CHAPTER 1
Nuclear Shielding
BY W. T. RAYNES
1 Introduction
'The most important single parameter to be derived from the n.m.r. spectrum is the chemical shift.' This contention, possibly controversial even when published in 1959, became, one suspects, increasingly less acceptable to the majority of n.m.r. spectroscopists during the course of the nineteen-sixties. However, the introduction of new techniques for signal enhancement in the past few years has meant that shielding data, in the form of proton and fluorine chemical shifts from the peripheral regions of molecules, can now be supplemented by phosphorus, nitrogen and, above all, carbon chemical shifts which yield, in principle, a much more intimate knowledge of electronic distributions in the interior of molecules. This, coupled with the enticing prospect of large amounts of new information on nuclear shielding and nuclear shielding components in solids, provides additional support for those who are inclined to support the above quotation.
The structure of the present Report does not differ in essence from that of Volume 1 of the present series. As before the emphasis will be on reported work in the review period (July 1st 1971 to May 31st 1972) which either leads to, or may lead to, an improved understanding of the phenomenon of nuclear shielding in isolated molecules. Therefore, as with last year's Report, no space has been devoted to any of the following topics: 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 can alter shielding constants. This third restriction forces the exclusion of all solution phenomena including the study of contact and pseudocontact shifts and of weak complex formation. These topics, however, are covered in Chapter 10.
The number of papers presenting new carbon chemical shift data during the review period — about eighty — is more than double the number referred to in Volume 1. In addition the number of papers with new phosphorus chemical shift data has increased to twenty-six — one more than that for fluorine — with nitrogen not far behind. With this large increase for C, P, and N it has been decided to limit the number of references to proton chemical shift studies (which total about two hundred and fifty) only to those of particular value for illustrating proton shielding mechanisms or to those of compounds of particular interest such as the annulenes, substituted derivatives of benzene, etc.
The following two conventions, used in last year's Report on nuclear shielding, have been adopted in subsequent sections of this Report. N.m.r. chemical shifts and shielding constants are occasionally given without the appellation p.p.m. (parts per million). Where substituent effects are considered and the chemical shift is referred to the unsubstituted compound, the shift has been given a positive sign if the nucleus under investigation has a higher shielding constant in the substituted compound than in the unsubstituted compound. During the period in which the present article was being written, a small number of journals were inaccessible to this reporter. Therefore, apologies must be offered to some authors for omission of any reference to their work.
2 Basic Aspects of Nuclear Shielding
A. General Theory. — Placing the origin of co-ordinates at the nucleus of interest and the origin of the vector potential of the uniform external magnetic field at a point having position vector ro from the co-ordinate origin, we obtain for the component σαβ of the nuclear shielding tensor the more general form of Ramsey's equation
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
The terms on the right-hand side of equation (1) are defined as follows:
[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)
In equations (2) — (5) the symbols μo, e, and m denote respectively the permeability of free space, the electronic charge, and the electronic mass; rk is the position vector of the k'th electron from the nucleus of interest; Wn represents the energy of the n'th excited state; pk denotes the linear momentum operator of the k'th electron; lk(=rk × pk) is the orbital angular momentum operator of this electron and the convention of summation over repeated suffices is used. The prime on the summations in equations (4) and (5) denotes a summation over all values of n except n = 0, including the continuum of excited states. σαβ is the substitution tensor (= 1 if α = β, = 0 if α ≠ β) and σβγδ is the alternating tensor [= 1 if (βγδ) is an even permutation of (xyz), – 1 if (βγδ) is an odd permutation of (xyz) and 0 if any two of (βγδ) are identical]. If ro = 0, equation (1) reduces to the familiar two-term expression [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] with the 'conventional' diamagnetic and paramagnetic terms. The terms all and all both dependent upon the origin of the vector potential, i.e. upon the gauge choice — hence the superscript g.
During the review period it has been pointed out that the nuclear shielding tensor is not, in general, symmetric. This means that the component σαβ will not, in general, be equal to σβα. From equation (4) the shielding σDαβ is obviously not necessarily equal to σDβα. However, equation (2) makes clear that σdαβ is always symmetric so that the 'conventional' diamagnetic part of the shielding tensor can be fully specified by six components. For a gauge choice away from the nuclear site of interest we see that σdgαβ and σpgαβ also not necessarily equal to σdgβα and σpgβα respectively. Buckingham and Malm divide the shielding into the sum of an isotropic part, a traceless symmetric part, and an antisymmetric part. Thus
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
where
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
They show that in deciding the number of independent components of the shielding tensor one must consider the symmetry appropriate to the particular nuclear site, and they give a table listing the number of independent components for the shielding tensor of nuclei located at sites possessing any of the possible kinds of symmetry. For a hydrogen atom in the presence of a uniform electric field and a uniform electric field gradient, Buckingham and Malm present expressions for the components of the proton shielding tensor which show the existence of non-zero values for the antisymmetric part of σ(a)αβ some of the components.
Weisenthal and de Graaf have shown that the quantum-mechanical expression for the diamagnetic susceptibility of neutral atoms and molecules can be expressed in a form that is independent of gauge choice ('gaugeless') even when approximate zero-order wavefunctions are used. This involves choosing the origin of co-ordinates for the electrons at the centre of the nuclear charge of the molecule. Comments on this approach have been made by Moss and Perry who show why the theory is only applicable to neutral species. The method of Weisenthal and de Graaf would appear to be applicable to Ramsey's equation for nuclear shielding although this application has yet to be made.
B. Basic Physical Aspects. — In this subsection will be discussed the results of a number of experiments which have a direct bearing on fundamental aspects of the nuclear shielding phenomenon.
In the previous Report a best experimental value for the proton shielding constant of liquid water (corrected for the bulk susceptibility effect of the water) was given. This value was
σ(H2O, 25 °C) = 25.97 (±0.30) p.p.m. (10)
A considerable improvement on this value can now be reported following the work of Winkler et al., who have measured very precisely the ratio of the magnetic moments of the electron and the proton by the simultaneous observation of an electronic and a nuclear magnetic transition in atomic hydrogen. By combining their result with that of Lambe who studied the n.m.r. frequency of protons in a spherical water sample, they give (presumably for 25 °C)
σ(H2O) = 25.64 (± 0.07) p.p.m. (11)
which is both substantially different from and more precise than the older value. To obtain the proton shielding constant of molecular hydrogen Winkler et al., employ a reported chemical shift
σ(H2O) – σ(H2)= -0.6(±0.3) p.p.m. (12)
thereby obtaining a value of 26.2 (±0.3) p.p.m. for the H molecule. Considerable improvement in precision is possible if one makes use of more recent results, viz.
σ(H2O, 1 q. 30°C) – σ(H2O, gas) = – 4.315 p.p.m. (13)
σ(H2O, gas) – σ(CH4, gas) = – 0.56(±0.02) p.p.m. (14)
σ(CH4, gas) – σ(H2, gas) = 4.35(±0.15) p.p.m. (15)
This leads to
σ(H2, gas) = 26.17(±0.17) p.p.m. (16)
A precise value of the shielding constant of molecular hydrogen is obviously of particular importance for theoretical reasons. As put by Winkler et al., 'it appears that the topic of chemical shifts in simple molecules is ripe for a more detailed elaboration'. From a purely experimental point of view the important result here is that of equation (11) which shows that precision of measurement of shielding constants is now nearly as high as that for the measurement of chemical shifts. The significance of this is that only a little more increase in precision will mean that nuclear magnetic shielding constants in any molecule can be determined precisely. However, as pointed out by Winkler et al., water is not a very good choice for a primary standard largely because of the high sensitivity of the shielding to slight changes of temperature. A further calculated result obtained by Winkler et al. is that for the shielding of an isolated hydrogen atom. With higher-order corrections included the proton shielding constant is 17.733 p.p.m. which is a little less than the 17.750 p.p.m. often quoted.
Cade and Ramsey have obtained values of the high-frequency part of the nuclear shielding in the lower rotational levels (J = 1 and 2) of the ground vibrational and electronic states of HD and D using the molecular-beam magnetic resonance method. The high-frequency contribution (i.e. σp) can be calculated from the electronic part of the spin-rotation interaction constant. Again a much increased precision is obtained. For the J = 1 state of HD they find for the proton σp = –5.65 (±0.08) p.p.m. and for the deuteron σp = – 5.61 (±0.08) p.p.m. as compared with earlier values of –5.96 (±0.30) p.p.m. and -5.91 (±0.30) p.p.m. respectively. Such results as these provide a valuable check on the results discussed in the previous paragraph once a good enough value for σdhas been obtained.
In the calculation of changes in molecular properties occurring upon isotopic substitution it is unusual to take into account changes in the static electric quadrupole moment of the substituted nucleus. Thus, for instance, in calculating the proton and deuteron shielding constants of HD one would normally assume them equal for stationary nuclei and ignore any effect of the deuteron quadrupole moment on the electronic wavefunctions. The validity of this assumption — especially for heavier nuclei for which the K-shell wave-function will be the most easily changed by the presence of an electric quad-rupole moment and for which the K-electrons provide a large diamagnetic shielding — is brought into question by an experimental result of Sen et al. who have detected an effect on the angular distribution of K-shell X-rrays of one of the nuclear states of Tm which they attribute to such an interaction.
The molecular-beam electric resonance method has been used to study the molecules CH3F and PH3. For methyl fluoride Wofsy et al. obtain values for the parallel and perpendicular components of σp for both the proton and fluorine shieldings. Of particular interest here is the observation that σp[parallel] for the fluorine nucleus is of large magnitude (and negative sign). Earlier, Hunt and Meyer observed for CHF trapped in clathrates that the anisotropy in the 19F shielding ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) was of different sign from that predicted from existing theory. Since shielding changes in F shielding are dominated by the paramagnetic term (with gauge origin at the 19F nucleus) and the C — F bond is cylindrically symmetrical, the theory predicts that σp[parallel] = 0 and therefore that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is negative. In fact, Hunt and Meyer found that Δσ = 66 (± 8) p.p.m. and suggested that σp[parallel] is large and negative. This result is confirmed by the work of Wofsy et al. who obtain for σp[parallel] a value of – 63.5 (± 1.5) p.p.m. Thus the simple theory of Karplus and Das, although good for σd and its components, does not work very well for σp.
For phosphine the measured value of σp for the 31P nucleus has enabled Davies et al. to set up for the first time an absolute shielding scale for this nucleus with the aid of the σd value calculated by the method of Flygare and Goodisman. They give for σ(31PH3) a value of 594.40 p.p.m. For the proton shielding in phosphine they give for σd an experimental value of 126.41 p.p.m., to be compared with 126.02 p.p.m. calculated by the method of Flygare and Goodisman. Part of the discrepancy here may be attributed to the fact that in obtaining a value of α (from which to subtract the measured σp) use had to be made of proton chemical shift data for phosphine measured in the solvent benzene which, as is well known, produces somewhat abnormal effects on the proton chemical shifts of dissolved solutes.
The first attempt to set up an absolute shielding scale for lead has been made by Lutz and Strieker. They obtain for the 207Pb2+ ion in D2O extrapolated to infinite dilution of the ion a shielding constant of –17 810 (± 60) p.p.m. The antishielding would appear to be present in a number of lead compounds. A very large solvent isotope effect is present since upon changing from the solvent D2O to H2O the shielding constant of the 207Pb2+ ion fell by 30 (± 3) p.p.m.
Although strictly speaking outside the scope of the present Report, we note here three papers involving the use of nuclear shielding and shielding anisotropy data for the estimation of the effects of spin-rotation interaction and chemical shift anisotropy upon nuclear spin-lattice relaxation times.
