Nuclear spin, inclusion field

One final result is required to analyse the weak field spectrum of CsF. We derived an expression for the matrix elements of the electric field perturbation earlier, without the inclusion of nuclear spin effects, in equation (8.278). We now repeat this derivation using the basis set employed above. Taking the direction of the electric field to define the p = 0 (Z) direction, the results are as follows ... 

Table 10.2 shows the perturbation operators arising from inclusion of a magnetic field and relativistic effects. The last three columns indicate the perturbation order with respect to an external (Bext) and internal nuclear (I) magnetic field, and with respect to the inverse speed of light. Only the most important operators up to order c have been included, with the exception of the diamagnetic nuclear spin-spin coupling operator, since the leading term for this quantity is of order c. ... 

When the field is absent and the nuclei are viewed as quantum particles, a complete description requires inclusion of electron-phonon and spin-orbit coupling operators. Now, the By( )-coefficients couple electronic states whose diabatic potential energy surfaces jrield degenerate functions for the nuclear dynamics. Finally, these geometry-dependent coefficients couple all diabatic electronic states whenever a fuUy quantum-mechanical molecular system is embedded in an external field. 

In a diamagnet we have only nuclear moments (if any at all). Their effect on muon spin depolarization is analogous to that of paramagnetic moments, only that local fields of nuclear origin are usually, but not necessarily, weaker and static. We immediately turn to the more important case of a paramagnet, where, for simplicity, we assume nuclear moments to be absent for the time being. Their inclusion will be treated in sect. 3.4. Furthermore, the muon will be assumed stationary at its interstitial site. 

For example, in many systems, we found the GIAO-HF method to yield H-NMR chemical shifts with an accuracy of typically 0.2-0.5 For other nuclei the inclusion of correlation effects can become more impor-The computation at the GIAO-DFT level is closely related. NMR chemical shifts are calculated as second derivatives of the energy with respect to the external magnetic field B and the nuclear magnetic spin m of a nucleus N ... 

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