The Green's function technique for numerical simulations of multichannel electron transfer reactions in electron-donor-acceptor complexes

A method for numerical solution of diffusion equations with delta-localized coupling terms is proposed and applied to the stochastic model of multichannel electron transfer (ET) reaction in the Debye polar solvent. The Green's function for the model equations is calculated using the Laplace transform technique for the time dependent reaction fluxes between the reactant and product states. Two computational schemes for ET simulations are suggested: (a) the particle-based Brownian algorithm, (b) the grid scheme, utilizing the probabilities of the diffusion-assisted electronic transitions. The suggested schemes are shown to be more efficient than the previously developed recrossing-algorithm (the RABS method) in the solvent-controlled ET regimes and for slow processes accompanied by rare reactive events. Test simulations with the QM2L code are carried out and demonstrate an accuracy of the method. The results of the simulations agree well with known analytical expressions for the rate of thermal ET and the quantum yield of nonequilibrium multichannel ET in different regimes from the nonadiabatic (the Fermi Golden Rule) limit to the solvent-controlled reactions.