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 state
s 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 ef
fect is briefly discussed.