Reaction yields in intramolecular dissipative kinetics

Intramolecular dissipation has recently been invoked by Schlag, Grotemeyer and Levine to interpret dynamical processes in highly excited large molecules. In such problems there is diffusive motion in the presence of a potential. In addition, there are two (or more) reaction processes which proceed at a finite rate. We present the solution of the Smoluchowski equation for the yields (branching fractions) of the reactions and consider its various limiting forms. When reaction is much faster than diffusion, the result of Schlag is recovered. In the opposite limit the reaction yield corresponds to that obtained from a simple kinetic scheme. The two limiting forms also correspond to "kinetic control" and "thermodynamic control" of physical organic chemistry. The derivation is equally valid if the source of dissipation is intermolecular.