Theory and Physical Models of Nuclear Magnetic Shielding

Theory and Physical Models of Nuclear Magnetic Shielding A. Molecular Shielding Terms 

Ramsey obtained ay, by first-order and op by second-order perturbation theory (76) variational treatments give similar results (14, 71, 73). The term wp is sometimes called the second-order paramagnetic term and sometimes the high-frequency term (14), because of the dependence of the (temperature-independent) paramagnetism in molecules on the high-frequency matrix elements of the orbital moments (91). 

The average values of the screening tensors for a particular nucleus can be written as 

Values of ag, are not very difficult to calculate, for Eq. (1) involves only ground-state wave functions. Furthermore, Flygare and Goodisman (25) have shown that Eq. (3) gives values of aa that are reasonably accurate (within 1 to 2 ppm), using tabulated values of the free atom (Lamb) term (7, 55, 56) and a knowledge of the molecular geometry  

Because of the r -dependence of aa, the innermost electron shells make the largest contribution, but the fall-olf is fairly gradual, as we shall see in examples below. For free atoms, aa increases steadily with the number of electrons, as shown in Fig. 2, but the increase is periodic in molecules, as shown in Figs. 6-8 for the binary hydrides and fluorides. 

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