Chemical-rate treatment of small-polaron hopping between inequivalent sites

A recently developed quantal-occurrence-probability treatment of small-polaron hopping is applied to electronic transfer between energetically inequivalent sites. A new analytic expression for the transition rate is derived. The expression is valid for a wide range of the main parameters, temperature T, energy difference ┘, and polaron binding energy 2E a, all in units of the mode frequency h ω. The hopping rate calculated with this expression is in excellent agreement with the complete multiphonon expression for the inequivalent-site case derived by Emin. The quantal-occurrence approach simplifies the application of the hopping-rate expression to a number of physical problems. We consider two problems: pair recombination and hopping in an applied field. We derive an analytic result for the non-exponential r-dependence of the hopping rate and for the intermolecular separation ―r corresponding to the maximal transition rate in an attractive Coulomb well. At low temperature ―r can be as large as ∼ 10, in units of the wavefunction localization radius, for a reasonable set of parameters. An exact result is also obtained for ―r as a function of electric field E. The consequences of these new results for pair-recombination luminescence and the Onsager model of photogeneration are discussed.