18 - Thermal Rates in a Bosonic Environment

Summary

Formulas are derived for the rates of elementary processes in nanoscale systems. Particularly we derive thermal rate constants for charge transfer in a condensed phase environment (Marcus formula), electronic energy transfer between chromophores (Forester resonant energy transfer), and radiation emission/absorption by electronic and vibronic transitions in molecules. All these processes are characterized by changes in the electronic state, strongly coupled to nuclear motions in the nano-system or in its surroundings. The relevant systems are mapped on a generic spin-boson model Hamiltonian, where different meanings are assigned to the model parameters in the different scenarios. In each case, rate constants are derived under appropriate approximations and are identified as different realizations of Fermi’s golden rule. A semiclassical (low-frequency) approximation applied for the nuclear degrees of freedom yields transparent, well-known formulas for the thermal transition rates. The underlying physics as well as practical consequence of the results are analyzed.