Quantitative insights about molecules exhibiting Jahn-Teller and related effects

Open-shell states of molecules undergo a variety of phenomena different fro m closed-shell states. Two such effects, with which this paper is concerned , are Jahn-Teller coupling and spin-orbit coupling. We first develop a gene ralized Hamiltonian for the Jahn-Teller coupling of the electronic and vibr ational motion and include the effects of spin-orbit coupling; we then cons ider the symmetry properties of the Hamiltonian in detail. The potential en ergy surfaces for various combinations of Jahn-Teller and spin-orbit coupli ng 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 eigen functions. The results of these calculations are compared and contrasted wi th 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 mome nta. We discuss at length the relationship between Coriolis coupling and th e spin-rotation interaction and show how these effects are related to the s pin-vibronic Jahn-Teller and spin-orbit parameters of the state. Because mo st of the experimental investigations of Jahn-Teller states have been via e lectronic spectroscopy, we derive formulae for the intensities of these tra nsitions 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 se veral organometallic monomethyl radicals and the ground states of the metho xy family of radicals. These examples illustrate the diversity of signature s that Jahn-Teller active molecules display in their electronic spectra, an d the different ways in which the Jahn-Teller and spin-orbit coupling can b e elucidated from these signatures.