Dynamical Study On Highly Excited Molecular Vibrational States: The Cases Of DCN, HCN And Its Isomers

Highly excited molecular vibration exhibits semi-classical nonlinearity due to its strong couplings among the vibrational modes. We take the coset space constructed by Lie algebra as the classical phase space for the molecular vibration to study its corresponding dynamical properties.Our method is first to build an algebraic Hamiltonian based on coupled Morse oscillators in the second quantization representation and fit its coefficients by spectroscopic experiments. With this algebraic Hamiltonian, we employed three parameters to describe the degree of dynamical chaos which were calculated by three independent approaches: (1) the Lyapunov analysis, based on the classical phase space for the levels, (2) the Dixon dip analysis, which integrates the concepts of pendulum dynamics and quantized levels and (3) statistical analysis of the distribution of the adjacent level spacings. We explored the chaotic dynamics of DCN. The results show evident correlation among these three algorithms.We analyzed the chaotic motion in HCN, HNC and their bending induced transition state by the above approaches. The three analyses show consistent conclusions: chaos appears only above the transition point and as the level energy increases, the degree of chaos does not increase in a monotonic way. Instead, it shows fluctuations, suggestive of band structure. We proposed a simple model of a pendulum coupled to a simple harmonic oscillator to reproduce the most significant chaotic signature of this HCN (and its isomers) system.Overlapping of resonances will lead to chaos, but the chaotic region is not only occupied by the chaotic motion. We studied the intramolecular vibrational dynamics due to extremely irrational couplings and contrasted it with that by the resonance couplings, for the three-mode case of H2O as an example. The extremely irrational couplings are shown to impose strong hindrance to intramolecular vibrational relaxation (IVR) that they act as barriers. They restrict the direct action/energy transfer between two O—H stretches, though they allow the transfer between one stretching and bending modes. Resonance couplings that lead to chaotic IVR are mainly mediated by the bending mode. There is also a region in which resonance and extremely irrational couplings coexist. Finally, we also introduced a model for the further study of multi-resonance dynamics.