Correlation between asymmetric and spherical top: imperfect quantum bifurcations

Abstract

The rotational energy level structures of quasi-spherical top molecules is investigated through the analysis of systems of stationary points on classical rotational energy surface. The series of simplest typical bifurcations of stationary points are given, as a quasi-spherical molecule evolves to the spherical top limit due to rotational excitation or molecular isotopomerisation. In this way the correlation between asymmetric and spherical top rotation energy multiplets is studied for A 4 and AB 4 molecules and corresponding isotopomers. It is demonstrated that the correlation depends on the point symmetry of the asymmetric top molecule. Slight symmetry breaking from C 2 v point symmetry down to C s results in the appearance of imperfect bifurcations [M. Golubitsky and D.G. Schaeffer, ‘Singularities and Groups in Bifurcation Theory’, vol. 1, Springer-Verlag, 1984]. The effect of imperfect bifurcation and its manifestation in molecular rotational spectra are discussed.