The effective valence shell Hamiltonian for spin-orbit coupling

Abstract

The size extensive, ab initio effective valence shell Hamiltonian method, which is based on quasidegenerate many-body perturbation theory, has been extended to treat spin-orbit coupling in atoms or molecules. Just as the exact projection of the nonrelativistic Hamiltonian into a prechosen valence space enables deriving the multireference perturbation expansion for the exact effective valence shell Hamiltonian, the addition of the Breit–Pauli spin-orbit operator to the original Hamiltonian (as an extra perturbation) enables the use of quasidegenerate many-body perturbation theory to produce the energy independent effective spin-orbit coupling operator that acts within the prechosen valence space. To assess the accuracy of the proposed method, test calculations are performed for the spin-orbit splittings in the valence states of C, Si, Ge, CH, SiH, and GeH and their positive ions using the one-electron spin-orbit approximation with standard values of the effective nuclear charge. The computed spin-orbit splittings are generally in good agreement with experiment and with the few available ab initio computations. Deviations appear in certain cases where the omitted coupling to Rydberg states is known to be relevant. One advantage of the method is that the spin-orbit coupling energies of all valence states for both the neutral species and its ions are simultaneously determined with a similar accuracy from a single computation of the effective spin-orbit coupling operator. Thus, fine structure splittings are predicted for a number of states of each system for which neither experiment nor theory is available. Another advantage stems from the fact that all off-diagonal spin-orbit matrix elements are also obtained.