Pseudorotations in Molecules: Electronic Orbital Triplets

Topological and geometrical methods are used to calculate the pseudorotational part of the vibronic spectrum for an electronic triplet of an octahedral, tetrahedral, or icosahedral molecule. The calculations take into account the nontrivial geometry inherent in the Jahn-Teller effect. It is shown that the Jahn-Teller effect gives rise to a geometry, which is related to the isoparametric geometry of E. Cartan. The pseudorotational spectra correspond to the spectra of connection Laplacians on nontrivial line bundles over base spaces with this geometry. Globally, the isoparametric submanifolds form a totally geodesic foliation of S^4 and the spectral flow of these connection Laplacians on this foliation is computed.