Nonadiabatic instanton calculation of multistate electron transfer reaction rate: Interference effects in three and four states systems

Abstract

For multistate electron transfer reactions with quantum reaction coordinates, nonadiabatic instanton theory can provide a powerful and direct means of calculating the reaction rate without any limitation to the magnitudes of electronic coupling constants. In order to examine its performance in detail, the theory is applied to simple model systems with three and four electronic states which have one and two bridge states respectively. Calculations for three states systems, varying the through–bond coupling constant, show that the nonadiabatic instanton theory reproduces the results of perturbation and adiabatic instanton theories in the limits of small and large coupling constants, respectively. In the absence of through–space coupling, the crossover between the two limits is smooth and monotonic. However, in the presence of through–space coupling, the crossover pattern becomes sensitive to the relative phase of the two electronic channels and demonstrates substantial interference effects. For a four states system that has two interfering through–bond coupling paths, similar interference effect was observed. These results show that the nonadiabatic instanton method can serve as a favorable means of understanding the general kinetics and exploring the interference effects in the low-temperature bridge mediated and/or proton coupled electron transfer systems.