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The role of Berry's phase in ordering the low-energy states of a T×τ2 Jahn-Teller system in strong coupling

The sequence of the low-energy vibronic states of a T* tau 2 Jahn-Teller system (an orbital triplet electronic state in cubic symmetry linearly coupled to T2 vibrational modes) corresponds in strong coupling to the number of nodes in the vibrational factor of the Born-Oppenheimer wavefunction on these states. Berry's geometrical phase in the electronic state corresponding to the lowest adiabatic potential energy surface causes the lowest singlet state to have more nodes than the lowest triplet, with the result that the triplet is the vibronic ground state, the opposite of the sequence expected for a particle tunnelling between four equivalent wells. Reduction factors reflecting Berry's phase are evaluated for this triplet ground state. Their behaviour in departing from their limiting values in the strong-coupling limit is shown to be different from that predicted by a widely used asymptotic approximation based on the crude adiabatic approximation.