Theory of Chemical Shifts

For a single free atom in a spherically symmetric S electronic state, Lamb49 showed that the effect of an imposed magnetic field is to induce an electron current that leads to a shielding factor, 

Here p(r) is the density of electrons as a function of radial distance from the nucleus, and e, m, and c are the usual fundamental constants. 

For molecules the Lamb theory is inadequate because it assumes that the electrons are free to move in any direction, whereas in a molecule electronic motion is severely restricted. Ramsey50 used second-order perturbation theory to develop a formula that in principle accounts for the shielding factor in molecules and has long provided a framework for qualitative understanding of the major factors 

For hydrogen, the Ramsey theory is relatively easy to apply, but, as we see in Section 4.5, external perturbations from neighboring functional groups and solvent molecules are of comparable magnitude to the basic electronic terms, so that the theory is quantitatively of little practical value. For other nuclei, this theory could predict chemical shielding rather accurately if we had true wave functions and knowledge of the energies of all excited states. In practice, approximations must be made, but acceptable results can be obtained provided some fundamental aspects are kept in mind. 

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It is not our concern here to delve into the theory of chemical shifts, since most studies mentioned are essentially empirical in their approach and have aimed to correlate the measured shifts with electronic factors. The main fact, however, is that unlike proton shifts, the shifts for other nuclei are governed by the Van Vleck second-order paramagnetic term, which is not easy to handle since its magnitude depends not only on the ground electronic state but also on the manifold of excited states. 

In this review, chemical shifts and coupling constants of simple dienes will first be summarized, and the theory of chemical shift for dienes and polyenes will then be reviewed. Finally, the recent applications of NMR spectroscopy to a variety of polyenes and dienes and specific systems (allenes, solitons and fullerenes) will be reviewed. 

The theory of chemical shifts of the nuclei of polyelectronic atoms is complicated and certainly does not yet produce results in quantitative agreement with theory. It is conceivable that a more qualitative use of these parameters might be more appropriate to the problem in hand and an example of this sort is illustrated in Fig. 8, due to Lauterbur (75), where the chemical shifts of the Si and nuclei in analogous com-... 

A more quantitative interpretation of chemical shift data cannot be made at present, with few exceptions, such as the calculations of ring current shifts. The theory of chemical shifts is by and large inadequate to deal with the subtleties of the observed changes. A priori calculations remain grossly inaccurate, because the large number of parameters contained in the equations cannot be derived from any experimental measurement. Even calculations of ring current shifts involve iterative fitting of these parameters to known crystal structure data. The view of molecular structure derived from a study of chemical shifts thus reveals a wealth of detail blurred in its essentials. 

A general theory of chemical shifts of magnetic nuclei has been given by Ramsey, and the screening constant for a particular nucleus has been conveniently expressed in terms of three main contributions by equation (9)—... 

Because it is almost impossible to disentangle the various contributory effects, the theory of chemical shifts can be used only as a general guide. For the solution of problems, empirical correlations are almost invariably used. Some of the more fundamental of these are given in Table 12.1. 

D. SitkofF, D.A. Case, Theories of chemical shift anisotropies in proteins and nucleic acids. Prog. Nucl. Magn. Reson. Spectrosc. 32 (1998) 165—190. 

Mauri F, Pfronuner BG, Louie SG 1996) Ab initio theory of chemical shifts in solids and liquids. Phys Rev Lett 77 5300-5303... 

The theoretical interpretation of chlorine, bromine and iodine chemical shifts is presently not very well understood. A general theory of chemical shifts in closed shell molecules was originated by N.F. Ramsey in the early 1950 s [25], The shielding constant of any... 

According to the approximate Karplus-Pople theory of chemical shifts, at least a large part of the 3 parameter may be understood as an in-... 

Both scalar relativistic effects and spin-orbit coupling have to be considered. Relativistic theories of chemical shifts and of spin-spin coupling constants, as well as their implementation at the semi-empirical extended Hiickel level, have been known for some time (see bibliography given in Ref. 22). However, only very recently have first efforts been made to include relativistic corrections in quantitative calculations of NMR properties. 

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