Critical Phenomena and Diabolic Points in Rovibrational Energy Spectra of Spherical Top Molecules

Abstract The qualitative modifications of the rovibrational energy-level structure under rotational excitation are studied for spherical top molecules. The ν 2 , ν 4 bands of 12 CD 4 and 120 SnH 4 and the ν 1 , ν 3 bands of 120 SnH 4 are treated as examples. Two types of qualitative changes are shown to exist: the critical phenomena corresponding to the modification of the cluster structure and the so-called diabolic points associated with the redistribution of energy levels between different branches as the rotational quantum number increases. A simple model interpretation of energy-level redistribution is given to show that such a phenomenon is typical for tetrahedral molecules. Manifestation of critical phenomena and diabolic point formation in high-resolution infrared spectra are discussed.