Stability of polyatomic molecules in degenerate electronic states II-Spin degeneracy

Abstract

In a previous paper (Jahn and Teller 1937) the following theorem was established: A configuration of a polyatomic molecule for an electronic state having orbital degeneracy cannot be stable with respect to all displacements of the nuclei unless in the original configuration the nuclei all lie on a straight line. The proof given of this theorem took no account of the electronic spin, and in the present paper the justification of this is investigated. An extension of the theorem to cover additional degeneracy arising from the spin is established, which shows that if the total electronic state of orbital and spin motion is degenerate, then a non-linear configuration of the molecule will be unstable unless the degeneracy is the special twofold one (discussed by Kramers 1930) which can occur only when the molecule contains an odd number of electrons. The additional instability caused by the spin degeneracy alone, however, is shown to be very small and its effect for all practical purposes negligible. The possibility of spin forces stabilizing a non-linear configuration which is unstable owing to orbital degeneracy is also investigated, and it is shown that this is not possible except perhaps for molecules containing heavy atoms for which the spin forces are large. Thus whilst a symmetrical nuclear configuration in a degenerate orbital state might under exceptional circumstances be rendered stable by spin forces, it is not possible for the spin-orbit interaction to cause instability of an orbitally stable state. 1—General theorem for molecules with spin Just as before we must see how the symmetry of the molecular framework determines whether the energy of a degenerate electronic state with spin depends linearly upon nuclear displacements. This is again determined by the existence of non-vanishing perturbation matrix elements which are linear in the nuclear displacements. These matrix elements are integrals involving the electronic wave functions with spin and the nuclear dis­placements, and we deduce as before from their transformation properties whether for a given molecular symmetry they can be different from zero.