The Unified Hamiltonian Formalism of Spin–Orbit Jahn–Teller and Pseudo-Jahn–Teller Problems in All Axial Symmetries

Spatial degeneracy of electronic states closely connects spin–orbit coupling and vibronic coupling, which together determine properties of materials, especially heavy element compounds. Accurate description of those materials entails accurate mathematical formulas for spin–orbit vibronic Hamiltonians. For the first time ever, we in this work derive the Hamiltonian formalism to describe all spin–orbit Jahn–Teller and pseudo-Jahn–Teller vibronic problems in all axial symmetries. The conventional one-electron approximation of spin–orbit coupling, which was the foundation of all previous studies in this field, is not involved in the present work. Actually, the present formalism is applicable to all time-reversal symmetric hermitian Hamiltonian that has a Rank-1 dependence on the spin operator, without any restriction on the type and the number of term symbols and vibrational modes.