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Qualitatively different systems of molecular energy bands are studied onexample of a parametric family of effective Hamiltonians describing rotationalstructure of triply degenerate vibrational state of a cubic symmetry molecule.The modification of band structure under variation of control parameters isassociated with a topological invariant "delta-Chern". This invariant isevaluated by using a local Hamiltonian for the control parameter valuesassigned at the boundary between adjacent parameter domains which correspond toqualitatively different band structures.

Qualitative features of the rearrangement of molecular energy spectra from a "wall-crossing" perspective