Significance of the Formal Quantum Number in the Highly Excited Vibration of the DCN molecule

For the eigenstates of the highly excited vibration of the simple molecule DCN with two stretching modes, a classical approach in a multi-dimensional coset phase space is employed to show that the formal quantum numbers are related to regular or least“irregular”trajectories, with zero or least Lyapunov exponents, and are always located in the inner regions of the phase space. This property reflects that they are the approximate constants of motion. It is also demonstrated that formal quantum numbers correspond to the significant phase space density.