Jahn-Teller Effect of an Orbital Triplet Coupled to BothEgandT2gModes of Vibrations: Symmetry of the Vibronic States

Abstract

When an orbital triplet in cubic symmetry is equally coupled to both $E_g$ and $T_{2g}$ modes, the Hamiltonian describing the Jahn-Teller effect has a symmetry much higher than cubic. This fact allows to reduce to a great extent the number of vibrational states coupled to an electronic state. The general expression for the fractional parentage coefficients involved in the calculation of the matrix elements of the interaction is given. A general relation between Ham factors is deduced from symmetry considerations. This model seems to apply very well to the excited level of the $F^{+}$ center in CaO.