The energy spacing distribution and the transition moment distribution of highly excited vibrational states are studied by numerical solution for a model of coupled Morse oscillators with typical molecular parameters. The results show the following: (a) The transition moment distribution differs considerably from the statistical (gaussian) Porter Model, even in the regime of strong coupling. Agreement of the numerical results with the statistical model improves for states that increasingly approach the dissociation limit (6) A much improved statistical model for the transition moment distribution can be constructed, using certain empirical statistical properties of the wave-functions involved, (c) For states differing substantially in energy, the relevant transition moment distribution exhibits ah energy gap dependence. (d) The energy spacing distribution for states in a small range of energies obeys the Brody form g(w)αwβ exp [-αw1+β]. β increases systematically with the energy of the states, with the distribution increasingly approaching the Wigner model. A significant difference between the two distributions persists even near dissociation.
ASJC Scopus subject areas
- Molecular Biology
- Physical and Theoretical Chemistry
- Condensed Matter Physics