Quantization of a classical analog for the E⊗e Jahn–Teller system at intermediate couplings

Abstract

The Meyer–Miller classical analog for the linear E⊗e Jahn–Teller system is quantized for vibronic coupling strengths ranging from 0 to twice the magnitude of the zeroth-order force constant. The dynamics of the classical analog, which range from near diabatic at small coupling to near adiabatic at large coupling, are strongly chaotic in this intermediate regime. To effect quantization we use a method recently proposed by Jaffé, in which a classical analog Hamiltonian matrix is obtained from the Liouville formulation of the problem. The eigenvalues of this matrix are the semiclassical energies, and the eigenvectors reflect the interaction of the zeroth-order basis distributions. The method is shown to yield exact agreement with quantum mechanics for the classical analog of a model, constant-coupled two-state Hamiltonian, provided the Langer modification is used. In the fully coupled Jahn–Teller system, good agreement with quantum mechanics is obtained over the parameter range, with deviations (at avoided crossings) that reflect need for more complete uniformization.