Determination of the electron transfer mechanism through decomposition of the density matrix

We present a modified Feynman and Vernon's path integral formalism which allows independent consideration of coherent superexchange and incoherent hopping pathways of charge transfer processes in order to determine the type of transport mechanism. By classifying the pathways between donor and acceptor into different mechanisms and by decomposing the density matrix of donor-bridge-acceptor triads into corresponding partial matrices, the contribution of each mechanism is obtained separately. Numerical tests confirm that the scheme is valid and efficient in exploring the transport mechanism and that the incoherent hopping mechanism tends to govern charge transfer processes even in systems with high-energy bridge states.