Nuclear Shielding

BY R. DITCHFIELD

1 Introduction

Since the phenomenon of n.m.r. was first detected in bulk matter some thirty years ago, the subject has expanded remarkably, with the result that high-resolution n.m.r. spectroscopy is now one of the most important branches of chemical spectroscopy. In measurements of n.m.r. spectra, nuclei are essentially being used to investigate local magnetic effects in a molecular system. The local magnetic field near a particular nucleus depends on the electronic environment of the nucleus and is determined by many factors. These include the electronic polarization of remote parts of the sample, magnetic moments (nuclear and electronic) of neighbouring molecules, and intramolecular effects due to other nuclei and electrons in the same molecule. Consequently, not only has n.m.r. spectroscopy become a powerful tool for elucidating molecular structure, but it also provides a sensitive probe into various aspects of the electronic structure of molecules.

As is well-known, information about molecular electronic structure is extracted from n.m.r. spectra in terms of nuclear magnetic shielding constants, σi, and nuclear spin–spin coupling constants, Jij. Early n.m.r. studies were mainly devoted to protons, and theories were proposed to explain proton shieldings in many types of molecules. On the whole, although such theories were highly approximate, they were successful in explaining the gross trends in the values of proton magnetic shielding constants.

In the early 1960's, theoretical methods were developed to interpret shielding constants for first-row atoms. Again the theories were rather approximate but of qualitative value in rationalizing the main trends observed in the then limited experimental data. Since the late 1960's, developments in instrumentation and experimental techniques have meant that magnetic shielding data are now readily obtained for many nuclei. Although advances have been made, developments in theoretical methods have not kept pace with experimental progress. Thus experimental data are still largely rationalized using empirical relationships developed some ten or fifteen years ago. For example, changes in shielding have been correlated with the changes in charge density, the changes in electric field effects, and the changes in magnetic anisotropy which occur when a substituent is varied. Although such empirical relationships can be valuable, the fact that there is a growing body of experimental data which cannot be explained adequately in this way suggests that an accurate theoretical understanding of the factors which contribute to nuclear magnetic shielding is still lacking.

This chapter deals with articles on nuclear shielding that were published during the twelve months to the end of May 1975. As in previous Reports in this series, the emphasis is on papers containing results which either do, or may, lead to a better understanding of the phenomenon of nuclear shielding in isolated molecules. Therefore, discussion of the following topics has been excluded: experimental methods of chemical-shift measurement, the details of methods for the quantum-mechanical calculation of shielding constants, and the mechanisms by which intermolecular effects alter shielding constants. Solution phenomena, including the study of contact and pseudocontact shifts and of complex formation, are discussed in Chapter 11. During the period of writing a few journals were unavailable in the Reporter's library because they were being bound; apologies are offered to any author whose work is thereby overlooked.

2 Basic Aspects of Nuclear Shielding

A. General Theory. — It has become the practice in this series of Reports to attempt to make them as self-contained as possible. Since readers have probably become accustomed to this kind of approach, the traditions so ably established by Drs. Raynes and Mallion will be followed here. The equations derived by Ramsey relating nuclear magnetic shielding constants to electronic structure are appropriate to the case where the origin of the vector potential describing the uniform external magnetic field and the origin of the co-ordinate system are taken at the nucleus whose shielding is of interest. In this Report, the generalization presented by Raynes in which the origin of co-ordinates, the gauge origin, and the nucleus of interest are located at different points will be followed.

The approach of Raynes is conveniently discussed with reference to Figure 1. Here O is the co-ordinate origin and G is the origin with respect to which the vector potential is referred; μ is a point magnetic dipole placed at the position where the shielding is required. R, S, and rk are vectors representing the position of G, the position of μ, and the position of electron k relative to O, respectively. Using Rayleigh–Schrödinger perturbation theory and the clamped-nuclei approximation the following eight-term expression for the αβ component of the shielding tensor is obtained:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

In equation (1), the superscripts 'd' and 'p' denote diamagnetic and paramagnetic contributions, respectively. A superscript 'g' indicates those contributions which depend on the choice of gauge origin; such terms clearly vanish when R = 0. A superscript 'μ' denotes the point magnetic dipole, and contributions labelled in this way will be zero when S = 0. The expressions derived by Raynes for the contributions presented in equation (1) are given, in SI form, in equations (2) to (9).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

From these equations, it is clear that the paramagnetic contributions require a knowledge of both ground-state |0> and excited-state wavefunctions |n>. In contrast, the diamagnetic contributions depend on the ground-state wavefunction, |0>, only. In equations (2) — (9), μ0, e, and m are the...