Manifestation of bifurcations and diabolic points in molecular energy spectra

Abstract

The general scheme of the qualitative analysis of finite-particle quantum problems is discussed. Theoretical methods for the qualitative analysis of energy spectra in quantum problems are applied to the study of the rovibrational energy levels of spherical top molecules. The existence of modifications in the rotational cluster structure and of redistributions of the energy levels between different branches under the rotational excitation is shown for the ν2 /ν4 dyad of the 12 CH4 and 28 SiH4 molecules. An interpretation of the qualitative features of energy spectra in terms of bifurcations and formations of conical intersection points (diabolic points) on the energy surfaces of the corresponding classical problem is proposed.