Intramolecular dynamics from a statistical analysis of vibrational levels: Application of two coupled Morse oscillator models to the HCN molecule

Two local-mode model Hamiltonians containing stretch-stretch couplings have been utilized to obtain the vibrational energy levels of the HCN molecule for the purpose of studying them statistically. The effect of the kinetic coupling has been clearly obtained from the statistical analysis which includes nearest-neighbor level-spacing distributions (NNLSD) and the 3 statistics of Dyson and Mehta. For NNLSD, a pronounced tendency towards the Wigner distribution has been found. The role of isotopic masses in the statistical properties of the vibrational spectra has also been elucidated. Comparison has been made between the results obtained from the two models. Correlation has been found between a transition to chaos (utilizing Poincaré sections and Lyapunov exponents) through classical mechanics and the above statistical behavior of the spectra.