Jahn-Teller without symmetry

Generally, one only thinks of the Jahn-Teller effect in the context of systems which have certain discrete symmetries leading to degenerate energy eigenvalues. However, one can take a different perspective on the applicability of the theoretical machinery which has been developed for treating such problems. This point is made at the beginning of an extensive review by Bersuker:

I begin this review with a statement that the so-called Jahn-Teller (JT) effect (hereafter JTE), pseudo- JTE (PJTE), and Renner-Teller effect (RTE), jointly JT vibronic coupling effects, are not limited to a restricted variety of molecular polyatomic systems in specific electronic states, as it is often presented in the literature. In fact... the JT vibronic coupling theory is an approach to (a tool for) solving molecular and crystal problems, which is in principle applicable to any system with more than two atoms. Practically, this approach is most efficient when there are two or more coinciding (degenerate) or relatively close in energy (pseudo-degenerate) electronic states that become sufficiently strongly mixed when the nuclei displace from their initial reference configuration.

This point is particularly important because of the ubiquity of conical intersections on potential energy surfaces for excited states of organic molecules.