Dynamical symmetry breaking and energy transfer pathways in local modes of benzene

Abstract

Local modes are discussed as a manifestation of dynamical symmetry breaking. For benzene C-H fundamentals, the symmetry is lowered from D/sub 6h/ to C/sub 2//sub v/ when the excitation process singles out one of the local modes. The paradox of symmetry breaking is removed, however, when one takes into account dynamical tunneling mechanisms which restore D/sub 6h/ symmetry through energy transfer among the local modes. The situation is related to permutation-inversion isomerism in molecules with identical nuclei, with restoration of full permutation-inversion symmetry by means of tunneling among the isomers. It is shown that mathematically, the analogy subsists in the treatment of both cases in terms of induced and subduced representations and the Frobenius reciprocity theorem. It is then shown how local modes symmetry breaking may be incorporated within the framework of fundamental permutation-inversion symmetry. Splittings in local modes spectra are parameterized phenomenologically by classifying the dynamical tunneling mechanisms, or energy transfer pathways among local modes, available to the system. The phenomenological analysis of observed spectra yields relative strengths for the various pathways. The results are compared with predictions of a recent model and with intuition.