Nuclear Shielding

BY W. T. RAYNES

1 Introduction

Three alternative procedures suggest themselves for a review on the subject of nuclear magnetic shielding in molecules. First, one could consider the various chemical and physical influences (e.g. the inductive effect, conjugation, magnetic anisotropy) which are believed to be responsible for the differences in shielding between different compounds. These could be discussed in turn, each one being illustrated by examples drawn from the shieldings of all species of magnetic nuclei in a wide range of compounds. Secondly, one could consider the shieldings of a particular nuclear species (e.g. the proton), illustrate the shielding changes that occur along several series of compounds containing that species of nucleus, and interpret these changes in terms of varying contributions from one or more of the above-mentioned phenomena. This would then be repeated in turn for other species of nucleus. The third approach involves selecting a particular compound (e.g. C6H5NO2) and showing how each of the chemical and physical influences makes its own contribution to the shielding of all the nuclei in the compound. This would then be repeated in turn for other compounds.

Of these procedures, it is traditionally the second that has been adopted for dealing with observed shieldings in a wide range of compounds. The third procedure is seldom used, partly because much of the information required (e.g. carbon, nitrogen, and oxygen shieldings) has been unavailable, at least until very recently, and partly because it is obviously unrealistic except when dealing with a group of closely related compounds. Since the present review is 'phenomenon-oriented' rather than 'compound-oriented' the first procedure will, for the most part, be adopted. However, because many workers tend to study the shieldings of only one nuclear species — presumably because of personal interest or limited experimental facilities — a brief survey of recent work in terms of individual species of nuclei has also been included.

This review covers work that appeared in the literature between July 1st 1970 and June 30th 1971. However, since this is the first in the present review series, some important papers appearing in the first half of 1970 will also be discussed. Because of the vast abundance of publications on nuclear shielding, some restrictions have had to be imposed. For instance, no space has been given to experimental aspects, and the details of wave-mechanical calculations have, for the most part, been excluded. The ways in which nuclear shieldings can be changed by intermolecular effects (e.g. dispersion forces, reaction fields) are omitted here but are discussed in Chapter 9. The main concern in this chapter is the interpretation of recent work on observed shieldings of isolated molecules in terms of the various physical and chemical influences which chemists have found to be useful for their understanding. A further omission, requiring the Reporter's apologies, is the discussion of papers in foreign language journals.

Two conventions that are used in this chapter will be stated at this point. For the sake of economy, most numerical values of shieldings and chemical shifts are given without the appellation p.p.m. (parts per million). Secondly, the convention has been adopted that the chemical shift is positive if the nucleus under consideration has a more positive shielding constant than the reference nucleus. The reason for this choice will be clarified in Section 2.

2 Chemical Shift Scales

It is appropriate to commence with a brief discussion of chemical shift scales — a topic which has aroused some controversy. The aim here is not to approve particular choices of reference for particular nuclei but to deal with two general points which need to be stressed. A more detailed review of the definition of chemical shifts has been given by Rummens.

In defining chemical shifts there are two possible starting points, which may be termed 'theoretical' and 'experimental'. The theoretical approach starts with a molecule in a uniform magnetic field B. The field Blocal at a selected point in the vicinity of a molecule is different from B because of the small field B' arising from the induced motions of the electrons. Thus:

Blocal = B – B' (1)

The negative sign is placed here explicitly so that one may refer to the phenomenon as 'magnetic shielding', as any point magnetic dipole (of very small magnitude) placed at the selected point would be shielded from the full effect of B by the influence of the induced electronic motions. We are implying that B' is positive but, of course, this does not exclude the possibility of a negative value of B', in which case the phenomenon is termed 'antishielding'. Provided that the field B is not too large, B' is proportional to B, so that:

B' = σ B (2)

where σ is the magnetic shielding constant. The value of σ obviously depends on the location of the selected point. (It also depends, in general, on the direction of B relative to axes fixed in the molecule. However, no loss of significance for the arguments given below occurs if we imagine the molecule to be tumbling freely in the field with the point-dipole held in a fixed position relative to molecule-fixed axes.) With the negative sign given explicitly in equation (1), it follows that σ is positive when shielding occurs and negative when antishielding occurs.

In practice, one is almost always interested in the value of σ at the site of a particular magnetic nucleus in the molecule. For these special positions σ is called the nuclear (magnetic) shielding constant. These nuclear shielding constants are, of course, fundamental physical properties of a molecule and are, therefore, the quantities which are obtained from quantum-mechanical calculations. From the standpoint of chemical theory, however, it is often the difference between the nuclear shielding constant in the compound of interest and that in some suitable reference compound (σref) with which one is concerned. This quantity δth is the chemical shift and is defined by equation (3). There are three points to be noted here. First, a definition of δth as being σref – σ would be unsatisfactory: as one would say in everyday language, it

δth = σ – σref (3)

would be 'illogical'. Secondly, the choice of reference depends on the particular nucleus in the particular compound of interest. For instance, the proton chemical shifts of the halogen derivatives of methane would be referred to the protons of methane. Again, the nitrogen chemical shifts of the substituted derivatives of pyridine would be referred to the nitrogen of pyridine. The chemical shifts of the protons of the methyl halides relative to tetramethylsilane in the first example, and the chemical shifts of the nitrogen nuclei of the substituted pyridines relative to the nitrogen of, say, Me4N+ in the second example, would be quantities devoid of theoretical interest. Thirdly, our definition of δth is in no way dependent upon the way in which chemical shifts are measured or, indeed, upon the very existence of nuclear magnetic resonance.

The experimental approach to defining the chemical shift starts with the observation of signals on an n.m.r. spectrometer. Two experimental procedures are used; 'frequency-sweep', in which the field is held at a fixed value and the frequency is varied through resonance, and 'field-sweep', in which the frequency is held fixed and the field is varied through resonance. For the frequency-sweep experiment one defines the chemical shift δv of the nucleus of interest from the reference nucleus by equation (4), where v and vref

δv = (v – vref)/vref (4)

are the frequencies required for resonance of the nucleus of interest and of the reference nucleus respectively. From the resonance condition of equation (5),

v = γB(1 – σ)/2π (5)

where γ is the magnetogyric ratio, we see that the definition δv becomes that given by equation (6), where we have assumed that the nucleus of interest

δv = (σref – σ)/(1 – σref) (6)

and the reference nucleus are of the same species. If these two nuclei are different then equation (6) is replaced by one involving γ and γref.

For the field-sweep experiment, the chemical shift dB is defined by equation (7), where B and Bref are the fields required for resonance of the nucleus of

δB = (B – Bref)/Bref (7)

interest and the reference nucleus respectively. Using the resonance condition of equation (5) this definition becomes equation (8), where, again, it has been

δB = (σ – σref)/(1 – σ) (8)

assumed that the nucleus of interest and the reference nucleus are of the same species.

The difference between the two experimental definitions, which is a difference of sign, will be discussed first. Which definition is preferable? In the early days of n.m.r. the definition δB was used exclusively. More recently, authors have been using δv. Since the concern here is with a definition, the answer to the question is a matter of opinion, based on physical intuition. I argue here in favour of the use of δB over δv. On the δB scale a nucleus that is highly shielded has a high chemical shift; whereas on the δv scale it has a low chemical shift. It runs counter to physical sense, for instance, that the protons of methyl fluoride be given a higher chemical shift than those of methane when, in fact, it is the protons of methane that are the more highly shielded. (One could define a temperature scale in which the boiling point of water was 0° and the freezing point 100°. However, this has never been done.) Another advantage of δB over δv is the near identity of the definitions of δB and δth on account of the smallness of σref. However, here it should be pointed out that with increasing accuracy in chemical shift measurement, δB and δth will cease to be equivalent in practice. For the important field of proton resonance, in which tetramethylsilane (TMS) is the most commonly used reference, our arguments favour the 'τ-scale' to the 'δ-scale'.

In a very recent paper the definition δv has been suggested on the grounds that 'most of the newer instruments for multinuclear studies use a frequency sweep, so that a scale with chemical shifts positive to increasing frequency seems logical'. Still more recently, Brey has supported δv on essentially the same grounds with the words 'such a convention seems absolutely necessary to maintain the sanity of anyone who tries to operate a modern spectrometer using a heteronuclear lock or applying internuclear double resonance'. To the present author there seems no real difficulty in using a chemical shift scale in the laboratory that is suitable for the purposes of measurement but reporting results on a scale most suitable for theoretical discussion. After all, molecular spectroscopists have for years measured their absorption or emission lines on a wavelength scale but reported their results on a frequency scale. (A frequency scale is necessary here since one is directly interested in energies and energy differences whereas in n.m.r. spectroscopy one is interested in shieldings and shielding differences.) Thus in reply to Becker and Brey one may pose the argument that if a defined scale of chemical shifts is to be set up, then the requirement that increased chemical shift should parallel increased shielding should take precedence over one based upon the particular fashion in which chemical shifts are measured. The former is absolute whereas the latter could conceivably change with time, as fashions sometimes do.

The second point to be considered is to question the need, in the long term, for any kind of chemical shift scale based on a chosen reference nucleus. The nuclear shielding constant is the molecular parameter in which one is interested. The experimental determination of the chemical shift using either definition δv or δB is only a step on the way to determining σ. What is required with some urgency is the direct determination by experiment of σ for some suitable chemical compound which would then serve as the primary reference standard. The best available value at present is for water at 25 °C, which has a proton shielding constant (corrected for the bulk susceptibility of the water):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

Obviously, considerable improvement in precision is called for. However, once a precise value for water or another chosen compound has been obtained it will be possible for accurate and precise values of the shielding constants of the secondary reference standards used in experiments (e.g. TMS at a given concentration in carbon tetrachloride) to be found. (Another quantity of particular importance, so far experimentally uninvestigated, is the temperature dependence of the shielding constant for any substance.) What is being argued for here is what one might call the 'σ-scale' i.e. the reference nucleus is any nucleus stripped of its electrons, in which case, of course, σref is zero.

3 Basic Aspects of Nuclear Shielding

A. Magnetic Field-dependent Chemical Shifts. — In an important paper Ramsey has examined the possibility of observing magnetic field-dependent nuclear shielding. For very large applied fields equation (2) will no longer adequately express the dependence of B' on B, since σ is itself field-dependent. For a particular component σαβ of the nuclear shielding tensor we would have to write (in standard tensor notation):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

where σ(0)αβ is the value of σαβ for low values of B (i.e. the usual shielding constant) and [??](2) is a tensor which allows for the initial change in shielding when the field is large. The tensor [??](1) has been omitted from equation (10) since all of its components are zero, as is required by the independence of the shielding to the sign of B.

Let it be assumed that the molecule is tumbling rapidly in the external field. Only averages over all orientations need be considered, so that equation (10) becomes equation (11), where σ(0) and σ(2) are obtainable from the

σ = σ(0) + σ(2) B2 + ... (11)

components of [??](0) and [??](2) respectively. For the observation of the chemical shift of a given nucleus from that of a reference nucleus, equation (11) gives equation (12), where δ(0) is the chemical shift at low field. It can be seen that if

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

δ(2) – δ(2)ref is large enough, or if the precision of the method of determining δ is sufficiently high, it will be possible to obtain different values of δ at, say, 100 MHz and 300 MHz.