Nuclear Magnetic Resonance Volume 9

A Review of the Literature published between June 1978 and May 1979

By G. A. Webb

The Royal Society of Chemistry

Copyright © 1980 The Royal Society of Chemistry
All rights reserved.
ISBN: 978-0-85186-960-5

Contents

Chapter 1 Theoretical, Physical, and Inorganic Aspects of Chemical Shifts By Cynthia J. Jameson and Joan Mason, 1,
Chapter 2 Organic Applications of Chemical Shifts By D. W. Jones, 25,
Chapter 3 Theoretical Aspects of Spin–Spin Couplings By K. G. R. Pachler, 49,
Chapter 4 Applications of Spin–Spin Couplings By D. F. Ewing, 68,
Chapter 5 Nuclear Spin Relaxation in Fluids By H. Weingärtner, 101,
Chapter 6 Solid State N.M.R. By S. M. Walker, 128,
Chapter 7 Multiple Resonance By W. McFarlane and D. S. Rycroft, 153,
Chapter 8 Natural Macromolecules By D. B. Davies, 182,
Chapter 9 Synthetic Macromolecules By F. Heatley, 204,
Chapter 10 Conformational Analysis By F. G. Riddell, 222,
Chapter 11 Oriented Molecules By C. L. Khetrapal and A. C. Kunwar, 245,
Chapter 12 Heterogeneous Systems By W. Derbyshire, 256,
Author Index, 308,

CHAPTER 1

Theoretical, Physical, and Inorganic Aspects of Chemical Shifts

BY CYNTHIA J. JAMESON AND JOAN MASON

1 Introduction

As the convenience and availability of multinuclear n.m.r. spectrometers have increased, the number of papers dealing with applications of the chemical shift has increased to the point where it seems reasonable to ‘separate the applications to organic systems from the inorganic systems. Thus, this Chapter is on the theoretical, physical, and inorganic aspects of chemical shifts, whereas applications to organic systems are treated in Chapter 2. This review covers papers published in the period June 1978 to May 1979. During this period reviews pertinent to the topics covered in this Chapter have appeared.

2 Theoretical and Physical Aspects of Nuclear Shielding

A. The Nuclear Shielding Tensor and the Question of Gauge Origin. — The nuclear magnetic shielding of a nucleus in a molecule in a uniform magnetic field is described by a second rank tensor, [??], whose components are defined by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where E is the total electronic energy in the presence of the nuclear magnetic moment, [??], and the uniform magnetic induction, [??].

The calculation of the components of the nuclear magnetic shielding involves the evaluation of the matrix elements of operators containing [??]i, (the position vector of the ith electron with respect to the chosen origin of co-ordinates) and [??]i × [??]i (the angular momentum of the ith electron with respect to the origin of co-ordinates). Of course, the nuclear magnetic shielding itself is independent of the choice of origin. Since approximate wavefunctions are used in numerical calculations, the calculated parts of σαβ, which may be denoted by σαβd and σαβp (the diamagnetic and paramagnetic terms), each of which is origin dependent, lead to a sum which is not invariant with respect to the choice of origin. In practical terms, the problem of gauge origin has led to alternative approaches to the calculation of nuclear magnetic shielding. These approaches have been discussed in previous reports and will not be repeated here.

B. Ab Initio Calculations of the Shielding Tensor. — There have been a great number of ab initio calculations of the magnetic shielding of various nuclei belonging to the first two rows of the Periodic Table from 1H to 19C, most of which have been reviewed in previous volumes. However, there have been no ab initio calculations of the full shielding (diamagnetic and paramagnetic terms) for heavier nuclei, probably because the large number of basis functions makes the costs prohibitive. An attempt to reduce the computational effort by separating the inner shells from the molecular calculation and the use of a pseudo-potential in the calculation of the valence shell to represent the overall repulsive effect of the inner shells have been reported by Ridard, Levy, and Millie. Their method employs the following steps: (i) compute the all-electron wavefunction of the free atom and the contribution of the inner shells to σd, (ii) compute the valence shell of the molecular system by means of the pseudo-potential and the molecular two-electron repulsion integrals; then orthogonalize the valence orbitals with respect to the inner shells of the free atom and compute the molecular matrix elements of LN and LN/r3N, (iii) compute σd and σp for the valence shell and (iv) add to the σp of (iii) the contribution of the inner shells of the free atom calculated in (i). This computational method was applied to the magnetic shielding of 29Si, 31P, 33S, and 35Cl in SiH4, PH3, H2S, and HCl. In their attempts to explore the method, the basis set used to describe the valence shell was not optimized (when the inner shells are not present it is possible to use a larger basis set for the valence shell). Nevertheless, the results are very encouraging. The error in the method relative to that of an all-electron molecular calculation for σd was less than half a percent. For σpthe error is much larger (18% in PH3), which could easily be reduced to half by improving the basis set for the valence shell. With the increasing interest in shielding of heavy nuclei, it is worthwhile to explore this method of calculation further.

C. Semi-empirical Calculations. — The ring-current concept has been used extensively to calculate 1H chemical shifts of cyclic conjugated hydrocarbons (see also Chapter 2, Section 2D). It has been shown, however, that the ring currents contribute only about half of the observed deshielding in benzene. The remaining part has been attributed to local anisotropic shielding effects. The combination of these effects appears to provide an explanation of the observed chemical shifts. During this review period, special attention has been paid to systems containing triple bonds. Vogler calculates the sigma core and pi contributions to the shielding separately, using the mean excitation energy approximation, and compares the calculated values with experimental proton shifts in acetylene, ethylene, and benzene. Calculated and experimental results for 42 different hydrocarbons are available as supplementary material. Agarwal and McGlinchey continue their calculations of local anisotropic contributions to proton shielding in pi systems by using the classical analogy of a current circulating in a loop of wire and incorporating the experimental 13C shielding components. Their recent application of this approximate method to an alkyne is displayed in the form of an isoshielding contour map. It is not possible to assess agreement with experiment since the rest of the contributions to the chemical shielding (due to the sigma framework) were not calculated.

The semi-empirical method used by Ellis and co-workers has been reformulated, in large part to use a new set of empirical molecular-orbital parameters chosen in a least-squares procedure so as to fit a set of experimental 13C shifts of some model compounds. The parameters were tested on a wide variety of hydrocarbons. Other semi-empirical calculations using extended Huckel, INDO, CNDO/S, and MINDO/3 have been reported.

D. Anisotropy of the Shielding Tensor. — Components of the shielding tensor have become more easily available since the development of high-resolution solid-state n.m.r. techniques. Using the cross-polarization technique of Pines, Gibby, and Waugh, all the 13C chemical shielding tensors in acetophenone and in p-xylene have been determined relative to an external reference of liquid benzene. Two studies which are of special interest are the first applications of n.m.r. to the study of matrix-isolated molecules reported simultaneously by Kohl, Semack, and White and by Zilm, Conlin, Grant, and Michl. In the former case, the proton spectrum of HC1 monomer and HC1 dimer were observed and the geometry of the HCl dimer was found to be in agreement with the infrared data, but the anisotropy of the argon environment was found to be greater than anticipated from the i.r. line-widths. In the second experiment the components of the 13C shielding tensor were obtained for matrix isolated ethylene, σ11 = 238±2, σ22 = 126±2, σ33 = 29±2 p.p.m. to high frequency of CH4, in fairly good agreement with the ab initio results using a large basis set. These experiments demonstrate that solid-state n.m.r. spectra of matrix-isolated species offer a means of acquiring chemical shielding anisotropies in small molecules for which the most accurate calculations can be done.

The largest 1H shielding anisotropy ever found has been reported for zirconium chloride monohydride; 102.6 p.p.m. Since the hydrogen is believed to insert into the metal–metal double layer, the observed anisotropy may be considered a Knight shift anisotropy. In [H2Os3(CO)10], [H4Os4(CO)12], and [H4Ru4(CO)12], the bridging protons were found to have a chemical shift anisotropy of less than 30 p.p.m. As expected, the 1H anisotropy of CaH2, SrH2, and BaH2 was found to be small. The relative orientation of the 1H chemical shift tensor principal axes in CCl3COOH dimer with respect to the molecular frame has been determined. The components of the 31P chemical shift tensors in single crystals of barium diethylphosphate and in the urea-phosphoric acid complex as well as the anisotropy of the 113Cd shielding in powder samples of CdCl2, CdBr2•4H2O, CdS, and CdSe have been determined.

When studies are carried out on partially oriented molecules in a liquid crystal, there is always some uncertainty associated with the results, apart from the difficulties associated with determining the order parameter. The anisotropy measured in a liquid-crystal environment is not necessarily the intrinsic anisotropy in the isolated molecule. It includes some contributions induced by the local fields generated by the liquid-crystal environment. To some extent this is true of measurements in solids and in matrix-isolated species too. An experiment to demonstrate just how large the anisotropy induced by a liquid-crystal environment might be was carried out by Fujiwara and Reeves. Spherically symmetric as an isolated ion, Cs ion when placed in lyophilic mesophase showed an induced anisotropy in the Cs shielding, varying from – 1 to 2 p.p.m. (relative to zero for the isotropic part) with the expected 3 cos2 θ – 1 dependence (where θ = the angle between the mesophase director and the magnetic field direction).

E. Magnetic and Electric Field Effects. — The electric-field and magnetic-field dependence of nuclear shielding has been discussed previously. For electric fields of small magnitude, it is convenient to expand the component σαβ of the shielding tensor as a power series in the electric field F

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where σαβ(0) is the value of the component in the absence of the field and the coefficients σαβγ(1) and σαβγδ(2) belong to tensors σ(1) and σ(2) which determine respectively the linear and quadratic field dependence of the shielding. In general there are nine components σαβ. The nuclear site symmetry determines the number of independent non-vanishing components. These have been previously tabulated by Buckingham and Malm. If a molecule is placed in a uniform electric field, the site symmetry of some or all of the nuclei may be reduced so that the non-vanishing independent components σαβγ(1) for a given γ are not necessarily the same set as the σαβ(0). Raynes and Ratcliffe tabulate the non-vanishing components of the tensors σ(1) and σ(2) for various nuclear site symmetries.

The effects of strong external fields on n.m.r. spectra are two-fold: an alignment effect and the effects due to the dependence of the n.m.r. parameters σ and J on the field. We are concerned here primarily with the dependence of σ on external electric and magnetic fields. However, it is noteworthy to mention the observation in high-resolution n.m.r. of a magnetic-field-induced alignment of molecules. The effect on n.m.r. spectra of the partial alignment of polar molecules in an electric field is well known. Recently the effect on the 2H n.m.r. of partial alignment of the molecules pyrene and naphthalene in solution, induced by the interaction of the anisotropy in the molecular susceptibility Δχ and the applied magnetic field, has been detected. The incomplete averaging of (3 cos2 θ – 1) over all orientations leads to splitting of the peaks by the quadrupole coupling constant. The splitting is expected to be proportional to ΔχB20 although this could not be verified. The splittings were observed at 9.3 T with a 400 MHz spectrometer.

The possibility that the magnetic-field dependence of the nuclear magnetic shielding for some substances could be observed by high-precision n.m.r. experiments in very strong magnetic fields was first pointed out by Ramsey in 1970. The magnetic field dependence of σ can be expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

The odd powers of B vanish because the magnitude of the shielding must be independent of the direction of the magnetic field. Ramsey estimated the magnitude of τ/σ and suggested the experimental verification of the magnetic-field dependence of the shielding in cobalt compounds. Since that time n.m.r. spectrometers have shown a trend to higher field strengths and currently spectrometers operating at 600 MHz for protons are in use. An approximate calculation of τ for diamagnetic cobalt(m) complexes using only the excited states arising from the (t2g)5(eg)1 configuration was carried out by Doddrell, Pegg, and Bendall. They obtain τB20 values of – 0.01 to – 0.09 p.p.m. for a magnetic field corresponding to a 1H frequency of 720 MHz. In other words, they estimate an effect which is opposite in sign to σ(0). In a footnote they report having observed experimentally a field-dependent chemical shift for 59Co of the order of 1 — 3 p.p.m. in the same direction as σ(0) upon changing the 59Co resonance frequency from 3.4 to 21.3 MHz. The discrepancy between the calculated and the experimental values was not explained. An ab initio calculation of the magnetic-field dependence of the related molecular property magnetic susceptibility, formulated by Riley and Raynes, was carried out for H2, HF, and BH by Zaucer and Azman. Results indicate a ratio of the order of 10-6 for B0 = 6.26 T for the diamagnetic molecules.

Ideally an experiment demonstrating the magnetic-field dependence of σ should be precise and show an unequivocal quadratic dependence on the field. The frequency separation between two narrow single peaks in a solution containing both species should be measured in several spectrometers covering a range of B0 values. The chemical shift plotted against B20 should give a straight line with non-zero slope. A heavy nucleus with a large range of chemical shifts would be the best choice. A related electronic property which has a similar magnetic-field dependence is the atomic hyperfine constant. In an elegant experiment reported during this review period, a shift in this constant due to the distortion of the atom in an external magnetic field has been observed for the first time. The hyperfine frequency of 85Rb atoms plotted as a function of the square of the magnetic field is found to be nicely fitted by a straight line with a slope corresponding to a shift of 93 Hz at 7.5 T out of a total hyperfine frequency of 3.035 GHz. Fields of 0.2 to 7.5 T were used.

(Continues…)Excerpted from Nuclear Magnetic Resonance Volume 9 by G. A. Webb. Copyright © 1980 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.