Stochastic theory of intramolecular vibrational energy redistribution and dissociation in the presence of radiation

A theory for internal vibrational energy redistribution and dissociation in polyatomic molecules in the presence of a strong radiation field is formulated. The fundamental assumption is that a random phase approximation is valid at specific time intervals. This results in the replacement of the Schrödinger equation by a master-type equation, which is further approximated by a Fokker-Planck diffusionlike equation. Energy transfer is described as a flow of probability among the quantum states, and the dissociation dynamics are embodied in the boundary conditions. By virtue of the continuous character of the Fokker-Planck equation, the computational difficulty of its numerical solution depends only on the number of degrees of freedom and not on the number of states. Due to the high density of levels encountered in a polyatomic molecule, this is of paramount importance in reducing the problem to a manageable size. A multiple time scale stochastic formulation, which allows for a mixed quantum-stochastic approach, is also described. No assumptions regarding the strength of the intramolecular coupling are made, and energy conservation is specifically enforced. The coefficients of the Fokker-Planck equation are shown to be expressible in terms of simple functions of the molecular potential, which involve raising and lowering operators. Finally, the coefficients of the Fokker-Planck equation are calculated using the best available potential information for the case of the ozone molecule in a strong infrared laser field, and their physical significance is discussed.