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...