Topological Chern indices are related to the number of rotational states in each molecular vibrational band. Modification of the indices is associated to the appearance of “band degeneracies,” and exchange of rotational states between two consecutive bands. The topological dynamical origin of these indices is demonstrated through a semiclassical approach, and their values are computed in two examples. The relation with the integer quantum Hall effect is briefly discussed.

• Received 20 December 1999

DOI:https://doi.org/10.1103/PhysRevLett.85.960