Pseudo Jahn-Teller couplings, linear

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. ... 

The general principles for the construction of the vibronic Hamiltonian and the symmetry selection rules are the same as indicated above and discussed in more detail in Chapter 7. The previous distinction between trigonal and tetragonal point groups does not play a role, and the first-order coupling is always accomplished by doubly degenerate (e) vibrational modes. In an analogous notation as in Eq. (3), the Hamiltonian for the linear (E + A) (g) e pseudo-Jahn-Teller effect is found to... 

In fullerene anions C%q, the n electrons outside closed shells occupy /lu triplet electronic states. Jahn-Teller (JT) coupling between these states and 5-fold h-type vibrations has important consequences for many properties of the fullerene anions. It is therefore important to understand the JT effect experienced by these ions from a theoretical point of view. We will study the cases of n = 2 and 4, where the lowest adiabatic potential energy surface is found to consist of a two-dimensional trough in linear coupling. The motion of the system therefore consists of vibrations in three directions across the trough and pseudo-rotations in two directions around the trough. Analytical expressions for states of the system that reflect this motion are obtained and the resultant energies determined. 

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