Energy-diffusion-limited unimolecular reactions in condensed phases

Unimolecular reactions of polyatomic molecules in condensed phases in the low-friction regime where the reaction rate is controlled by the energy transfer rate between the molecule and the media are investigated. It is assumed that the intramolecular degrees of freedom are strongly coupled and thus the microcanonical rate of the molecule is described by statistical theories. The generalized Kramers' model is employed and the rate constant is calculated by numerically solving the general energy-diffusion equation, which we refer to as the "‘exact’' result. Using a simple model system that employs the harmonic approximation, we demonstrate the dependence of the "‘exact’' rates on the number of molecular degrees of freedom and compare them with those obtained by assuming the low-friction limit. It is shown that the "‘exact’' rates may be orders of magnitude smaller for high-dimensional systems even at extremely low friction, indicating that the commonly used solutions obtained in the low-friction limit are not applicable to large molecules. To investigate the practical aspects of applying the generalized Kramers' theory to treat reactions of polyatomic molecules in condensed phases, we study the reaction of a large molecule (dimethylnitramine) in liquid xenon. This study suggests that the energy-diffusion-controlled region may be experimentally observable for polyatomic systems, and that the theory may provide a practical means of obtaining the rate constants for such processes.