Spin-Orbit Vibronic Coupling in Jahn-Teller and Renner Systems

A systematic analysis of spin-orbit coupling effects in Jahn-Teller and Renner systems is presented. The spin-orbit coupling is described by the microscopic Breit-Pauli operator. In contrast to most previous work for molecules and crystals, the spin-orbit operator is treated in the same manner as the electrostatic Hamiltonian, that is, the Breit-Pauli operator is expanded in powers of normalmode displacements at the reference geometry, matrix elements are taken with diabatic electronic states, and symmetry selection rules are used to determine the non-vanishing matrix elements. Choosing trigonal systems, tetrahedral systems and linear molecules as examples, it is shown how the generalized symmetry group of the spin-orbit operator can be determined. The vibronic Hamiltonians including spin-orbit coupling up to first order in the vibrational displacements are derived. It is shown that there exist linear vibronic-coupling terms of relativistic origin which are particularly relevant in systems where the vibronic coupling by the electrostatic Hamiltonian arises in second (or higher) order in the vibrational coordinates.