Unified one-electron Hamiltonian formalism of spin–orbit Jahn–Teller and pseudo-Jahn–Teller problems in tetrahedral and octahedral symmetries

Heavy element compounds with high symmetries often feature both spin–orbit coupling and vibronic coupling. This is especially true for systems with tetrahedral and octahedral symmetries, whose electronic states may be threefold degenerate and experience complicated Jahn–Teller and pseudo-Jahn–Teller interactions. To accurately describe these interactions, high quality spin–orbit vibronic Hamiltonian operators are needed. In this study, we present a unified one-electron Hamiltonian formalism for spin–orbit vibronic interactions for systems in all tetrahedral and octahedral symmetries. The formalism covers all spin–orbit Jahn–Teller and pseudo-Jahn–Teller problems in the symmetries with arbitrary types and arbitrary numbers of vibrational modes and generates Hamiltonian expansion formulas of arbitrarily high order.