Jahn–Teller degeneracies of Thorson and Moffitt

Abstract

In computer studies of the Jahn–Teller system Γ₈⊗τ_2g, Thorson and Moffitt showed that periodic coalescences of the energy levels occur as the interaction between the electronic part Γ₈ and the vibrational mode τ_2g is increased. These near degeneracies have been analyzed by drawing a correspondence between the Γ₈⊗τ_2g system and a displaced one‐dimensional oscillator. It is shown that the degeneracies correspond to the zeros of the Bessel functions J₁(z). In terms of the interaction parameter D and the oscillator number n_τ of Thorson and Moffitt, z is 4D^1/2(n_τ+3/2)^1/2 in the limit of large n_τ. Second‐order effects have been cast in an analytic form and do not affect the existence of the degeneracies in that limit. Third‐order effects have also been studied. The theory is applied to the Jahn–Teller system E⊗ε.