Effective Hamiltonian approach to doubly degenerate electronic states

Effective vibronic Hamiltonian models are built for E ⊗e Jahn-Teller systems and analytical solutions are obtained through Lie algebraic methods. Although approximate, we show that these models allow in particular to recover the possible ground state crossover when quadratic couplings are present. The equivalence of E ⊗e and G' ⊗e vibronic systems in cubic symmetry is precisely established through a particular realization of the electronic operators for an orbital quadruplet. We show how this equivalence is broken by a rovibronic interaction which, for a G' ⊗e system, still gives an exactly solvable model.