Quantitative insights about molecules exhibiting Jahn-Teller and related effects

Open-shell states of molecules undergo a variety of phenomena different from closed-shell states. Two such effects, with which this paper is concerned, are Jahn-Teller coupling and spin-orbit coupling. We first develop a generalized Hamiltonian for the Jahn-Teller coupling of the electronic and vibrational motion and include the effects of spin-orbit coupling; we then consider the symmetry properties of the Hamiltonian in detail. The potential energy surfaces for various combinations of Jahn-Teller and spin-orbit coupling are also presented. The vibronic and spin-vibronic energy levels for a C-3v molecule are discussed in depth, with particular attention paid to the results of our rigorous numerical calculations of the eigenvalues and eigenfunctions. The results of these calculations are compared and contrasted with many assumptions about the energy levels that have been made in the past. While Jahn-Teller coupling has its largest effects on the vibronic energy levels, it also has non-negligible effects on the rotational energy levels. The rotational structure of Jahn-Teller states is developed, with special emphasis on the coupling of the vibronic, rotational and spin angular momenta. We discuss at length the relationship between Coriolis coupling and the spin-rotation interaction and show how these effects are related to the spin-vibronic Jahn-Teller and spin-orbit parameters of the state. Because most of the experimental investigations of Jahn-Teller states have been via electronic spectroscopy, we derive formulae for the intensities of these transitions in the presence of Jahn-Teller and spin-orbit coupling. The final portion of this article is a review of the application of the theory to the analysis of the spin-vibronic structure of the lowest excited states of several organometallic monomethyl radicals and the ground states of the methoxy family of radicals. These examples illustrate the diversity of signatures that Jahn-Teller active molecules display in their electronic spectra, and the different ways in which the Jahn-Teller and spin-orbit coupling can be elucidated from these signatures.