Jahn-Teller effect in EPR spectra: Multistate theory forE2orbital states in cubic symmetry

Abstract

The Jahn-Teller effect for an orbitally doubly degenerate state is considered for the case of cubic symmetry. Reduction factors are defined which describe the matrix elements of the orbital operators for $E$ doublets between the various vibronic states. For the lowest six vibronic states $E$, ${A}_{1}$, ${A}_{2}$, and $E$, the reduction factors are calculated for the cases of no or weak linear vibronic coupling and strong linear vibronic coupling. In the latter case the effects of anharmonic potential energy and nonlinear vibronic coupling are also included in the reduction factor calculations. Using the reduction factors to determine the matrix elements of the orbital operators within the vibronic states, an effective Hamiltonian is formulated which describes the mixing of the vibronic levels. This defines the multistate theory in which several vibronic levels are included in the manifold of states used to describe electronic interactions. Electron-paramagnetic-resonance spectra from $^{2}E$ orbital states are predicted for a six-state vibronic manifold by calculating the strain dependence of the $g$ factor. Particular attention is given to those spectral fectures appearing in the ground state which are the result of the second excited singlet. The relationship between $p$-type and $q$-type reduction factors is discussed.