On the existence of tunneling splitting in the dynamic Jahn-Teller effect

Abstract

In ref. (~) the tunnel ing theory of the dynamic Jahn-Tellcr effect, firstly discussed by B~RSV~R (~), has been re-examined. I t is found that the low lying levels of an octahedral complex, subject to tetragonal static Hahn-Teller distortions, are a singlet and a doublet of species A and E, respectively. Recently this result has been criticized (a) by the consideration that a T level in a given symmetry cannot be split by a perturbat ion of the same symmetry. Therefore the introduction, as a perturbation, of nonadiabatic operators should not lead to a splitting of the ground state T-+ A O E. Note, however, tha t these considerations are not applicable to our case since we are not concerned with a perturbation procedure. In fact the nonadiabatic operators, that the author of ref. (3) supposes erroneously to be considered as a perturbation in our previous work, are introduced ab i n i t i o in the SchrSdinger equation. This procedure is necessary since nonadiabatic terms are not small : their expectation value is ----10 -2 eV (1), which is comparable with the energy differences between vibronic levels. The main conclusion can therefore be drawn tha t the symmetry argumentations of ref. (s) are misplaced in dealing with our problem: the only prerequisite of the eigenfunctions of the SchrSdinger equation being that of transforming according to the irreducible representations of the point group (~). Moreover the author of ref. (a) tries to prove that the system (3.2.19) of ref. (~) cannot lead to a coupling between the equivalent states. I t is easily seen that the proof given in ref. (8) is incorrect; in what follows we will use symbols defined in ref. (~). Let us start from the system (3.2.19) of ref. (~):