Classification of the highly excited vibrational eigenstates by the nominal quantum numbers retrieved from the zero-order states: the diabatic correlation technique

The diabatic correlation method is employed to assign the highly excited vibrational eigenstates of formaldehyde and acetylene with the quantum numbers of the zero-order states of an algebraic Hamiltonian whose inter-mode couplings are switched off, consecutively. Reconstruction of the vibrational eigenstates with these nominal quantum numbers is shown with very regular patterns. The possibility of unzipping the apparently very irregular spectra of highly excited vibration for even more complex molecules, especially when there are equivalent bonds, is also discussed with this algorithm.