Time-reversal symmetry spin-orbit interaction

In the non-relativistic domain one-electron operators can be classified as triplet and singlet operators, depending on whether they contain spin operators or not. In the relativistic domain the spin-orbit interaction leads to an intimate coupling of the spin and spatial degrees of freedom, and spin symmetry is therefore lost. It can to some extent be replaced by time-reversal symmetry. We may choose the orbital basis generating the matrix of Hx to be a Kramers paired basis, that is each orbital j/p comes with the Kramers partner = generated by the action of the time-reversal operator We can then replace the summation over individual orbitals in (178) by a summation over Kramers pairs which leads to the form... 

The scheme outlined above (Sjpvoll et al. 1997) has been implemented in the program LUCIA. The program also exploits both double-group symmetry and time-reversal symmetry. The main computational costs over a nonrelativistic Cl arise from the presence of vector operators, from the need to use complex arithmetic, and from the extended interaction space due to the fact that the spin-orbit operators connect determinants of different spin multiplicity. 

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