E. Fluck

Introduction and Foreword

The usefulness of solvent effect studies on NMR chemical shifts need not be elaborated here; many applications of solvent effects continue to be published in great profusion. Quite a few intermolecular phenomenae may contribute to solvent shifts, but there is always the ubiquitous Van der Waals effect σw. Contrary to such other effects as neighbour anisotropy σa, reaction field contribution σE or complexation effects σc, no major direct use has yet been found for the Van der Waals effect. So far the role of the Van der Waals effect has been that of a nasty, disturbing phenomenon, something to be eliminated at all costs. But it is precisely in this latter respect where almost all solvent effect studies fall short. Not only is σw usually large (larger than σa and σE even in 1H NMR and probably the dominating term with heavier nuclei), but it is strongly variable from one solute to another and even from one nuclear site to another in the same solute molecule. No referencing technique, however cleverly devised, will be capable of eliminating the σw contribution from the other, presumedly more interesting contributions.

The Parameters B

In this Chapter we shall summarise what is known of the parameter B. We will discuss the various quantum mechanical calculations for B and will also summarise the empirically obtained B parameters for non-polar molecules. The parameter B has only real significance in the formulations of \( {\sigma _{w}} = - B\overline {{F^{2}}} \) (or σw = -BE 2 ). However, there are theories which calculate σw directly, without any intermediate electric field. In these cases it is still possible to equate such σw with -\( - B\overline {{F^{2}}} \) where some model for \( \overline {{F^{2}}} \) has been inserted. With such a “simulated” field one then arrives at “simulated” B parameters. Such calculations have also been included in the present chapter. Therefore the material of this chapter will allow a comparison between the effective electric field theories and the direct interactive theories for σw.

Alternate Referencing Systems

With very few exceptions we have concerned ourselves in the foregoing with externally referenced measurements, either in the gas phase or in the liquid phase (solution phase). The reasons for our evident disdain for internally referenced studies should be obvious; the results so obtained are always the difference between two σw effects; that of the solute and that of the reference compound. In general, solute and reference will exhibit σw effects in various solvents, which are not related in a simple way. This is even true if the “reference” is a chosen signal of the solute molecule itself; as we have seen (Chapter 4 section 6.1), intramolecular differences in σw can be just as substantial as intermolecular differences.

σw in Dense Media

Whereas the macroscopic continuum theories for medium effects (Chapter 2) pretend to be universal in their applicability to all conditions of temperature, pressure and density in all phases, we shall see that the experimental evidence is contrary to this. With the statistical mechanical model of Raynes, Buckingham and Bernstein [15] there is a clear alternative. While at low densities the σw effect can be accounted for by binary collisions, the virial theorem of Eq. (37) leaves the possibility of adding terms to account for ternary and higher order collisions. Such an approach seems reasonable at least for gases at high density. According to the virial theorem one would therefore expect that at high density the dependence of the medium shift on density would become non-linear. An interesting example of such a non-linear shift has been found with 129Xe. Initially a linear behaviour was found with densities up to 300 amagats. Streever and Carr [78], and Hunt and Carr [79] report σ 1 = -0.43 ppm/amagat at 25 °C. More recently, working with greater precision, Kanegsberg, Pass and Carr [80] found a distinct non-linearity, requiring a third virial term σ2. They also found a distinct temperature dependence for σ 1 and σ2. Their results are σ 1 = -0.61, -0.54, -0.51 and -0.49 ppm/amagat at 20, 40, 60, and 80 °C respectively (σ 1 = -0.695 + 4.8 • 10-3t – 2.8 • 10-5t2), and σ 2 = 4.7, 2.6, 1.3 and 0.6 • 10-4 ppm/amagat2 at these same temperatures (σ 2 = +7.31–0.15 t +0.78 • 10-3t2). Jameson, Jameson and Gutowsky [66] observed that actually the shift is only linear up to 100 amagats.

The Effects of Higher Order Dispersion Terms

We have already mentioned previously (section 6.2) that Raynes’ treatment of a solvent site factor is, at least formally, equivalent to the inclusion of higher order dispersion terms. It should be realised, however, that even solvent atoms have higher order dispersion terms. Mohanty and Bernstein [52] have remarked that they tried to incorporate these effects but that they found no improvement. No details were given, but one may presume that only a new set of empirical B values emerged with the same sort of statistical scatter.

σw of Nuclei other than 1H and 19 F

We discuss these two nuclei together because the only reports on pure Van der Waals solvent effects of these nuclei are from one source (i.e. Maciel and co-workers [100, 108, 109]), where these two resonances were studied simultaneously. We also will deviate from our general rule of discussing only gas shifts or gas-to-liquid shifts, because of the paucity of such data. The first report on σw of 13C and 29Si is due to Bacon, Maciel, Musker and Scholl [108], who for TMS in 20 vol % TMS, 80 vol % C6H12 reported susceptibility corrected values, relative to pure TMS, of σw (13C) = +0.12 ppm and σw (29Si) = -0.05 ppm. In subsequent paper [109] several more of such data were given, but a full discussion of the 13C, 29Si and 1H solvent effects of TMS and cyclohexane by Bacon and Maciel [100] includes all previous data. In Table 41 all the relevant data (i.e. pertaining to pure σw effects only) is given.

Historical Development (Up to 1961)

The first mention of a medium effect for the chemical shift in high resolution NMR was made in 1951 by W. C. Dickinson [1]. Based on classical magnetostatics he showed that there is a finite contribution ΔH to the time averaged magnetic field at the nucleus under study given by

The Temperature Dependence of σw

\Delta H = \left[ {\frac{{4\pi }}{3} - \alpha } \right]M