Renner-Teller effect order coupling

Higher Order Coupling in Some Jahn-Teller and Renner-Teller Effects... 

Historically, the study of the Jahn-Teller (1937) effect was preceded (Renner, 1934) by that of the Renner-Teller effect in linear molecules. It arises if linear, or more generally odd-powered, terms in Q cannot contribute to the adiabatic coupling operator for synunetry reasons. We shall use the term (pseudo-) Renner-Teller coupling for all such couplings between states that are (almost) degenerate. The term thus applies to every nontotally symmetric mode coupling two electronic states of the same symmetry. The lowest order contribution to the adiabatic coupling operator is then of the form JQ. ... 

Simple examples of these effects were discussed in Section IV as limiting cases of the pseudo-Jahn Teller and pseudo-Renner-Teller effects. There it was shown that instead of using the adiabatic approximation, we should, in the interest of convenience, adopt a diabatic approximation in which the electronic degeneracy is maintained in zeroth order. The splitting can then simply be ascribed to adiabatic coupling proportional to Q, (or Qf, etc.) or to Qf (or Qf, etc.) between the two electronic components that remain degenerate at Q, = 0. The selection rule for pseudo-Jahn Teller coupling is thus <0° 0 or, iff denotes representation, T , x F,- x F 3-4,. 

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