Renner-Teller effect linear molecules

Jahn-Teller effect, 18-20 Linear triatomic molecules, Renner-Teller effect ... 

There is a clear distinction between conically intersecting surfaces and two surfaces which touch, as in the so-called Renner-Teller effect for the degenerate states of linear molecules 142,43 (Fig. 7). For such a situation the electronic wave function is single valued and although there may be strong mixing between Born-Oppenheimer terms, one such term can always be taken as a first approximation to any state. 

Linear molecules are the only exception to the Jahn-Teller effect. But linear molecules may also have instabilities in their degenerate electronic states and this is called the Renner-Teller effect. It was first described by Renner in a theoretical paper on the degenerate first excited electronic state of carbon dioxide [86], It took more than twenty years to find the first experimental evidence of this effect, in the electronic absorption spectrum of the NH2 radical [87], The NH2 radical has one electron on an orbital and thus a n electronic state... 

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. ... 

Y. liu, 1. B. Bersuker, W. Zou, and J. E. Boggs, Pseudo Jahn-Teller versus Renner-Teller effects in instability of linear molecules, Chem. Phys. 376, 30-35 (2010). 

For the quantum numbers of the bending vibration, the correlation between linear- and bent-molecule notation is V2(linear) = 2v2(bent) + Kg +1 see for example [3, 4]. Most authors prefer the linear molecule notation which is used in this chapter. Energy levels due to vibronic splitting (Renner-Teller effect, see p. 171) [5] are shown in Fig. 6, p. 172. 

The Jahn-Teller theorem has a footnote this is always true with the only exception of linear molecules. So the amusing story of the Jahn-Teller effect is that I first worked with my student, Renner, on a paper that presented the only general exception to the Jahn-Teller effect. It really should be the Landau-Jahn-Teller theorem because Landau was the first one who expressed it, unfortunately using the only exception where it was not valid. 

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