Reactive dynamics in energy transfer problems

Abstract

An approach to energy transfer due to microscopic interactions between moving acceptor and donor molecules is described. The theory is based on a set of coupled evolution equations, assuming that the displacements of the reacting particles obey a diffusion equation. A general expression for the transfer rate holding for any microscopic interaction form is derived and its asymptotic behavior at long and moderately long times is examined. Special emphasis is given to the influence of the molecular motion. In the fast diffusion limit, the transfer rate is independent of the mobility of the particles and given by the integral of the microscopic interaction form over space. In a finite diffusion limit, a characteristic transfer length is introduced; it may be interpreted as the radius of a sphere within which trapping is complete in spite of outward diffusion. Its exact expression is derived for multipolar and exponential interactions.