Spin-dipolar contribution

An anisotropic spin-dipolar contribution B arising from nonspherical distribution of the electronic spin density. 

Each of the eight hyperfine resonances is an unresolved quadmpole doublet, due to the quadmpole interaction of Os in the hexagonal Os metal source. The authors have interpreted the hyperfine fields in terms of core polarization, orbital and spin-dipolar contributions. 

Hyperfine tensors are given in parts B and C of Table II. Although only the total hyperfine interaction is determined directly from the procedure outlined above, we have found it useful to decompose the total into parts in the following approximate fashion a Fermi term is defined as the contribution from -orbitals (which is equivalent to the usual Fermi operator as c -> < ) a spin-dipolar contribution is estimated as in non-relativistic theory from the computed expectation value of 3(S r)(I r)/r and the remainder is ascribed to the "spin-orbit" contribution, i.e. to that arising from unquenched orbital angular momentum. 

On the basis of their ENDOR results and crystal field theory. Brown and Hoffman(18) have made empirical estimates of these three factors for the copper hyperfine interaction these are shown in Table II. The spin dipolar contributions may be estimated from o, the population of the unpaired electron in the Cu dxy orbital ... 

Beer and Grinter (143) using the finite perturbation theory at the INDO level of approximation indicate that the combined orbital and spin-dipolar contributions are less than 1 % of the observed coupling. 

FC = Fermi contact contribution OB = orbital contribution SD = spin-dipolar contribution. 

Recent INDO-FPT calculations predict that, for the N=C bond, the orbital and spin-dipolar contributions to /(N-C) become significant. (20) The results of these calculations by Schulman and Venanzi (20) are... 

Two groups of workers (110, 118, 119) have carried out sum-overstate INDO calculations, which also indicate that the orbital and spin-dipolar contributions are significant across the C=N triple bond. Calculated results for /(N-C) in acetonitrile are summarized in Table IX. Although there is lack of agreement in the total. /(N-C) calculated, the Fermi contact contribution is consistently positive while the other two mechanisms give rise to negative contributions. 

Most values of V(F-C) fall between —158 Hz, observed for methylfluoride, and —369 Hz observed for FCHO. (130) Calculations by Blizzard and Santry (16, 17) predict substantial orbital and spin-dipolar contributions to /(F-C). 

Jab the Fermi contact, (FC) the orbital paramagnetic and diamagnetic and the spin dipolar contributions to the coupling constant,... 

The last term is the SD (spin-dipolar) contribution which arises from the interaction between the second term in the operators H011 for nuclei TV and M (see Eqn. (12)). In the case of the nuclear magnetic moments in the... 

Table 4.1. Values of the spin dipolar contribution to the reduced spin coupling constant (k( )) in halogen bonds, calculated using = 1 and AE =...

Although the orbital and spin-dipolar contributions may be relatively small compared to the contact contributions for coupling between elements from H to N, this may no longer be the case for coupling between heavier nuclei. The counterpart of 5 (0) in the noncontact terms is p. This, like 5 (0), varies in a periodic fashion. 

Vab> V(AB) Spin-spin coupling constant over n bonds between nuclei A and B V(ABCD) shows a coupling path Fermi contact contribution to J Spin-dipolar contribution to J Orbital contribution to J Spectral density at angular frequency co Reduced spin-spin coupling constant (as above)... 

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