Non-Condon theory of nonadiabatic electron transfer reactions in V-shaped donor–bridge–acceptor complexes

Abstract

The rate of nonadiabatic long-distance electron transfer (ET) is derived for the direct and superexchange electronic coupling between the donor and acceptor. The model takes into account a non-Condon thermal modulation of the electronic coupling through the interaction of the system transition dipoles with the polarization fluctuations of the solvent. Going from a linear donor–bridge–acceptor complexes to a bent, V-shaped geometry lowers the system symmetry resulting in several novel properties of the ET matrix element based on the fact that permanent and transition dipoles in the system are not polarized along the direction of ET. The effective ET matrix element HET gains two zeros as a function of the donor–acceptor vertical energy gap. The positions of zeros of HET depend on the sign relations between the donor–bridge and bridge–acceptor electronic couplings and corresponding transition dipoles. The ET matrix element becomes dependent on solvent through the solvent refractive index and the inhomogeneous width of the donor–acceptor optical transition. The former factor is mainly responsible for the temperature slope of |HET|. The derivative d|HET|/dT switches its sign at the zero points of HET. The distance decay parameter of the donor–acceptor coupling is shown to vary linearly with the inhomogeneous width of the optical transition between the donor and acceptor.