Intermediate coupling spin-orbit configuration interaction

However, the quantum numbers L and S are not rigorous, due to the existence of the spin-orbit interaction between the respective momenta. Therefore, the above-mentioned selection rules hold only approximately. In intermediate coupling the selection rules with respect to L and S change and allow many more transitions. For example, the isolation of the condition AS = 0 leads to the occurrence of the so-called intercombination E 2- and M 1-lines. For the configuration 3d3 in intermediate coupling, instead of (27.10) and (27.11) we obtain... 

An accurate procedure for performing calculations that incorporate spin-orbit and other relativistic effects, and that represents intermediate coupling states for molecules containing heavy atoms, is based on A-S coupling in conjunction with the use of the ab initio REP-based spin-orbit operator and extended configuration interaction. The coupling scheme is more familiar than co-co coupling to chemists and physicists. In addition, the complexity of calculations necessary to achieve reliable results is computationally tractable. 

Judd-Ofelt (JO) theory has been established within the frame of the crystal-field concept and it provides a simple model for reproducing the intensities of f-f transitions both in solids and solutions. It only takes into account the 4f" electronic configuration, that is inter-configurational 4f"-4f" 5d interactions are neglected. On the other hand, spin-orbit coupling is treated within the frame of the intermediate... 

In practice, one finds the case of intermediate coupling, and thus it is always necessary to describe a state by a superposition of several states, be it in the jj coupling scheme or the LS coupling scheme, which makes the opposite assumption as concerns the relative strength of Coulomb interaction and spin-orbit effects. Apart from the fact that a one-determinant approximation for a heavy system is usually more accurate in jj coupling, both coupling schemes are equivalent in a configuration interaction picture. 

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