The Jahn-Teller effect in a p state equally coupled to Eg and T2g vibrations

The Jahn-Teller Hamiltonian for an electronic p state equally coupled to Eg and T2g vibrations in cubic symmetry, is diagonalized numerically. The invariance of the phonon Hamiltonian under the five dimensional rotation group, R5, is used to get the matrix elements, and for this some fractional parentage coefficients for the reduction of R5 to R3 are calculated. The reduction factors K(E) and K(T1) are calculated, lineshapes and zero phonon line intensities are given for s to p and p to s transitions. The wavefunction in strong coupling is worked out in a new coordinate system, and its properties match those derived from the numerical diagonalization. The s to p lineshapes are markedly different from those calculated by semiclassical methods, even in strong coupling.

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