Redfield Treatment of Multipathway Electron Transfer in Artificial Photosynthetic Systems

Coherence effects on electron transfer in a series of symmetric and asymmetric two-, three-, four-, and five-site molecular model systems for photosystem I in cyanobacteria and green plants were studied. The total site energies of the electronic Hamiltonian were calculated using the density functional theory (DFT) formalism and included the zero point vibrational energies of the electron donors and acceptors. Site energies and couplings were calculated using a polarizable continuum model to represent various solvent environments, and the site-to-site couplings were calculated using fragment charge difference methods at the DFT level of theory. The Redfield formalism was used to propagate the electron density from the donors to the acceptors, incorporating relaxation and dephasing effects to describe the electron transfer processes. Changing the relative energies of the donor, intermediate acceptor, and final acceptor molecules in these assemblies has profound effects on the electron transfer rates as well as on the amplitude of the quantum oscillations observed. Increasing the ratio of a particular energy gap to the electronic coupling for a given pair of states leads to weaker quantum oscillations between sites. Biasing the intermediate acceptor energies to slightly favor one pathway leads to a general decrease in electron transfer yield.