Formal quantum numbers as retrieved by the diabatic correlation and their classical interpretation for the highly excited vibrational eigenstates

Formal quantum numbers retrieved via diabatic correlation to the zero-order states where all inter-mode couplings are switched off can be assigned to the eigenstates of the molecular highly excited vibration. These formal quantum numbers help the classification and assignment of the highly excited vibrational states. They are shown as the approximate constants of motion. A classical approach in a coset phase space is employed to show that the trajectories corresponding to the formal quantum numbers have zero or least Lyapunov exponents and that formal quantum numbers correspond to significant phase space density.