Electronic structure spin-orbit coupling

Having application codes available that can be used to calculate spectroscopic and structural properties of a range of electronic states of heavy-element-containing molecules and that treat electron correlation, spin-orbit coupling and other relativistic effects in a manner that allows for systematic improvements is invaluable to their detailed understanding. Accurate theoretical models of such systems... 

The vibronic structure of a electronic state at variable strengths of the vibronic and spin-orbit coupling is presented in Figure 5. The splitting of the... 

Notice that the fine structure term found here has the same form (and the tensor is given the same symbol) as that obtained from the electron dipolar interaction. Unlike the dipolar D-tensor, however, the spin-orbit coupling D-tensor in general does not have zero trace. Nonetheless, we introduce analogous parameters ... 

Although it is unfortunate that spin-orbit coupling and the electron dipolar interaction give fine structure terms of the same form, it is possible to separate the effects. Since the spin-orbit contribution to D is related to the g-tensor ... 

High spin Fe2+ has the configuration 3 de (tig eg). Although we could examine the relationship between Rv and dS as for Mn2+, Co2+, and Ni2+, we prefer in this case to look at Ry as a function of the occupation of the combination of 3d and 4s orbital by ligand electrons which is measured by the Mossbauer isomer shift. In general, the coefficient f0, fn, and fs are not known for Fe2+. In addition, possible spin-orbit coupling makes it difficult to determine the spin reduction by magnetic structures. However, the isomer shift allows us to determine approximately the occupancy of the 4 s orbitals and there are many experimental results available. 

Transition-metal and rare-earth atoms that contain partially occupied d or f valence subshells also give rise to spectral tine structure, often with very complicated multiplet splitting [2,27,28]. The spin-unpaired valence d or f electrons can undergo spin-orbit coupling with the unpaired core electron (remaining in the orbital from which the photoelectron was removed), producing multiple non-degenerate final states manifested by broad photoelectron peaks [2,27]. 

The other relativistic effect entirely neglected so far is the spin-orbit coupling. For systems in nondegenerate states, the only first-order contribution to TAE comes from the fine structures in the corresponding atoms. Their effects can trivially be obtained from the observed electronic spectra, and hence the computational cost of this correction is fundamentally zero. 

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