Vibronic mean-field and perturbation theory for Jahn-Teller and pseudo-Jahn-Teller molecules

A generalisation of vibrational mean-field theory is developed for non-adiabatic Jahn-Teller and pseudo-Jahn-Teller molecules with coupled vibrational and electronic degrees of freedom treated within a quasi-diabatic framework. Solutions to the vibronic self-consistent field equations of motion generate qualitatively correct zeroth-order vibronic wavefunctions even in the strong coupling limit. These serve as an efficient basis for further perturbative or variational corrections. Particular attention is paid to complications arising in multi-mode Jahn-Teller systems, where the degenerate ground state exhibits artificial symmetry-breaking in the mean-field approximation. This effect is shown to behave like a second-order phase transition, with the symmetry of finite-temperature mean-field solutions restored above a critical temperature.