Nuclear Magnetic Resonance Volume 6

A Review of the Literature published between June 1975 and May 1976

By R. J. Abraham

The Royal Society of Chemistry

Copyright © 1977 The Chemical Society
All rights reserved.
ISBN: 978-0-85186-302-3

Contents

Chapter 1 Nuclear Spin-Spin Coupling By K. G. R. Pachler, 1,
Chapter 2 Experimental Techniques By D. I. Hoult, 51,
Chapter 3 Multiple Resonance By W. McFarlane and D. S. Rycroft, 67,
Chapter 4 Nuclear Spin Relaxation in Fluids By M. Holz and M. D. Zeidler, 92,
Chapter 5 N.M.R. of Paramagnetic Molecules By C. L. Honeybourne, 122,
Chapter 6 Synthetic Macromolecules By F. Heatley, 141,
Chapter 7 N.M.R. of Natural Macromolecules By G. E. Chapman, 154,
Chapter 8 The Solid State By P. S. Allen, 174,
Chapter 9 Liquid Crystals and Micellar Solutions By G. J. T. Tiddy, 207,
Chapter 10 Solvent Effects By M. I. Foreman, 233,

CHAPTER 1

Nuclear Spin–Spin Coupling

BY K. G. R. PACHLER

1 Introduction

The arrangement of material in this chapter adheres closely to the pattern developed by the previous Reporter. Section 3, which reports correlations between coupling constants and other parameters, has been added since it was found difficult to accommodate most of its contents under other headings. Some sections of a compound-oriented nature have been omitted as well as the section ‘Experimental Advances’. Sections 4 — 6 have been subdivided in accordance with the proposals made in the Introduction to Chapter 2 in Volume 4 of this series. Sub-headings to the section on long-range couplings have been dictated by the available material.

The nomenclature used in this chapter conforms as far as possible with earlier Reports on coupling constants. The term ‘long-range coupling’ is often differently understood. This report classifies couplings as directly bonded, geminal, and vicinal, or one-bond, two-bond, and three-bond couplings, respectively, and refers to all couplings over more than three bonds as long-range. ‘Through-space coupling’ is written in quotation marks since it is — in the Reporter’s opinion — an ill-defined term, the use of which should be discouraged.

Standard abbreviations and symbols have been used extensively and the reader is referred to the list at the beginning of this volume for definitions.

2 Theoretical Work

A. Ab Initio Calculations. — Sänger and Voitländer have given a detailed account of their variational calculations of coupling constants in HD using a nonsingular contact operator. The principle of the calculations has been described in a previous Report (Vol. 4, p. 68). Numerical results obtained by minimizing (i) the total second-order energy, (ii) the self-coupling energy only, and (iii) the hetero-coupling energy only deviate considerably. Pyykkö, however, has pointed out that the use of a Blinder operator, supposed to reduce the singularities of the δ-function of the FC operator, gives no improvement in the calculation of second-order energies. In particular, in the calculations of Sänger and Voitländer the hetero-coupling energy, which is proportional to J, depends on the self-coupling energy, explaining the divergence in Voitländer’s numerical results. Sänger and Voitländer have subsequently repeated their calculations with a modified ‘Ansatz’ which allowed an independent variation of short-range (nuclear dimensions) and long-range (atomic dimensions) terms. The results do not depend on the short-range part. Consistent hetero-coupling energies are obtained for all three approaches and 1J(DH) (39 Hz) agrees reasonably well with the experimental value of 42.94 Hz. Rayez-Meaume and Hoarau have reported calculations which avoid the problems associated with the δ-function of the FC operator by introducing terms which cancel the singularities arising in the first-order perturbation equation. Results on the HD molecule obtained with a minimal Slater basis set are of the right order of magnitude. Calculations with larger basis sets are in progress.

Kowalewski et al. have calculated (H,H) coupling constants for several small molecules considering the FC term only. Their perturbation calculations use eight different sets of contracted GTO’s with large configuration interaction and include all singly and doubly excited triplet states. The results are analysed in view of contributions from various occupied and virtual orbitals. Configuration interactions are important for couplings over two bonds, but have little influence on vicinal couplings. Numerical agreement with experimental values is poor. Discrepancies are attributed to the neglect of other coupling mechanisms (SD or OB) and of vibrational effects. A subsequent paper on vibrational effects in ammonia, however, has indicated these to be small though couplings varied strongly with the HNH angle. The effect of bond-angle variations has been discussed in relation to experimental results on RNH2 compounds.

Barbier et al. have calculated geminal (H,H) and (C,H) coupling constants in saturated hydrocarbons with a double-perturbation method including electron correlation. Quasi-localized orbitals have been obtained from minimal basis sets of STO’s with exponents optimized for CH4. Calculations on methane, ethane, and propane gave very similar results. Increasing the HCH angle in methane resulted in a decrease of the absolute value of 2J(HH). Introduction of electronegative substituents also decreased [absolute value of 2J(HH)] due to changes in the carbon hybridization and the two-centre integrals.

Albrand et al. have performed MO SCF calculations using contracted GTO’s of V(PP) in four conformations of P2H4. FC, SD, and OB terms have been included, the first term being dominant. The value of 1J (PP) increases rapidly from – 283.03 Hz in the eclipsed conformation to +10.92 Hz in the staggered form with a dihedral angle of 180°. The angular dependence is mainly due to changes in the FC term. Sign and magnitude of the experimentally measured coupling in diphosphine agree well with the coupling calculated for the stable gauche-conformation.

Oddershede, Jørgensen, and Beebe have proposed a self-consistent time-dependent Hartree-Fock scheme based on a Green’s function approach as an economic alternative to configurational interaction for introducing electron correlation into second-order properties. FC contributions to the coupling constant in HD, using a basis set of 14 optimized STO’s, have been calculated on various levels of approximation. The J(DH) value obtained by the SPPA method (self-consistent polarization propagator approximation) agrees reasonably well with the experimental result and the best-to-date ab initio calculation by Kowalewski et al. The remaining discrepancy is attributed to the use of a limited basis set.

Similar calculations of 1J (FH) in the HF molecule indicate that large numbers (> 55) of particle-hole excitations (equivalent to states in an SOS approach) have to be included to reach convergence in J. Introduction of electron correlation did not affect the convergence but improved the numerical value of J(FH).

Pyykkö et al. have used a spectral-density function to calculate spin-spin coupling constants. Reference 12 reports calculations for XH4 hydrides. The X — H bond is described in terms of a simple LCAO model using a hydrogen atomic orbital and solutions for the heavy atom in a Hulthén-screened Coulombic potential gave the X-wave functions. FC contributions to the coupling constant are obtained as integrals over the spectral density function. Calculated coupling constants are too small by a factor of two, but the 23-fold increase in the reduced coupling for Group IVB hydrides from CH4 to PbH4 is well reproduced.

The calculation of homonuclear (H,H) couplings has been discussed in reference 13 and values for hydrogen, acetylene, and disilicon dihydride have been given. The ground state wave functions have been obtained from normal ab initio calculations using Slater or Gaussian-type orbitals. The usual summation over excited states in the calculation of the coupling constant is replaced by an integration over a spectral density function. The method may be viewed as a continuous version of the SOS approach. The continuous nature of the calculations allows a discussion of the results in terms of relativistic contributions, importance of various excited states and completeness of the set of virtual orbitals in SOS calculations. Results obtained for the coupling constant in H2 have led to the conclusion that discrepancies between various SOS type calculations are caused by the use of an incomplete set of excited states rather than by the limited size of basis sets. This appears to confirm conclusions drawn by Oddershede et al.

B. Semi-Empirical Calculations (Excluding those on π-Electron Systems). — Ellinger et al. have reviewed and discussed in detail the calculation and interpretation of (H,H) couplings in terms of localized MO’s using a double perturbation theory.

Coupling constants obtained with the Fermi contact term formulation of Pople and Santry have been compared for several semi-empirical approaches by Barbieri et al. Directly bonded (C,H) and (C,C) couplings as well as (C,H) and (H,H) couplings over two, three, and four bonds have been calculated for a variety of compounds. The EHMO method with a particular choice of parameters was found to be superior to CNDO/2 and INDO calculations. Charge-iterated EHMO calculations gave only slightly better results and the additional computational effort does not seem to be warranted. The EH MO method has the added advantage of being readily applicable to larger molecules and organometallic compounds.

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Barfield et al. have studied the conformational dependence of geminal (H,H) coupling constants in compounds which provide models for the peptide fragment (1) (N-methylacetamide, Nα-acetylglycinamide). Detailed INDO FPT calculations of the FC coupling in both these compounds have been performed. Both carbonyl and amide groups cause angle-dependent changes of 2J(HH). The contribution from the CO group is negative, that from the NH group positive. The total variation of the coupling constants has been calculated to be approximately 8 Hz. Theoretical [absolute value of 2J] values were generally too small though substituent effects and angle dependence appeared to be adequately reproduced. Addition of a constant negative term to the calculated couplings resulted in a reasonable quantitative agreement with experimental values. The theoretical results have been expressed in explicit formulae. Equation (1) has been derived for Nα-acetylglycinamide.

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Values calculated with this equation have been compared to experimental couplings in cyclic peptides for which structural information was available. Agreement was found to be quite satisfactory. Discrepancies could not be explained by conformational averaging nor by intramolecular hydrogen bonding and are thought to be caused mainly by uncertainties in the structures. The authors conclude that despite the complexity of the physical situation, geminal (H,H) coupling constants can complement other n.m.r. parameters as a probe of peptide structure in solution.

The INDO FPT method has been used by Jaworski et al. to study the influence of ionization of a hydroxyl group on vicinal (H,H) coupling constants. 3J(HH) has been calculated for ethanol and its anion for dihedral angles φ from 0 to 360°. The results have been described in terms of truncated Fourier expansions. Orientation of the hydroxyl group (lone-pair electrons) has relatively little effect on the couplings. Ionization of the hydroxyl group increases the vicinal coupling in the range φ = 135 — 265°, but decreases it from 265 to 360°. Little change occurs for dihedral angles between 0 and 135°. Altering the C — O- bond length, which is not known precisely, does affect the numerical results but not the general features of the effect.

Vicinal (H,H) couplings in norbornane and norbornene have been calculated by Marshall et al. The theoretical [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in norbornane (2) has been found to be approximately 3 Hz larger than other cis vicinal couplings in both compounds, in agreement with experimental results. The influence of neighbouring groups on the couplings was investigated by setting corresponding overlap integrals in the off-diagonal elements of the Fock matrices equal to zero. It was shown that the endo, endo-coupling in norbornane is decreased by the interaction of the C2- and C3-methylene groups with the C7-methylene bridge. In norbornene, a decrease of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] by about the same amount is caused by interactions of the rear lobe of the exo-hydrogens with the pz orbitals of the olefinic bond. The importance of these results lies in the finding that groups several bonds from, but in close proximity to the coupling nuclei, may provide significant alternative mechanisms for the transmission of coupling.

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Barfield et al. have calculated long-range (H,H) coupling constants in 2,5-dihydrofuran (3) and phthalan (4) in terms of the INDO FPT approximation. The (H-2, H-5) couplings over two pathways and the allylic couplings in 2,5-dihydrofuran have been obtained as a function of the angle of buckle of the five-membered ring. The (H-2, H-5) couplings are positive, the allylic couplings negative. 2-Substitution by an electronegative substituent reduces the absolute magnitude of all couplings, an effect which is thought to be of electronic nature. Sign, magnitude, dependence on angle and on substitution agree satisfactorily with experimental results. Calculated (H-1, H-3) couplings in phthalan are smaller than the corresponding values in 2,5-dihydrofuran in line with experimental findings. The numerical agreement, however, is not as good as for the dihydrofuran derivatives. Benzylic couplings calculated for phthalan agree well with measured values.

Giessner-Prettre and Pullman have reported INDO FPT calculations of ortho-benzylic (H,H) couplings in three phenylethylamines of biological importance (5a, b, c) as a function of the dihedral angle τ1. The coupling constants are negative.

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Their absolute values are at a maximum for a perpendicular arrangement of the Cα — H bond and the aromatic ring and reach minima whenever the C — H bond lies in the plane of the ring. The calculated couplings vary with substitution and depend also on the angleτ2. Experimentally determined and calculated coupling constants for the three phenylethylamines have been discussed in terms of the expected conformations in solution.

Ohkubo et al. have performed TNDO MO calculations of (H,H) couplings in protonated formic acid and methyl formate as well as of (C,H) couplings in formic acid, methyl and ethyl formate, and protonated formic acid. The numerical results are too small, but experimental trends are reproduced.

2J(CH) in an O — C — C — H fragment varies in sign and magnitude as a function of the dihedral angle θ between the O — C and C — H bonds according to CNDO/2 calculations of the FC term coupling in ethanol performed by Schwarcz et al. Mutual atom–atom polarizabilities Π, which are proportional to J, are negative for θ = 0°, pass through zero at 9 — 90° and reach a positive maximum at θ = 180°. 1,1-Ethanediol shows a very similar behaviour though strict additivity of the effects of the two OH groups is not observed. The results agree qualitatively with experimental 2J(CH) values measured in carbohydrates.

All (H,H) and (C,H) couplings in 1,3-dioxole and in the gauche- and trans-conformations of bis-l,3-dioxolyl (6) have been calculated by Schaefer et al. with INDO and CNDO/2 FPT methods. The 2J(CH) couplings over single bonds in gauche– and trans-bis-l,3-dioxolyl differ considerably (Jgauche > Jtrans).

(Continues…)Excerpted from Nuclear Magnetic Resonance Volume 6 by R. J. Abraham. Copyright © 1977 The Chemical Society. Excerpted by permission of The Royal Society of Chemistry.
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