The Jahn-Teller and Barnett effects

In the usual formulation of the Jahn-Teller effect a simplification is made in going from the adiabatic to the crude adiabatic approximation in which the electronic parts of the vibronic wavefunction are assumed independent of the nuclear coordinates. This then neglects momentum coupling in the vibronic coupling matrix. The momentum coupling has been termed the molecular Barnett effect when the active vibration transforms as the irreducible representation of a relation in the molecular point group. Experimental evidence for the molecular Barnett effect has recently been found. In this paper the various point groups in which momentum and Barnett coupling can occur are investigated. A vibration capable of momentum coupling is contained in the asymmetric direct product of the degenerate electronic state and, as with the Jahn-Teller effect, is possible in the orbitally degenerate electronic states of molecules of all non-linear point groups. A static distortion along such a coordinate will lift the electronic degeneracy. Unlike the Jahn-Teller effect, however, in some point groups a minimum complexity of the molecule is required before such coupling can occur. In particular it will be absent in the degenerate electronic states of such simple molecules of the form X(3)(D-3h); XY(3)(C-3v, D-3h); XY(4)(T-d); and XY(6)(O-h).