Nuclear Shielding

BY R. B. MALLION

1 Introduction

'The last thing one discovers in writing ... is what to put first.' This remark of Pascal (Blaise, that is — not the pioneer in the field of magnetic susceptibilities!) is the one which springs most immediately to mind as I take over the chapter on 'Nuclear Shielding' from Dr. Raynes, who contributed this chapter for the first three volumes of these Reports. I can, however, start by saying that I shall adhere, as far as possible, to the structure and general format of the Report which he very satisfactorily evolved over the past three years, i.e. it will be what the earlier Reports described as 'phenomenon-oriented rather than compound-oriented'. No major change has been made for two reasons: firstly, such a policy should be helpful to regular readers who, by now, have become accustomed to Dr. Raynes' presentation, and secondly, it seemed worthwhile to capitalize, as much as is proper, on the previous Reporter's very successful experimentation in this regard.

Adopting such a scheme has, however, presented a mild dilemma; whether to repeat, almost verbatim, the basic equations required for each of the separate phenomena discussed, or whether simply to cite the relevant equations detailed explicitly in the earlier Reports. The former policy would ensure that all the requisite information were in one volume, thus obviating the necessity for readers to refer back to the earlier Reports, and the latter policy would save space. Since this Report is meant to be a digest of the literature — in fact, the sort of compendium which (to use F. A. Cotton's quotation of J. S. Waugh's description of another eminently assimilable publication) 'one can read in bed without a pencil' — I have decided, somewhat reluctantly, to trade brevity for readers' convenience, and (again following Raynes' practice) have repeated all the basic equations which are pertinent to the appropriate discussion in the various sections of the Report. There are, however, some minor changes: I prefer to discuss chemical shift anisotropy in the section headed 'Basic Physical Aspects'; n.m.r. measurements relating to the concept of 'aromaticity' are discussed with 'ring current' effects (Section 4E), since authors frequently link these two subjects in the literature; and I have not been nearly so conscientious as Dr. Raynes was about distinguishing between the various sorts of 'transmitted effects' (e.g. the so-called 'inductive effects' and what are often dubbed 'resonance effects') discussed in Section 4. Finally, the section on 'Shieldings of Particular Species' (Section 5, devoted to 19F, 31P, and 'other nuclei') will tend more to be simply lists of papers reporting data, for those works concerning mechanisms or calculation of the shielding of such nuclei will have been dealt with earlier in the appropriate sections.

According to the Reviewer's 'brief', this Report should include articles on nuclear shielding which were published between June 1st 1973 and May 31st 1974. As before, only experimental and theoretical papers relating to nuclear shielding in isolated molecules have been considered [although, actually, this restriction has been somewhat arbitrarily relaxed in Section 2 ('Basic Aspects'), where I have wanted to discuss the effects of pressure and anisotropic media]; as was the case in the previous Reports, this policy precludes examination of purely experimental techniques of chemical shift measurement (covered in Chapter 4), the quantum-mechanical details of shielding-constant calculations, the mechanisms of intermolecular shielding effects (thus excluding consideration of all solution phenomena as well as the study of contact and pseudo-contact shifts and of weak complex formation, all of which are dealt with in Chapter 10). Studies in the nematic phase have also been excluded, except when such investigations have led explicitly to information concerning chemical shift anisotropy.

Some attempt has been made to include coverage of certain foreign-language journals; I hope, in particular, that the literature in the French language has been covered as adequately as that in English; I must, however, apologize in advance to writers in the German language for a less than satisfactory review of their work; and papers in Russian (unless available in translation or summarized in Chemical Abstracts) have had, regrettably, to be omitted from consideration entirely. Finally, during the period of writing, some journals were unavailable in the Reporter's library because they were being bound; apologies are, therefore, offered to the authors of any papers which are, thereby, overlooked.

2 Basic Aspects of Nuclear Shielding

A. General Theory. — Ramsey's familiar 'two-term' expression for the component, σαβ, of the shielding tensor of a given nucleus,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where the superscripts 'd' and 'p' denote 'diamagnetic' and 'paramagnetic', respectively, is valid only for the very special case in which the gauge origin (i.e. the origin of the vector potential due to the uniform, external magnetic field) and the origin of co-ordinates coincide at the nucleus whose shielding is being calculated; a four-term expression that allows for arbitrary choice of the gauge origin but still requires the position of the nucleus of interest to be the origin of co-ordinates has been detailed by Raynes.' In last year's Report, Raynes gave a yet more general version of the Ramsey equation, applicable when the co-ordinate origin, the gauge origin, and the nucleus in question may be different points; for reference purposes these expressions are now repeated here.

The formulae which follow should be studied with reference to Figure 1. The origin of co-ordinates is denoted O, and the gauge origin is at G, related to O by the vector R. An infinitesimal 'test' dipole of moment μ is then placed at the pointf at which it is required to calculate the shielding (which point may, or may not, be the position of a nucleus). The kth electron is, at any given time, displaced from O by the vector rk; the nuclei are assumed to be fixed. An eight-term expression then results:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

In this expression, calculation of the diamagnetic terms (with superscript 'd') requires knowledge only of the unperturbed ground-state wavefunction, whereas the paramagnetic terms (superscripted 'p') are also a function of the excited-state wavefunctions (and are, thereby, that...