 120.0 180.0 5 6 7 12 1.07 120.0 180.0 Dihedral angle of CD relative to AB, measured clockwise along the direction B to C. - 147 -Figure 25. Contours of normalized variance as a function of lanthanide position for aniline. Internal rotation about the C-N bond is assumed to be completely free (unhindered). "D N S 132.0 124.0 I I6 .0 -S T A T I C ^ = 6 6 - 148 -T 1 1 Ii 1——1 1 1 1 1— 2 . 0 2 . 4 2.8 3 . 2 3 .6 R ( A ) 1 1 1 1 1 — 1 1 1 1 r 2.0 2 .4 2 .8 3 . 2 3 .6 R ( & ) 0) *—^  Figure 26. 1 2 4 . 0 -1 1 6 . 0 -1 0 8 . 0 f 3 0 \ .20 J U M P S cp = 0° , I8O0 1 2.0 T T 3.2 3.6 2 .4 2 .8 R ( & ) Contours of normalized variance as a function of lanthanide position for aniline. Top: fits based on experimental shifts for o, m and p protons, assuming no internal rotation about the C-N bond. Middle: fits based on experimental shifts for o, m and p protons assuming no internal rotation about the C-N bond. Bottom: fits based on experimental shifts for o, m and p protons, assuming rapid jumps between fixed <j>-values of 0° and 180°. - 149 -the vicinity of 4> = 6 6° , and the f i t at <J> = 90° was very poor. This o leads to the conclusion that the complex is rigid, with R = 2.55 A, £1 = 12 4°, and (}) = 6 6° . The problem with this conclusion is that the experiment shows a single resonance for both o and m protons on opposite sides of the aromatic ring! Thus, the symmetry of aniline must be maintained in the complexed state. Here then is a case where the agreement with experimental shift ratios for three protons is excellent, the Eu-N bond distance which results is reasonable, but the "determined" geometry is wrong. Since the "static" f i t s at <j) = 90° were poor, apart from free rotation, the remaining possibility, which is chemically unreasonable (vide infra), is that of random jumps between (J)-values of 0° and 180°; the contours from this model are shown as the bottom plot of Fig. 26. The " f i t " for this "jump" model o is very sharply-defined, with R = 2.75 A, fi = 115°. These "good" fits obtained for random jumps between <}>-values of 0° and 18 0°, although in agreement with experimental shift ratios, are unreasonable from a point of view of steric hindrance which would be a maximum in this position. Thus in conclusion, only the free rotation model produces chemically meaningful results for the aniline:Eu(dpm) complex. So far a distinct chemically meaningful f i t has been obtained after treating each molecule with several possible models for internal ft When a l l five protons were included in a static model at the (only possible) <J)-value of 9 0° , a contour plot identical to that in the middle graph of Fig. 26 was obtained, with even poorer agreement (higher "R-value" contours). - 150 -rotation. This situation is considerably altered for the binding of 5-hydroxy-l,2,3,4,7,7-hexachloronorborn-2-ene, 11, to a lanthanide shift reagent. This compound was particularly suitable for geometry determinations of the sort described here because of its rigid stereochemistry and because the chemical shifts of the individual protons were well separated i n i t i a l l y , thus permitting very accurate measurement of the changes which occurred with added lanthanide. In addition, related compounds (borneol and isoborneol) had previously been used as 34a 41 model compounds to study complex geometry by several other groups, ' none of which had made any allowance for internal rotation about the carbon-donor atom bond. It is not possible to predict in advance what model for internal rotation is applicable to the complex, nevertheless, it is improbable that the lanthanide will be rigidly attached. Table 13 lists the values of the shift ratios which were used to determine the geometry of this Eu(dpm)_:ll complex. The binding - 151 -constant for this complex was too large to be measured and thus the stoichiometry can only be assumed 1:1. Table 16 lists the bond lengths,bond angles and dihedral angles which were used as input to COORD to generate a set of cartesian co-ordinates which were * subsequently used in the geometry program. Fig. 27 shows the contours which were obtained for this substrate, 11, under the assumption of completely free internal rotation about the C-0 bond, "pood" fits (perhaps not quite as well defined as that o for aniline, free rotation) were obtained, but at a value of 2.9 A for the Eu-0 bond distance which is quite large in comparison with the 0 55 X-ray range of 2.3-2.4 A. This result would seem to indicate the need to examine other models for internal motion in this substrate. Fig. 28 illustrates some of the other models considered and some of the difficulties which may be encountered. The top plot gives the contours for a (j>-value giving an excellent "static" f i t at <J) = 23 6°, Q = 112° o and R = 2.65 A. This " f i t " is reasonable except perhaps in view of the rather long Eu-0 bond distance and consequently other models for internal motion were investigated. The middle plot of Fig. 28 shows that the above f i t can be made to give even better agreement with experiment, i f a Gaussian weight factor is applied to the (|)-values, with the Gaussian s t i l l centered at (J) = 236° with 14° rms width. However, the very best fits (smallest normalized variance) were obtained in the bottom plot, Fig. 28, which is a Gaussian distribution in cj) centered at (J) = 248° with rms width of 1 4° . The embarrassing feature of this plot is the very wide range in values of R and 9, over which * Only the ethane fragment need be defined for this chlorinated bicycloheptenol. - 152 -Table 16. Bond distances, bond angles and dihedral angles used to calculate a set of cartesian co-ordinates from COORD for 5-hydroxy-l,2,3,4,7,7-hexachloronorborn-2-ene. Numbering scheme for portion analyzed is as shown below with atom #1, the oxygen of the hydroxyl group. 1-2.Bond Distance = 1.43 A; 2-3 Bond Distance = 1.54 A; 123 Bond Angle = 108.9°. _ -Atoms Bond Distance(A) Bond Angle(deg.) Dihedral Angle (deg.) A B C D CD BCD ABCD 12 3 5 1.107 108.9 120.0 12 3 6 1.107 108.9 0.0 6 3 2 4 1.107 108.9 240.0 Dihedral angle of CD relative to AB, measured clockwise along the direction B to C. - 153 -~ T 1 1 1 1 1 1 1 — : — I 2 . 5 6 2 . 7 2 2 . 8 8 3 . 0 4 3 . 2 0 R(A> Figure 27. Contours of normalized variance as a function of lanthanide position for 11. Internal rotation about the C-0 bond is assumed to be completely free (unhindered). - 154 -2 . 2 2 . 4 2 . 6 2 . 8 3 . 0 R ( & ) G A U S S I A N eft = 2 3 6 ° 2 . 2 2 . 4 2 . 6 2 . 8 3 . 0 R ( A ) Figure 28. Contours of normalized variance as a function of lanthanide position for _11. Top: no internal rotation about C-0 bond. Middle: Gaussian distribution in <fi, (A/A") exp [-A2 ((*>-<*)0) 2]dcf) with A = 1, centered at <j> = 236°. Bottom: Gaussian of the same width, but centered at <j>0 = 248°. - 155 -equally good fits could be obtained; so that virtually no information about R and can be derived from the experiment. For substrate 11, the bound conformation probably exhibits some internal rotation, with the Eu more often opposed than adjacent to the apical chlorines. This result would seem to have quite a severe consequence on the results reported elsewhere for related compounds where a claim to a single unique static f i t has been made. The.results for the substituted bicycloheptenol, JA, provide one final point of interest. Although the method of fitting shift ratios from the best number of individual conformations is not determinative as to Eu-0 distance or even Eu-O-C angle, there is a dependence on <J> (see Fig. 28) which shows for the present compound a definite minimum at ca. 2 5 0°, the orientation expected for the exo-hydroxyl position on the grounds of minimal intramolecular steric interaction. In confirmation of this claim, comparison of shift ratios for _11 with 44 those for the exo- and endo-bicycloheptanol shows that the shift ratios for _11 match nicely with those for exo-bicycloheptanol, but do not match the rather different values for endo-bicycloheptanol. This assignment of configuration at C-2 (numbering scheme as shown in Table 16) could not have been made on the basis of coupling constant data. For the analysis of complex conformation in the systems discussed up to now, i t has been necessary to first define a particular (most reasonable) configuration of the substrate whose co-ordinates were then calculated using the computer program COORD. These cartesian co-ordinates and the observed shift ratios were then put into the appropriate geometry program for internal rotation and several metal co-ordination schemes were examined. - 156 -The molecule, pyridine, 17_, appeared at first sight to present a rather well defined rigid system on which to perform a geometry calculation according to the above procedure. Bond lengths and 87a bond angles were available from a number of X-ray and microwave studies^k'C and could be used to generate a set of cartesian co-ordinates using the computer program COORD. The directional lone pair of the nitrogen donor group left l i t t l e doubt as to which model for internal rotation was most likely - namely a rigidly locked complex where only internal rotation about the Eu-N bond was possible, which would not affect either r or 6 in Eq. II]. In addition, X-ray data for Eu(dpm)3(py)2 were available which reported an average Eu-N bond ; o distance of 2.65 A. Even though this value was for an eight co-ordinate lanthanide complex whereas our present analysis was for a seven co-ordinate lanthanide complex, (vide infra), there seemed l i t t l e doubt as to what the value for the Eu-N bond distance determined from the present system of analysis could be. Table 13 lists the values of the shift ratios which were used to determine the geometry of the pyridine:Eu(dpm)^ complex. These ratios were calculated from the appropriate A -values listed in Table 12, B Chapter II. The binding constant was in the range where accurate determination was possible and thus the stoichiometry can be accurately determined to be 1:1. Using the computer program for a rigidly locked complex, several attempts were made to f i t the observed shift ratios with those calculated for several reasonable conformations of the * 71 Selbin . has reported the preparation and properties of the stable Eu(dpm)„(py) complex and other seven co-ordinate lanthanide complexes. - 157 -pyridine ring. No_ fits were obtained over any reasonable Eu-N bond 0 distance (2.2 to 3.5 A); even when the geometry of the pyridine ring was defined using X-ray data for transition metal complexes with AAA 8 8 pyridine. The inability to f i t the observed shift ratios was particularly disconcerting, especially when one considers the well-defined nature of this system. There are three possibilities which may contribute to the above result. They are, in order of ascending importance: (i) the principle magnetic axis may be other than along the Eu-N bond, (ii) the possibility of a contact contribution to the induced shift -if present, this would be most probable for the o-protons , and, ( i i i ) the geometry of the substrate bound in the complex may be different than that for the free substrate in solution. We s t i l l allow for rapid internal rotation about the Eu-N bond which, as discussed in the theory, ensures effective axial symmetry. Also, i t can hardly be assumed at this juncture that a contact contribution is present in the induced shift, even in view of the aromatic character of this 89 system. This brings us to the third possibility about which we are unable to make any definite comments and which i f correct, would inhibit the success of the present system of analysis unless fortuitously the required conformation for pyridine was chosen. A specific computer program was written to attempt to resolve the problems encountered with pyridine. This program will not be listed and although written specifically for pyridine, i t would be applicable, in a slightly modified form, for any planar system. * It should be emphasized, however, that for geometry determinations, protons with small r and wide angle 6 will be the most sensitive to configurational changes. - 158 -The only molecular dimension which is input to this program is ° 88 the C-3 - H-3 bond distance, which is taken as 1.02 A. In addition, a minimum value for the Eu - H-3 distance, and as before, the observed shift ratios are input. It is assumed (and not unexpectedly), therefore, that the Eu atom lies in the plane of the pyridine ring and along the axis. The computer then varies the Eu - H-3 distance in increments o of 0.06 A to a maximum possible value which would correspond to a c 2 Eu-N bond distance of 3.5 A. At each increment the quantity, [(3cos 6^  -3 l ) /1^ ] * is calculated for H-l and H-2 and the ratio compared with the observed (Table 13). The output of this program is a series of plots to which one manually fits a structure of pyridine, assuming C-C bond o o lengths of 1.40 A and C-H bond distances between 1.02 and 1.08 A. The geometry of pyridine which resulted from such a treatment is shown below. - 159 -The significant difference in this structure with any tried in the previous treatment, is the position of the o-protons which are displaced towards the point of complexation with the shift reagent. This result may reflect a possible stabilized structure with these hydrogens participating in H-bonding with the (dpm) ligand of the lanthanide complex. Although this change in geometry of the pyridine ring is not large, i t was enough to prevent any fits being obtained for the several proposed geometries when treated in the regular manner. o o The resulting Eu-N bond distance, R = 2.67 A+ 0.1 A (fi = 118° +2°) is in excellent agreement with the reported X-ray value for R o of 2.65 A. The method of analysis used above can be applied, in principle, to molecules which are not planar but the display of the results would best be viewed in 3-D, using graphical displays of the sort used by 2 2b R.J.P. Williams. No attempt was made to develop our technique to this degree. The results for pyridine provide one final point of interest. We have stated that one of the distinct aspects necessary, before any attempt can be made to determine molecular geometry, is the experimental determination of reliable values for the bound chemical shifts, for each proton involved. Other less precise ways for determining this parameter were discussed in Chapter II, but i t was not until the data Using this calculated geometry, a set of cartesian co-ordinates was generated and these plus observed shift ratios were put into the regular geometry program for the static case (Appendix C). An excellent f i t was obtained (expected) thus confirming the above treatment. - 160 -for pyridine had been collected and reduced as a plot of IS ]Q versus (1/6) that the vital importance of this particular aspect became apparent. In Table 17 are listed the A -values for the protons of pyridine a 90 91 determined by ourselves and those from twoother independent groups. ' It can be seen that the values for this parameter differ significantly from one group to another. It is particularly interesting that the 90 limiting shifts of Group I (for {S] of 0.5 M) are larger than the 91 limiting shifts from Group II (for [S]q of 0.15 M). This is consistent with a probable dependence of the slope of a plot of 6 versus 44 IL] /IS] (method used to determine A^-values by groups I and II ) on IS] as discussed in Chapter II. This dependence of the slope on IS3 suggests that the binding constant is small enough to affect the bound shift determinations and in fact we have measured the binding constant and found i t to be 76 liter mole 1 and thus from our data can accurately determine the stoichiometry to be 1:1. Of particular significance in Table 17 is the variation in shift ratios among Ihe various measurements. Other than ourselves, only Group II has made use of the shift ratios to determine the complex geometry and thus the geometry of the pyridine ring. Using the ratios as shown, they found the best agreement with calculated shift ratios o was with a Eu-N bond distance of 4.0 + .4 A. This calculated value for the Eu-N bond distance was based on measurements taken from a molecular model and not from a detailed computer analysis. However, the results from a detailed computer analysis using the ratios reported by Group II were even less encouraging. The best " f i t s " between calculated and - 161 -Table 17. Induced chemical shift data for association of pyridine with Eu(dpm)3 : three independent determinations. Group - Pyridine A -Values,^ p. . p.m. A_-Ratios 15 Solvent 0 28.7 o/m = 2.90 CDC13 I3 m 9.9 o/p = 3.12 P 9.2 o 25.9 o/m = 2.88 CC1. 4 IIb m 9.0 o/p = 3.16 P 8.2 o 23.8 o/m = 3.05 CDC13 IIIC m 7.8 o/p = 3.22 P 7.4 a b From ref. 90. From ref. 91. Our own work. For (a) and (b), this parameter was determined by linearly extrapolating [L]Q [L]o a plot of 6 versus , to a f -. ratio of 1.0 (see ref. 44). LbJo LbJo For (c), the A^-values were obtained from a plot of [S] versus (1/6) ij o as explained in Chapter II. - 162 -experimental shift ratios were obtained with a Eu-N bond distance of o ca. 3.5 A and with the Eu some 40° out of the plane of the ring. It is d i f f i c u l t to find any chemical evidence which would substantiate either of these values and there is obviously l i t t l e interest in doing so in view of the excellent and chemically meaningful results presented previously. This chapter has provided a number of models for derivation of molecular conformation in the presence of internal rotational motion by use of lanthanide shift reagents. A l l four molecules studied were ri g i d except at the point of attachment to the lanthanide and so provided the simplest type of problem for the analysis. The results show that determination of molecular geometry is straightforward and gives chemically reasonable results only in cases where: (i) the entire complex is relatively rigid as with _1 and J_7_ and, ( i i ) there i s completely free internal rotation as with _16. For _16_ and 1_1 i t was shown that the presence of internal rotational motion, even when present only at the site of attachment to the lanthanide, can lead to either erroneous or un-determinative results respectively for attempts to find the "best" single (static) conformation of the bound complex. These results clearly demonstrate the d i f f i c u l t i e s , even for r i g i d substrates, which may be encountered when attempting to determine the bound conformations of substrates bound to lanthanide shift reagents. Thus, there is need for considerable caution (and a variety of motional models) in any attempt to treat polyfunctional and non-rigid substrates or both. - 163 -GENERAL CONCLUSIONS The foregoing investigations warrant a few general conclusions to bring the work presented in this thesis into perspective with present and certainly the future application of lanthanide shift reagents to organic n.m.r. spectroscopy. More specific conclusions have been presented within the Chapters and will not be reiterated The primary theme and objective throughout this thesis has been to develop the necessary chemical and theoretical understanding for the ultimate use of lanthanide shift reagents to the determination of molecular conformation in solution. As a whole, therefore, this thesis represents the successful progression of our understanding and evaluation of the applications of lanthanide shift reagents to organic n.m.r. spectroscopy. We have described numerous experimental optimizations and in addition have presented a detailed theoretical analysis of the lanthanide-substrate equilibrium which has permitted, for the first time, the chemical aspects of this equilibrium to be fully understood. In addition, this latter understanding has provided the basis on which rests present and future applications of lanthanide shift reagents to the determination of molecular structure. In Chapter III, we have successfully described in detail this particular aspect, as it pertains to a series of rigid organic substrates. We have demonstrated that geometry determinations are possible but not simple and considerable caution is advised in future applications to polyfunctional and/or non-13 rigid systems. In this connection, the use of C shift ratios in - 164 -conjunction with shift ratios, the use of broadening reagents, chemical derivatization and more detailed computer programing will assist in overcoming some of the problems which will be encountered when attempting to determine solution conformations of these more complex molecules. In conclusion, i t is the belief of this author that lanthanide shift reagents have become and will continue to be a routine and integral part of organic n.m.r. spectroscopy. - 165 -EXPERIMENTAL The Experimental for this thesis has been divided into two parts. A. Techniques and experimental methods, synthesis and/or purification of compounds, for Chapter I. B. Techniques and experimental methods, synthesis and/or purification of compounds not previously described in part A, for Chapters II and III. The reason for this partitioning of the Experimental is two-1 13 fold. (i) All H and C n.m.r. measurements discussed in Chapter I were made with a modified Varian HA-100 spectrometer, operating in the frequency-swept mode with a probe temperature of 32.0°C. Whereas, al l n.m.r. measurements reported in Chapters II and III were made on a Varian XL-100 spectrometer, operating in the frequency-swept mode with a probe temperature of 40.0°C. (ii) In Chapter I, chemical shift changes induced by various Ln(dpm)3 complexes were measured as a function of the change in the concentration of the lanthanide shift reagent. In Chapters II and III on the other hand, the concentration of the lanthanide shift reagent was maintained constant (ca. 0.006 M) and the substrate concentration was varied. - 166 -For both parts A and B, extreme precautions were taken to exclude moisture at a l l stages of the experiments. A. General Methods (a) All n.m.r, measurements were made with a modified Varian HA-100 spectrometer, operating in the frequency-swept mode with a probe temperature of 32.0°C. For experiments using the europium, thulium, and gadolinium reagents, 5_, 6_, 9_, deuterochlorof orm solutions were used, with internal tetramethylsilane (TMS) as the reference signal for the field-frequency lock. Experiments with the praseodymium reagent, 7_> were made with chloroform solutions and the chloroform resonance was used to provide a lock signal; some TMS was added to provide a chemical shift reference. (b) An account of the modifications necessary for the measurement 1 13 2 13 of H-( C) INDOR spectra has been described elsewhere. C chemical shifts are reported in p.p.m. relative to TMS. (c) When applicable, analyses of the n.m.r. spectra were made with a modified version of the LA0CN3 program and an I.B.M. 360-67 computer. (d) Melting points were performed on a Thomas-Hoover capillary m.p. apparatus and are corrected for thermometer error. (e) Deuterochloroform (99.8%) from Merck Sharp and Dohme, Montreal, was stored over Linde molecular sieve (4A), which had been * Modifications were performed by R.B. Malcolm of the Department of Chemistry, U.B.C. - 167 -heated In an oven at 110°C for 24 hours, to both dry i t and remove traces of acid which decompose the lanthanide complex. Carbon tetrachloride (A.R. Grade) was distilled and stored over NaOH pellets prior to use. Ethanol-free chloroform was obtained by standing A.R. Grade chloroform over granular, self-indicating silica gel. (f) A sample of the lanthanide reagent was vacuum sublimed immediately prior to an experiment. The lanthanide was dissolved in either deuterochloroform, chloroform, or carbon tetrachloride (ca. 0.04 g/ml). Aliquots of this standard solution were added via a 0.10 ml syringe to a solution of the carbohydrate (ca. 0.18 g/ml). After purification and/or sublimation, a l l further handling of the lanthanide reagent and carbohydrate was carried out in a glove bag flushed with dry nitrogen. (g) The preparation of a l l solutions was conducted under dry nitrogen in a glove bag using apparatus that had been baked at 110°C immediately prior to use. Synthesis and Purification of Compounds (a) The carbohydrate derivatives, _1, 2^, and 3_, were stock samples which were recrystallized twice from CHCl^-hexane 1:2 v/v. Crystals were then dried in vacuum at the temperature of boiling methylene chloride for 12-20 hours, immediately prior to use. M.p.s were determined as follows: 1 103-105°C 2 73.5-74.8°C 3 57.5-58.5°C - 168 -The n.m.r. parameters were in entire accord with the assigned structures. (b) 2,2-Dimethyl-l-propanol (neo-pentanol), 8^ , was purchased from Matheson Coleman and Bell and was purified by distillation from calcium hydride. The material had a b.p. of 114°C. (c) Tris (dipivalomethanato) europium (III), 5_, was prepared from ft europium oxide (99.99%) following the method of Eisentraut and 16 Sievers. Yield was greater than 95%. The material from the reaction was stored in a vacuum desiccator containing phosphorus pentoxide. A small sample was vacuum sublimed at 140°C at 0.1 mm Hg or lower immediately prior to an experiment. In the above synthesis, the europium oxide is dissolved in an excess of 15.4 M HNO^  to prepare the hydrated europium(III) nitrate - Eu(NO^)-xH^O. Care must be taken at this stage to ensure all excess HNO^  is removed with the help of a steam bath or preferably using a rotary evaporator. Any excess acid remaining at this step will cause a decomposition of the final product - Eu(dpm)3. The thulium reagent, 6_, the praseodymium reagent, ]_, and tie gadolinium reagent, 9_ were prepared by the same method, ft starting with the corresponding nitrate salt. 2,2,6,6-Tetramethyl-3,5-heptanedione (dpm) was purchased from Eastman Organic Chemicals. (d) 3-0-Acetyl-l,2:5,6-di-O-isopropylidene-a-D-allofuranose, k_, was prepared from 1,2:5,6-di-O-isopropylidene-a-D-allofuranose, 2, as 92 described in the literature, using excess acetic anhydride in dry pyridine. Product was recrystallized twice from ethanol-water mixture and then vacuum dried for 48 hours at the b.p. of methylene chloride. Obtained from Alfa Inorganics, Inc. - 1 6 9 -The yield was approximately 70% and had a m.p. of 73.5-74°C. (e) 5-Hydroxy-l,2,3,4,7,7-hexachloronorborn-2-ene, 11, was prepared from the hydrolysis of the adduct of vinyl acetate with 93 hexachlorocyclopentadiene following the procedure of E.K. Fields. This procedure was deviated from in that the alcohol adduct JUL was extracted from the water with CHCl^ which was subsequently evaporated off under reduced pressure to give a syrup. This was then treated twice with decolourizing charcoal and the resulting crystals recrystallized from n-heptane. Product was further purified by vacuum sublimation immediately prior to use and had a m.p. of 153.5-154.0°C. B. General Methods (a) All n.m.r. measurements were made with a Varian XL-100 operating in the frequency-swept mode with a probe temperature of 40.0°C. Tetramethylsilane (TMS) was used as the internal reference signal for the field-frequency lock for the experiments using deuterochloroform, deuterobenzene or carbon tetrachloride as solvents. Experiments with chloroform or benzene solutions used the chloroform resonance or the benzene resonance respectively to provide a lock signal; some TMS was added to provide a chemical shift reference. (b) Deuterobenzene (99.8%) from Merck Sharp and Dohme, Montreal, and benzene (A.R. Grade) were stored over Linde molecular sieve (4A), which had been heated in an oven at 110°C for 24 hours prior to use. Other solvents were purified and/or dried as described in part A. - 170 -(c) The preparation of a l l solutions was conducted under dry nitrogen in a glove bag using apparatus that had been baked at 110°C immediately prior to use. (d) All plots of the experimental data were made with a Hewlett-Packard Calculator (model 9100B) and a Hewlett-Packard Calculator Plotter (model 9125A). (e) Method 1. Constant [S] , Varying [L] Q i 2 o A series of standard solutions, each containing a known amount of the substrate (ca. 0.6, 0.2, 0.08, 0.04 M) was prepared. One particular standard solution was then selected and 1.0 ml of this solution was used to dissolve a known quantity of the lanthanide reagent (ca. 0.015 g, 0.02 M of Ln(dpm>3; ca. 0.190 g, 0.175 M of Ln(fod)3). The spectrum of this mixture then gave the maximum shift. Further spectra were run after each successive addition of a 0.10 ml aliquot of the standard substrate solution. In each case the observed shift decreased. (f) Method 2. Constant [L] , Varying [ S] Q J. a 0 The lanthanide reagent (ca. 0.042 g, 0.012 M of Ln(dpm)3; ca. 0.070 g, 0.012 M of Eu(fod)3) was dissolved in 4.8 ml of solvent and 0.2 ml tetramethylsilane in a 5.0 ml volumetric flask. The substrate was separately dissolved in 5.0 ml of the same solvent. Aliquots (0.50 ml) of the lanthanide solution were then added to each of a series of 5-10 graduated 1.0 ml flasks. To each of these flasks was now added varying amounts of the stock solution of substrate; e.g., vial 1, 0.5 ml; vial 2, 0.4 ml; etc. The content of each flask was then made up to 1.0 ml by further addition of solvent. Each solution - 171 -was then placed in a separate n.m.r. tube which was capped and stored in a thermostatted water bath prior to measurement. (g) Appendix B, C and D contain a listing of the computer programs used to determine the complex conformation. Details, for the understanding and possible use of these programs, are provided in the form of comment statements which have been appropriately situated throughout the programs. A brief discussion of the necessary input data for each of these programs will be presented at the beginning of each Appendix. Synthesis and Purification of Compounds (a) Tris(2,2-dimethyl-6,6,7,7,8,8,8-heptafluoro-3,5-octanedionato)-europium(III), 13, was prepared from europium oxide (99.99%) following 94 the method of Springer et a l . Yield was greater than 95%. The complex was recrystalllzed twice from methylene chloride and was thereafter stored in a vacuum desiccator containing phosphorus pentoxide. This is important because i t has been reported"^ that the anhydrous fod complex absorbs one mol equiv of water when allowed to stand unprotected in a moist atmosphere. All further manipulations were carried out in a glove bag which had been flushed several times with dry nitrogen. (b) n-Propylamine, 12, from Eastman Organic Chemicals was purified by distillation from KOH pellets into a sealed receiver also containing KOH pellets. The material had a b.p. of 49.0°C. (c) Bicyclo[2.2.1]heptan-2-one(norcamphor), 14, from Aldrich Chemical Company was vacuum distilled at 120°C into a receiver contain-ing KOH pellets. The material had a m.p. of 94-95°C. - 172 -(d) n-Propanol, 15_, was purified by distillation from calcium hydride. The material had a b.p. of 98.7°C. (e) Aniline (reagent grade), 16, from British Drug Houses Ltd. 95 was purified as follows. 10.0 ml was distilled from a small amount of zinc dust and a 4.0 ml fraction collected from the middle: b.p. pf 183°C. (f) Pyridine, 17_, was purified by refluxing over KOH pellets for ca. 1 hour and then distilling into a sealed receiver also containing KOH pellets. The material had a b.p. of 114.2°C. (g) 2,2-Dimethyl-3-butanone, 18, from Aldrich Chemical Company was purified by distillation from MgSO^  into a sealed receiver also containing MgSO^ . The material had a b.p. of 106-107°C. (h) The carbohydrate derivatives, 19_, 2(), and 21^, existed as pure stock samples in the laboratory. Crystals were dried in vacuum at the temperature of boiling methylene chloride for 12-20 hours, immediately prior to use. The n.m.r. parameters were in entire accord with the assigned structures. (i) Acenaphthenone, 22_, was a stock sample which was vacuum sublimed at 85°C at 0.3 mm Hg immediately prior to use: m.p. of 118-119.5°C. (i) The dimethylaminocyclophosphonitriles, 23_ to _27, were obtained from N.L. Paddock and J.N. Wingfield, Department of Chemistry, U.B.C. The stable complex which was obtained by reacting Eu(fod)^ (1.0 mole equivalents) with 1.0 moles of NgPgtNMe^g was prepared by the following method. 0.255 grams of Eu(fod)„ was added to a solution of 0.292 grams N P (NMe )1 f i in anhydrous carbon tetrachloride. The - 173 -flask was sealed and the solution stirred at room temperature for 80 hours. Solvent was removed by vacuum distillation to give a white solid which melted to a paste at 606C in a water bath. A l l attempts to purify the product by recrystallization and by eluting the product down an alumina column failed, giving only the pure nonamer, m.p. 232-234°C. The n.m.r. spectrum shown in Fig. 19C was thus recorded for the crude product. - 174 -APPENDIX A Calculation of and 6^ from R, Q, and <j>. Referring to Figures 21A and 21B, i t is convenient to deal with the following quantities: r^ = distance vector between lanthanide atom and i'th proton of substrate; R = lanthanide-donor atom distance vector; R' = lanthanide - x-axis distance vector; ~r^ = distance vector from donor atom (origin) and i'th proton Ithis vector is not shown in the figure]; 0^ = angle between R and r^; ft = angle between R and the x-axis; <|> = angle between R' and y-axis (a measure of the angle of internal rotation of the lanthanide-donor bond axis about the bond axis from the donor atom to atom #2). 2 It is expedient to compute cos 0^ directly from the dot product of R _^  and r^: 2 V * 2 Eq [1] cos 0. = {-—=——} |r.||R| One can now write, 3cos20 - 1 3(r-t)2 ~ \t\2 |r |2 Eq 12] ^ 3 - A 2 = — | r±|3 | t |2 \r.\5 but r. = R - r.' , l i ' - 175 -and r ' = x. i + y. j + z. k, where x., y., z. are i 1 7i J 1 l J± l co-ordinates of the i'th proton, R = |R|cosfi i + |R|sinfi coscj) j + |R|sinfi sin<(> k. Substitution into Eq. [2] followed by some rearrangement gives the final result: 3cos26i - 1 2|R|2 - 4|R|Q + 3Q2 - \P±\2  P ] 1^13 = ( | r l | 2 + | R | 2 - 2|f|Q)5/2 12 2 ^  2 2 where r. = x. + y. + z. , 1 l1 l •'i l ' and Q = x^ cosfi + y^ sinfi costf) + z^ sinfi sin<|>, - 176 -APPENDIX B This computer program, COORD, written in Fortran was used to calculate the atomic cartesian co-ordinates for molecules given bond lengths, bond angles and dihedral angles. These values must be obtained from X-ray or microwave studies of the molecule or related molecules. Comment statements, appropriately spaced throughout the program explain the operational procedures of the program and the format required to read in the necessary data. The substrate atoms are numbered consecutively and i f the calculated cartesian co-ordinates are required for input data to the geometry programs (Appendices C and D), atom #1 must be assigned to the donor atom. - 177 -C THIS PROGRAM AS STANDS MILL TAKE DP TO 24 ATOMS PER MOLECULE C C C C THIS PROGRAMME CALCULATES THE COORDINATES IH A 3 DIMENSIONAL C SPACE GIVEN THE BOND LENGTHS, BOND ANGLES, AND DIHEDRAL C THIS IS AN ADAPTATION OP PROGRAM COORD WBITTEN ORIGINALLY BY DBWAR C THE FIRST CARD HAS THE NAME OF THE MOLECULE (OB OTHER HEADING) C IS THE FIRST 36 COLUMNS C C C NOAT IS THE NUMBER OF ATOMS. B12 IS THE EOND DISTANCE FROM ATOM C 1 TO ATOM 2, R23 IS THE BOND DISTANCE FROM ATOM 2 TO 3 , ETC. TH123 C IS THE 123 BOND ANGLE C C C C C c DIMENSION X (24) , Y (24) , Z (21) , R (21,24) , NAME (9) CALL PLOTS C IKQ IS THE NUMBER OF MOLECULES FOR WHICH THE PROGRAM HILL CALCULATE C THE COORDINATES FOR IKQ=1 DO 1111 LOVEU = 1,IKQ 45 READ 900 , (NAME (I) ,1=1,9) 900 FORMAT ( 9A4) WRITE(6,950) (NAME(I),1= 1 ,9) 950 FORMAT(1H1,9A4) REAL(5,901)NOAT, R12;H23,TH123 901 FORMAT( I2,2F7.4,F14.7) WRITE(6,952)R12,R23rTH123 ,NOAT 952 FORMAT (7H R12 = F7.4, 10H R23 = F7.4,10H TH123 = ,1PE10.3,5X, 117HNUMBER OF ATOMS= ,12) 3 THETA=TH123*3.1415926536/180. CCOS=COS (THETA) SSIN=SIN (THETA) 4 DO 51 1=1,3 X (I)=0.0 Y (I)=0.0 51 Z (1)^0.0 X (2) = R12 X(3)=R12~R23*CC0S Y(3)=R23*SSIN DO 5 I = 4, NOAT 5 X(I) - 10000.0 WRITE(6,953) 953 FORMAT (88H0 NA NB NC ND ILAZY RCD 1 THBCD PHABCD/) C C C ATOHS NA, NB, NC, HAVE KNOWN COORDINATES AND ARE NOT COLLINEAR. C THBCD IS THE BCD BOND ANGLE IN DEGREES AND PHABCD IS THE DIHEDRAL C ANGLE OF CD RELATIVE TO AB, MEASURED CLOCKWISE ALONG THE DIRECTION C B TO C. ILAZY ALLOWS AUTOMATIC CALCULATION OF ANGLES IN NORMAL C TETRAHEDRAL AND PLANAR SYSTEMS. 2LAZY = 0,1,2,3,4,5 ; TETRAHEERAL C WITH DIHEDRAL ANGLES OF 0,60*120,180,240, AND 310 DEGREES C RESPECTIVELY. ILAZY= 6,7 ; PLANAR CIS, TRANS RESPECTIVELY. - 178 -C ILAZY=8 ; ATOMS B,C,D ARE COLLINEAR. ILAZY = 9 ; DATA HILL SUPPLY C ANGLES. C DO 52 I=4,NOAT READ(5,902) NA,NB,NC,ND, ILAZY,RCD,THBCD,PHABCD 902 FORMAT(412,2X*I1,F7.4, 2F14.7 ) C C CBECK TO SEE THAT COORDINATES OF ATOM NA,NB, AND NC HAVE BEEN C CALCULATED C 7 IF (X(NA) • X(!SB) • X (NC) - 7000.0) 8, 50, 50 8 WRITB(6,954)NA,NB,NC,ND, ILAZY,RCE,THBCD,PHABCD 954 FORMAT (3X,12, 3X,12,3X,12,3X,12, 18X,11,7X,F7.4,8X,E14.7,4X, 1E14.7) IF (ILAZY - 8)/ 79, 78, 79 78 RBC=SQRT ( (X (NC)-X (HE) ) **2* (Y (NC)-Y (NB)) **2+ (Z (NC)-Z (NB) ) **2) X(ND) = X(NC) + (X(NC) - X (NB)) *RCD/RBC Y(ND) = Y(NQ • (Y(NC) - Y (NB) ) *RCD/RBC Z(ND) = Z(NC) + (Z(8C) - Z (NB)) *RCD/RBC GO TO 52 C C C MOVE ATOM HC TO THE ORIGIN C 79 XA = X (NA) - X (NC) YA = Y (NA) - Y (NC) ZA = Z (NA) - Z (NC) XB = X (NB) - X (NC) YB = Y(NB)| - Y(NC) ZB = Z (NB) - Z (NC) C C ROTATE ABOUT Z AXIS TO MAKE YB=0, XB IS POSITIVE. IF XYB IS TOO C SMALL, ROTATE FIRST 90 DEGREES ABOUT Y AXIS C XYB=SQRT(XB**2+YB**2) K = 1 IF (XYB - 0.1) 9, 10, 10 9 K = 0 XPA = ZA ZPA = -Xli XA = XPA ZA = ZPA XPE = ZB ZPE = -XI3 XB =XPB ZB = ZPB XYB=SQRir (XB*»2*YB**2) 10 COSTH = XB/XYB SINTH = YB/XYB XPA - XA*C0STH • YA*SINTH YPA = YA*COSTH - XA*SINTH C C ROTATE ABOUT Y AXIS TO MAKR ZB VANISH C 11 RBC=SQHT (XB**2 + YB**2 + ZB**2) SINPH = ZB/RBC COSPH=SQRT (1.-SINPH**2) XQA = XP A*COSPH • ZA*SINPH ZQA = ZA*COSPH - XPA*SINPH - 179 -C ROTATE ABOUT X AXIS TO MAKE ZA=0 , YA POSITIVE 12 YZA=SQRT (YPA**2+ZQA**2) COSKH = YPA/YZA SINKH = ZQA/YZA IF (ILAZY - 1) 13, 14, 15 13 COSD = 1.0 SIND = 0 C C COORDINATE A, (XQA,YZA,0); B,(RBC,0,0); C, (0,0,0); NONE ARE NEGATIVE C COORDINATES OF C NOW CALCULATED IN NEW FRAME C GO TO 21 14 COSD = 0.5 SINE=0.5*SQRT(3.) GO TO 21 15 IF (ILAZY - 3) 16, 17, 18 16 COSD = -0.5 SIND=0.5*SQRT(3.) GO TO 21 17 COSD = -1.0 SIND = 0 GO TO 21 18 IF (ILAZY - 5) 19, 20, 22 19 COSD = -0.5 SIND=-0.5*SQRT (3.) GO TO 21 20 COSD = 0.5 SINE=-0.5*SQRT(3.) 21 COSA = -1.0/3.0 SINA=(2./3.)*SQRT(2.) GO TO 2 9 22 IF (ILAZY - 7) 23, 24, 26 23 COSD = 1.0 SINE = 0 GO TO 25 24 COSE = -1.0 SIND = 0 25 COSA = -0.5 SINA=0.5*SQRT (3.) GO TO 29 26 IF (ILAZY - 9) 27, 28, 28 27 CONTINUE GO TO 29 28 THBCD=THECE*3.1415926536/180o PHABCD=PHABCD*3.1415926536/180. SINA=SIN (THBCD) COSA=COS(THBCD) SINE=SIN (PHABCD) COSE=COS (PHABCD) 29 CONTINUE XD = RCD*COSA YD = BCD*SINA*COSE ZD = BCD*SINA*SIND C C TRANSFORM COORDINATES OF D BACK TO ORIGINAL SYSTEM C 30 YPD = YD*COSKH - 2D*SINKH ZPD = ZD*COSKH • YD*SINKH XPD = XD*COSPH - ZPD*SINPH ZQD = ZPE*COSPH • XE*SINPH - 180 -31 32 52 C C XQD = XPD*COSTH - YPD*SINTH YQD = YPD*COSTH + XPD*SINTH IF (K - 1) 31, 32, 31 XBD = -ZQC ZRD = XQD XQD = XRD ZQD = ZRD X (NC) Y (ND) Z(NE) = XQD = YQD = ZQD X (NC) Y (NC) Z (NC) CONTINUE 69 PRINT 69 FORMAT(/// 94H THE ABOVE FEW LINES ARE JUST A REHASH OF THE INPU 1T INFO. IN CASE ONE LACKS SELF-CONFIDENCE / 32H NA=ATOM A 2, N1 = ATOM 1 , ETC. / 96H COORDINATES FOR ATOMS A,B, AND C ARE 3 KNOWN, EACH CARD THEN SOVBS FOR THE POSITION OF ATOM D / 4 95H RCD= DISTANCE FROM ATOM C TO ATOM D : THBCD= ANGLE DEFINED 5 BY ATOMS B,C,D; C EEING THE APEX: / 50HPHABCD= DIHE 6DRAL ANGLE OF THE ABC AND BCD PLANES ) C C 955 956 881 41 88 957 C C C c c C ) X-COORDINATE Y-COORDINAT C C WRITE(6,950) (NAME (I) ,1=1,9 WRITE (6,955) FORMAT (78H0NO. OF ATOM 1E Z-COORDINATE/) DO 41 1=1,NOAT WRITE (6,956) I, X (I) , Y (I) ,Z (I) FORMAT (1H ,5X,I2,15X,F10.7,11X,F10.7,11X,F10.7) PUNCH 881 , X(I), Y ( I ) , Z(I) FORMAT(3 (1PE10.3)) CONTINUE CO 88 1=1,NOAT DO 88 J=1,NOAT R (I, J)=SQRT ( (X (I)-X (J)) **2+ (Y (I) -Y (J) ) **2* (Z (I) -Z (J) ) **2) WRITE (6,950) (NAME (I) ,1=1,9 ) WHITE (6,957) FORMAT(1H0,21HINTERATOMIC DISTANCES,//) THE NEXT TWENTY OR SO STATEMENTS FORM A PRINT LOOP WHICH DOES NO MORE THAN PRINT OUT THE ELEMENTS OR MATRIX R , THE INTERATOMIC DISTANCES MATRIX. NC= NUMBER OF COLUMNS IN PRINT OUT. PLEASE NOTE FORMAT111 BEFORE BECOMING ORIGINALo LET'S LET NC =10. NC= 10 KK=0 NCM1= NC-1 NICE =0 DO 105 IZ=1,NOAT, NC JOY = IZ+ NCM1 IF(JOY.GT. NOAT) JOY=NOAT THE NEXT STATEMENT MAKES SURE YOU DON'T HAVE A DATA SET STRATIFIED BETWEEN TWO PAGES. (I.E. 52 LINES/PAGE MAX.) NICE = NICE* NOAT IF(NICE-52) 106,107,107 107 LIKE= 0 NICE = 0 GO TO 108 106 LIKE =1 - 181 -108 CONTINUE IF (LIKE *KK-1) 102,103, 103 101 FORMAT (1H1) 102 PRINT 101 103 PRINT 104 , (MUCK, MUCK=IZ,JOY) 104 FORMAT(1H0,/10I10) 109 DO 112 IRS=1,NOAT 112 PRINT111, IRS, (R (IRS,ICS) , ICS-IZ,JOY) 111 FORMAT (1H I2,2X,10 (1PE10.3)) 105 CONTINUE C CAII TRAIL (NOAT, X,Y,Z) 1111 CONTINUE GO TO 665 50 WRITE (6,958) 958 FORMAT(1 HO,38HCCORDS.OF 1 REFERENCE ATOM UNAVAILABLE) 665 CONTINUE CALL PLOTND STOP END SUBROUTINE TRAIL (NOAT, X,Y,Z) C C TRAIL PLOTS OUT THE POINTS IN 2: (WITH A 3D FLAVOR) C NOAT IS THE NUMBER OF ATOMS TC BE PLOTTED C X,Y,Z ARE THE COLUMN MATRICES CONTAINING THE ATOMIC COORDINATES C N IS THE NUMBER OF DIMENSIONS X,Y, AND Z ARE GIVEN IN THE MAIN C CAN HANDLE UP TO NOAT =24 C DIMENSION X (24),Y(24),Z (24),ZP (24), YP (24) , HT (24) XMAXI = 0. XMINI = 0. CALL PAT(X, XMAXI, XMINI, NOAT) QP = XMAXI- XMINI DO 79 MP= 1,NOAT ZP(MP) = -X(MP)*0.5 + Z(MP) YP(KP) = -X (HP) *0„5 • Y(HP) 79 HT (MP) = (X(MP) -XMINI) /QP *0„56 • 0.14 CALI SCALE (ZP,NOAT, 10., YMIN„ DY, 1) CALL SCALE (YP,NOAT, 10., XMIN5 DX, 1) DO 779 MP=1,NOAT ZZZ=MP 779 CALL SYMECL (YP (MP), ZP(HP), HT (MP), 01, 0., -1) CALL PLOT (12. ,0. ,-3) RETURN END SUBROUTINE PAT(X, XMAXI* XMINI,NOAT) C C X IS A VECTOR OF NOAT DIMENSIONS OF WHICH THE LARGEST AND C SMALLEST VALUES ARE TO BE FOUND. N IS THE DIMENSION OF THE TOTAL C RESIDING SPACE OF WHICH NOAT MAY BE ONLY A SUBSPACE C XMINI AND XMAXI WILL EE RETURNEE AS THE MAXIMUM AND MINIMUM VALUES C OF X C DIMENSION X(24) XMAXI = X (1) CO 3 J=2,NOAT IF (XMAXI-X (J)) 2,2,3 2 XMAXI= X(J) - 182 -3 CONTINUE XMINI = X (1) DO 1 J=2,NOAT IF (XMINI-X (J) ) 4,4,5 5 XMINI = X(J) 4 CONTINUE RETURN END - 183 -APPENDIX C This computer program was used to determine complex conformation for a rigidly locked complex (Eq. [3], Chapter III). Input data to this program includes: the i n i t i a l value for the Eu-donor atom bond distance (R) , bond angle (ft), dihedral angle (<})), and the range over which these values are to be varied5 the experimentally observed shift ratios; the cartesian co-ordinates for each atom considered. Numerous comment statements are appropriately spaced throughout the program to assist in explaining the specific computations carried out in this program. - 184 -DIMENSION X ( 2 4 ) , Y ( 2 4 ) , Z (24) , DX (24) , DY (24) , DZ(24) , DIST (24) 1 ,DOT (24) ,SD (6) ,UNCER(6) , RATIO (6) , WT (6) DIMENSION ZZ (24,24) ,THEDAA (24) , RR(24) DIMENSION NAME (6) PI ~ 3.141593 C C THIS PROGRAM IS FOR A RIGIDLY LOCKED COMPLEX C TAKE NOTE OF CO-ORDINATE CONVENTION C READ 700,(NAME(I) , 1=1,6) PRINT 701 , (NAME ( I ) , 1=1,6) 700 FORMAT (6A4) 701 FORMAT(1H 1, 6A4) READ 1, NUMHYD 1 FORMAT (II) C C NUJ = NUMHYD-1 C NUMHYD IS THE NUMBER OF HYDROGENS WHICH SHIFT RATIOS ARE TO BE C CALCULATED THEORETICALLY AND FITTED TO EXPERIMENTAL VALUES C C READ 101, NTHEDA,NPHI, NRAD, BTHEDA, DPHI, DR 101 FORMAT ( 3(12) , 3 (E10.3) ) C C C AIL INPUT ANGLES AND INCREMENTS ARE IN DEGREES C DISTANCES I . E . RINT AND DR ARE IN ANGSTROMS C NTHEDA = NUMBER OF INCREMENTS OF THEDA TO BE CONSIDERED (<21) C NPHI = NUMBER OF INCREMENTS OF PHI TO BE CONSIDERED (<21) C NRAD = NUMBER OF INCREMENTS OF BOND DISTANCES TO BE CONSIDERED C DTHEDA = SIZE OF INCREMENT OF THEDA TO BE CONSIDERED C DPHI = SIZE OF INCREMENT OF PHI TO BE CONSIDERED C DR = SIZE OF INCREMENT OF BOND TO BE CONSIDERED C NOTE: NTHEDA*DTHBDA-1= RANGE CF VALUES OF THEDA SCANNED, SAME FOR C OTHER VALUES C C READ 102, THEDAI, P H I I , RINT 102 FORMAT(3(E10.3)) C C C THESE ARE THE INITIAL VALUES FOR THEDA, PHI AND BOND DISTANCE C RESPECTIVELY C PRINT 337 337 FORMAT(1H1, 9HVARIABLE ,5X13HINITIAL VALUE, 5X21HINCREMENTAL INCRE U S E ,5X21HNUMBER OF INCREMENTS /) PRINT 338 ,RINT,DR,NRAD,THEDAI,BTHEDA,NTHEDA,PHII ,DPHI, NPHI 338 FORMAT (2X, 9HBOND DIST , 5 X F 5 . 2 , 1 8 X F 5 . 3 , 18X12 / 1 1X5HTHEDA ,8XF6 .1 ,2X3HDEG,15XF5 .2 , 3HDEG , 15X13 / 2 1X5HPHI , 8 X F 6 . 1 , 2 X 3 H D E G , 1 5 X F 5 „ 2 , 3HDEG , 15X13 / ) THECAI = THEDAI*PI /180 . PHII = PHII *P I /180 . DTHEDA = DTHEDA*PI/180. DPHI = DPI1I*PI/180. C PRINT 612 612 FORMAT(//99HSTOP A MOMENT; DO THESE NUMBERS BELOW LOCK AT ALL FAMI - 185 -1LIAB? IF NOT WE HAD BETTER QUIT HERE! ) C C C C C AA = 0.0 C AA IS A PARAMETER TO BE USED LATER ON IN NORMALIZING ERROR MEASURE DO 661 MM=1,NUJ READ 2, RATIO (MM) , UNCER (MM) , WT (MM) AA = RATIO (MM)*RATIO (MM)* WT (MM) * A A PRINT 2, RATIO (MM) , UNCER (MM) ,WT(MM) C WT DEFINES THE WEIGHTS ASSIGNED TO EACH RATIO FOR FINDING THE LEAST C DISTANCE VALUES. N . E . SUM OF THE WEIGHTS = 1. 2 FORMAT (3 ( E10.3)) 661 CONTINUE C C THE RATIOS ARE THE EXPERIMENTALLY DETERMINED SHIFT RATIOS FOR ATOM C ONE /ATOM 2; ATOM 1 / ATOM 3; ATOM 2 / ATOM 3 : IF NUMHYD = 3 C IN THAT ORDER * « • • » • ? ? ? C C IF NUMHYD = 4 THEN RATIOS ARE 1/2; 1/3; 1/4; 2/ C UNCER GIVES THE UNCERTAINTIES IN EACH RESPECTIVE SHIFT RATIO. I . E . , C IF THE CALCULATED RATIO IS WITHIN UNCER OF THE EXPERIMENTAL RATIO, C THEN THE POINT WILL WARRANT FURTHER CONSIDERATION C C C C THIS STATEMENT READS IN THE VALUES OF THE X , Y , AND Z CO-ORDINATES C FOR EACH ATOM (MUST BE COMPUTED ELSEWHERE, I . E . COORD ETC.) DO 3 1=1,NUMHYD READ 29,X (I) , Y (I) , Z (I) PRINT 29, X (I) , Y (I) , Z (I) 29 FORMAT(3 ( E10.3)) 3 CONTINUE C C PRINT 333 333 FORMAT (1H1 , 1 X , 1 2HDISTANCE-ANG ,5X,9HTHEDA-DEG ,6X 1,3HPHI ,10X, 7HEPSILON / / ) C C PHI = FHII DO 23 LP =1,NPHI HI = 180. *PHI / P I R = RINT DO 21 LR = 1, NRAD T H E E ft = TliEDAI DO 22 LT=1,NTHEDA HEDA = 180 . * THE DA/PI XE = R*COS (THEDA) YE = R*SIN (THEDA)* COS (PHI) ZE = R* SIN (THEDA) *SIN (PHI) C NOTE N . B . THE ATOM TO WHICH EU IS "BONDED" TO IS ASSUMED TO C HAVE MOLECULAR COORDINATES ( 0 , 0 , 0 ) . BE SURE YOUR DATA POINTS ARE C RELATIVE TO THIS REFERENCE POINT DO 8 L=1,NUMHYD C C C THIS NEXT PORTION GIVES THE POSITION VECTORS TO EACH ATOM WITH - 186 -C VECTORS READ SET AT THE EU ATOM C DX (L) = (XE - X (L) ) DY (L) = (YE - Y (L) ) DZ (L) = (ZE - Z (L) ) C C DIST GIVES THE ABSOLUTE VALUE FOR EACH OF THESE ATOMIC POSITION C VECTORS. C DOT GIVES THE SCALAR PRODUCT OF EACH POSITION VECTOR DOTTED WITH TH C EU-COMPLEX BOND VECTOR. C DIST(L) = SQRT (DX (L) *DX (L) + DY (L) *DY (L) • D Z ( L ) * D Z ( L ) ) DOT (L) = ( XE *DX(L) + YE *EY (L) + ZE *DZ (L) ) / (DIST (L) *R) 8 CONTINUE DO 108 KB=2,NUMHYD SD(KB-1) = (3.*DOT(1 )*DOT(1 ) - 1 . ) *BIST(KB) * * 3 / 1 ((DIST(1 ) * * 3 ) * (3.*DOT(KB) *DOT (KB) - 1 . )) SD(KB-1) = SD(KB-1) • SB 108 CONTINUE EPS = 0. DO 62 IG=1,NUJ 62 EPS = WT(IG) * ( (RATIO (IG) - SD ( IG) ) * *2 ) + EPS EPSQ = SQRT ( EPS/AA) PRINT 33, R , H E D A , HI , EPSQ 33 FORMAT ( 2X, F 5 . 2 , 10X,F6 .1 , 10XF6.1 , 10X,1PE10.3 ) 67 CONTINUE ZZ (LR,LT) = EPSQ THEEAA(LT) = HECA 22 THEDA = THEDA+ DTHEDA SR (LR) = R 21 R= R+ DR C C C PLOTTING INSERTION C C CALL SCALE ( RR , L 0 , 10 . , XMIN, DX,1) CALL SCALE (THEDAA, I T , 10 . , Y?UN,DY, 1) CALL AXIS( 0 . , 0.,12HBOND DISTo , - 1 0 , 1 0 „ , 0 . , XMIN, DX) CALL AXIS( 0 . , 0 . , 10HBOND ANGLE , 10, 1 0 . , 9 0 . , YMIN, DY) CALL NUMBER (2. , 10 .2 , 0 .14 , HI , 0 . , -1) CALL SYMBOL(4. , 10 .2 , 0 .14 , 17HCOMPOUND NAME , 0 . , 17) C PLOT THE CONTOURS CN = 0.02 CALL CNTOUR (RR, LR, THEDAA, L T , Z Z , 24, CN, 3 . , CN ) CN = 0.04 DO 200 1=1,7 CALL CNTOUR(RR, LR, THEDAA, L T , Z Z , 24, CN, 3 . , CN ) 200 CN= CN + 0.04 CALL P L O T ( 1 2 . , 0 . , -3) 23 PHI = PHI + DPHI CALL PLOTND STOP END - 187 -APPENDIX D This computer program, also written in Fortran, was used to determine complex conformation when there is free internal rotation about the carbon-donor atom bond of the complex (Eq. [2], Chapter III). Input data to this program includes: the in i t i a l value for the Eu-donor atom bond distance (R), the bond angle (f2) , and the range over which these parameters are to be varied; the experimentally observed shift ratios; the cartesian co-ordinates for each atom considered. To assist in the use and understanding of this program, several comment statements are appropriately situated throughout the program. - 188 -EXTERNAL C02AVE COMMON X ( 2 4 ) , Y(24) , Z ( 2 4 ) , R, THEDA, N, ETA DIMENSION AVE (24) ,ONCER (10) , RATIO(10) , S D (10) , HT ( 10) DIMENSION ZZ (24,24) ,THEDAA (24) , RR(24) DIMENSION NAME (6) READ 700,(NAME(I) , 1=1,6) PRINT 701 , (NAME (I) , 1=1,6) 700 FORMAT (6A4) 701 FORMAT (1H1, 6A4) C C THIS PROGRAM IS FOR FREE OR ESSENTIALLY FREE INTERNAL ROTATION C BE SORE TO TAKE NOTE OF CO-ORDINATE AND ROTATION CONVENTIONS C PI = 3.141593 C CALL PLOTS READ 1, NOMHYD 1 FORMAT(11) C NUMHYD IS THE NUMBER OF HYDROGENS WHICH SHIFT RATIOS ARE TO BE C CALCULATED THEORETICALLY AND FITTED TO EXPERIMENTAL VALUES NUJ = NUMHYD -1 C READ 101, NTHEDA,NETA, NRAD, DTHEDA, DETA, DR 101 FORMAT ( 3(12) , 3 (E10.3) ) C ALL INPUT ANGLES AND INCREMENTS ARE IN DEGREES C DISTANCES I . E . RINT AND DR ARE IN ANGSTROMS C NTHEDA = NUMBER OF INCREMENTS OF THEDA TO BE CONSIDERED (<21) C NRAD = NUMBER OF INCREMENTS OF BOND DISTANCES TO EE CONSIDERED C DTHEDA = SIZE OF INCREMENT OF THEDA TO BE CONSIDERED C DR SIZE OF INCREMENT OF BOND TO BE CONSIDERED C NOTE: NTHEDA*DTHEDA-1= RANGE OF VALUES OF THEDA SCANNED, SAME FOR C OTHER VALUES C READ 102, THEDAI, ETAI ,RINT C THESE ARE THE INITIAL VALUES FOR THEDA, PHI AND BOND DISTANCE C RESPECTIVELY 102 FORMAT(3(E10.3)) C PRINT 337 337 FORMAT(1H1, 9HVARIABLE ,5X13HINITIAL VALUE, 5X21HINCREMENTAL INCRE 1ASE ,5X21HNUMBER OF INCREMENTS /) PRINT 338,RINT,DR,NRAD,THEDAI,DTHEDA,NTHEDA 338 FORMAT(2X, 9HBOND DIST , 5 X F 5 . 2 , 1 8 X F 5 . 3 , 18X12 / 1 1X5HTHEDA ,8XF6 .1 ,2X3HDEG,15XF5 .2 , 3HDEG , 15X13 / ) THEDAI = THEDAI*PI /180. DTHEDA = DTHEDA*PI/180. ETAI = ETAI*PI /180. DETA = DETA*PI /180 . C PRINT 612 612 FORMAT (//99HSTOP A MOMENT; DO THESE NUMBERS BELOW LOOK AT ALL FAMI 1LIAR? IF NOT WE HAD BETTER QUIT HERE! ) C C C c c R = RINT AA = 0.0 - 189 -C AA IS A PARAMETER TO BE USED LATER ON IN NORMALIZING ERROR MEASURE DO 661 MM=1,NUJ READ 2, RATIO (MM), UNCER(MM),WT(MM) C WT DEFINES THE WEIGHTS ASSIGNED TO EACH RATIO FOR FINDING THE LEAST C DISTANCE VALUES. N . B . SUM OF THE WEIGHTS = 1. AA = RATIO(MM)*RATIO (MM)* WT (MM) • AA PRINT 2, RATIO (MM) , UNCER (MM) ,WT(MM) 2 FORMAT (3 ( E10.3)) 661 CONTINUE C C THE RATIOS ARE THE EXPERIMENTALLY DETERMINED SHIFT RATIOS FOR ATOM C ONE /ATOM 2; ATOM 1 / ATOM 3; ETC. C IN THAT O R D E R " " " ? ? ? C C IF NUMHYD = 6 THEN RATIOS ARE 1/2; 1/3; 1/4; 1/5; 1/6. C UNCER GIVES THE UNCERTAINTIES IN EACH RESPECTIVE SHIFT RATIO I . E . , C IF THE CALCULATED RATIO IS WITHIN UNCER OF THE EXPERIMENTAL RATIO, C THEN THE POINT WILL WARRANT FURTHER CONSIDERATION C C C THIS STATEMENT READS IN THE VALUES OF THE X , Y , AND Z CO-ORDINATES FO C EACH ATOM (MUST BE COMPUTED ELSEWHERE, I . E . COORD ETC.) CO 3 1=1,NUMHYD READ 29,X (I) , Y (I) , Z (I) PRINT 29, X (I) , Y (I) , Z (I) 29 FORMAT (3 ( E10.3)) 3 CONTINUE C C PRINT 333 333 FORMAT (1H1 ,1X,12HDISTANCE-ANG ,5X,9HTHEDA-DEG ,6X 1 , 16X ,7HEPSILON / / ) C c DO 21 LR = 1, NRAD THEDA = THEDAI DO 22 LT=1,NTHEDA HEDA = 180 . * THEDA/PI C C C ETA = ETAI DO 23 LN =1,NETA TA= E T A * 1 8 0 . / P I C C STEP TO CARRY OUT THE NUMERICAL INTEGRATION C A IS THE LOWER BOUND OF INTEGRATION, B THE UPPER C PLEASE USE NORMALIZED WEIGTING FUNCTIONS W . R . T . PHI DO 72 N=1,NUMHYD A=0. B= 2 . * P I 72 AVE (N) = FGAU08(A,E,C02AVE) / (B-A) C 8 POINT GAUSS-LEGENDRE QUADRATURE WAS USED TO CARRY OUT NUMERICAL C INTEGRATION C STANDARD SUBROUTINE U . B . C . C PRINT 73, (AVE(LS) , LS= 1,NUMHYD) 73 FORMAT ( 10 (1X,1PE11 .4 ) ) - 190 -DO 108 KB=2,NUMHYD SD(KB-1) = AVE(1) / A V E (KB) 108 CONTINUE EPS = 0. DO 553 IG=1,NUJ EPS = WT (IG) * ( (RATIO (IG) - SD (IG) ) * *2) • EPS 553 CONTINUE EPSQ = SQRT ( EPS/AA) PRINT 33, R,HEDA, TA, EPSQ 33 FORMAT ( 2 X , F 5 . 2 , 2 ( 1 0 X , F 6 . 1 ) , 10X,1PE10.3 ) 67 CONTINUE Z Z ( L R , I T ) = EPSQ 23 ETA = ETA+DETA THEDAA(LT) = HEDA 22 THEDA = THEDA* DTHEDA RR(LR) = R 21 R= R+ DR C C C PLOTTING INSERTION C C CALL SCALE{ RR , L R , 1 0 . , XMIN, DX,1) CALL SCALE (THEDAA, L T , 10 . , YMIN,DY, 1) CALL AXIS( 0 . , 0.,10HBOND DIST. , - 1 0 , 1 0 . , 0 . , XMIN, DX) CALL AXIS ( 0 . , 0 . , 10HBOND ANGLE , 10, 10 . , 9 0 . , YMIN, DY) CALL SYMBOLS* . , 10 .2 , 0 . 14 , 17HC0MP0UND NAME , 0 . , 17) C PLOT THE CONTOURS,CNTOUR IS A STANDARD SUBROUTINE AT U . B . C . CN = 0.05 DO 200 1=1,6 CALL CNTOUR(RR, LR, THEDAA, L T , Z Z , 24, CN, 3 . , CN ) 200 CN= CN + 0.05 CALL PLOTND STOP END FUNCTION C02AVE (PHI) COMMON X ( 2 ^ ) , Y ( 2 4 ) , Z ( 2 4 ) „ R, THEDA,N, ETA PI = 3. 141593 Q = (R*R + X(N)*X(N) + Y(N)*Y(N) • Z (N) *Z(N) - 2 . * R * 1 (X (N) *COS (THEDA) • SIN (THEDA) * (Y (N) *COS (PHI) • Z (N) *SIN (PHI) ) ) ) C02AVE= ( 3 . * (R-(X (N) * COS (THEDA) • SIN (THEDA) * ( Y (N) *COS (PHI) 1 + Z ( N ) * SIN (PHI)))) * *2 - Q ) / 2 (Q** (2.5) ) C TO DO A GAUSSIAN WEIGHT ABOUT PHI NOUGHT, SIMPLY ADD A GAUSSIAN C WEIGHT FACTOR, EQ(4) , TIMES THE QUANTITY ABOVE RETURN END - 191 -REFERENCES 1. F.A. Bovey. Nuclear magnetic resonance spectroscopy. Academic Press, New York (1969). 2. (a) P.R. Steiner. Ph.D. Thesis. University of British Columbia (1971), and references therein; (b) R. Burton, L.D. Hall and P.R. Steiner, Can. J. Chem. 49, 588 (1971). 3. F.A.L. Anet, J. Amer. Chem. Soc. £4, 1053 (1962). 4. (a) J. Manville. Ph.D. Thesis. 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