Distributions of energy spacings and wave function properties in vibrationally excited states of polyatomic molecules. I. Numerical experiments on coupled Morse oscillators

Abstract

Vibrational eigenvalues and eigenfunctions in the strongly coupled regime at intermediate and at high vibrational energy content are characterized in terms of distributions, both of observable and of wave functionproperties. In this regime, state‐by‐state description in terms of uncoupled modes is both difficult and too detailed; the distributions provide an adequate characterization of the vibrational behavior. We present results from numerical studies of realistic coupled‐vibrational problems; the latter include local‐mode Morse oscillators coupled by the Wilson interaction. The distributions studied are g(ω) (the distribution of nearest‐neighbor energy spacings), G(ω) (the distribution of all energy spacings), π(χ) (the distribution of transition moments), and two different but related wave function expansion coefficient distributions. We find that in the strongly coupled regime, the parameters of the distributions depend only weakly on the Hamiltonian, and, moreover, that simple analytic forms can be found to represent the distributions over a wide range of systems and energies. We conclude that the distributional description of vibrational systems seems potentially very useful and that dynamical elucidation of the distributional parameters seems a desirable aim. Comments are made on the relation to mode mixing, and chaotic‐like behavior.