Renner-Teller coupling

In Chapter XI, Peric and Peyerimhoff discuss the Renner-Teller coupling in triatomic and tetraatomic molecules. For this purpose, they describe some of their theoretical tools to investigate this subject and use the systems FeH2, CNC, and FICCS as adequate examples. 

The concept of Renner-Teller coupling has become essential for understanding the complex optical spectra of many triatomic molecules (BH2, NH2, HCO, NCO, N02, S02, etc.). For reviews of the Renner-Teller effect, its theory and applications, see, for instance, Refs. [4-10]. 

Fig. 3. Bending potential energy curves for weak (a) and strong (b) Renner-Teller coupling.

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. ... 

In principle, coupling terms of this type also arise in the Herzberg-Teller scheme (Section IV,A), but are of little importance there, since they give intensity to (weak) bands that also derive intensity via Franck-Condon effects. However, if two electronic states are close in energy, pseudo-Renner-Teller coupling can shift levels and redistribute intensities in a way comparable to the real Renner-Teller effect. 

Although little is known about the analytical form of pseudo-Renner-Teller coupling, a coupling operator of the form JQ is probably unphysical... 

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