Charge Transfer in Donor-Bridge-Acceptor Systems: Static Disorder, Dynamic Fluctuations, and Complex Kinetics

The influence of static and dynamic torsional disorder on the kinetics of charge transfer (CT) in donorbridge-acceptor (D-B-A) systems has been investigated theoretically using a simple tight-binding model. In such systems, variations of the torsion angle often give rise either to static changes in the magnitude of electronic coupling along the bridge length or to dynamic fluctuations of this quantity on the certain characteristic time scale τrot. These lead to the functional breakdown of the Condon approximation. Modeling of CT beyond the Condon approximation reveals two types of non-Condon (NC) effects. If τrot is much less than the characteristic time, τCT, of CT in the absence of disorder, the NC effects was shown to be static. Due to self-averaging of electronic coupling in this fast fluctuation limit, the breakdown of the Condon approximation manifests itself as a static correction to the time-independent rate coefficient calculated for the ordered bridge with the same time-averaged electronic coupling for all pairs of adjacent subunits. As a consequence, the CT process exponentially evolves with time and therefore can be characterized by a time-independent rate coefficient wa for the charge arrival on the acceptor (also termed the rate constant). For larger τrot, however, the NC effects become purely kinetic. In this case, the process of CT in the tunneling regime exhibits time scale invariance, the corresponding decay curves become dispersive, and the rate coefficient wa turns out to be time dependent. In the limit of very slow dynamic fluctuations, where τrot . τCT, the NC effects in kinetics of CT are found (as anticipated) to be very similar to the effects revealed for bridges with the static torsional disorder. Both analytical and numerical results obtained within this limit allow the conclusion that for very slow fluctuations and/or for static disorder, the nonexponential time evolution of the CT process is due to the configuration averaging of electronic coupling. Several consequences of our theoretical findings for the interpretation of experimentally observed transients are briefly discussed. In particular, we argue that the minimal value of the falloff parameter describing the distance dependence of the time-independent rate coefficient in tunneling regime can not be less than 0.2-0.3 Å-1 and that the smaller experimental value of this parameter reported in the literature for several D-B-A systems must be attributed to the multistep hopping mechanism of charge motion rather than to the mechanism of single-step tunneling.