Rate of Reaction of Electron Transfer over a Long Range and Mediated by a Solvent

We present a simple quantum mechanical model for solvent bridge‐mediated long‐range nonadiabatic electron‐transfer reaction rate. A perturbation theory using a one‐electron model is employed to treat the electronic transition element that includes donor, acceptor and bridge unit wave functions. Reaction‐coordinate activation is treated by high‐temperature approximation. The pre‐exponential factor in the rate coefficient becomes dependent on the distance between donor and acceptor; the decay length depends strongly on the driving force and is effective at a large range if the level of energy of the donor is nearly that of the bridge. This condition is satisfied for a process of electron transfer with excited donor molecules or in the highly exothermic regime. According to a simple model calculation, the non‐existence of an “inverted” regime in highly exothermic reaction is favored for solvent media with large relative permittivity and low‐lying HOMO (highest occupied molecular orbital) or LUMO (lowest unoccupied molecular orbital). In the normal regime in which the driving force (ΔG°) is positive or nearly zero this effect at large‐range is negligible, and transfer of the electron occurs mostly at the distance of contact.