Symmetry, invariants, and topology in molecular models

Description of intra-molecular dynamical behavior is usually made in terms of effective Hamiltonians for different degrees of freedom. In such a way, rotational, vibrational, rovibrational, etc., dynamical systems arise in a natural way in the classical limit as corresponding to effective quantum Hamiltonians. The main idea of this paper is to answer the following general question: What kind of features of the quantum energy spectra can be predicted on the basis of qualitative (symmetry+topology) analysis of corresponding classical systems.