Quantifying electron transit in donor-bridge-acceptor systems using probabilistic confidence

A probabilistic approach to characterizing transit times for quantum particles is generalized to a system of more than two spatial regions and applied to the transport of charge in donor-bridge-acceptor systems. The approach is based on applying conditional probability analysis to a discrete representation of the time-dependent probability density as generated by numerical solution of the time-dependent Schrödinger equation for an initially localized electron. To carry out this analysis, it is first necessary to cast the conditional probability analysis approach in matrix form. The results afford a quantification of the electron transit time and may provide a tool to gain insight into the mechanism of charge transport.