A nonadiabatic theory for electron transfer and application to ultrafast catalyticreactions

Abstract

We propose a general formalism which extends those used for the standard theory ofelectron transfer (ET) in chemistry but also becomes equivalent to it far from theinversion point. Our model yields different results essentially in the vicinity ofthe inversion point when the energy barrier for ET is small. In that regime, theelectronic frequencies become of the order of the phonon frequencies and theprocess of electron tunnelling is nonadiabatic because it is strongly coupled tothe phonons. The consequence of nonadiabaticity is that the effective electrondynamics becomes nonlinear and that there is energy dissipation through the phononbath. Thermal fluctuations appears as a random force in the effective equation.We use this formalism for a careful investigation of the vicinity of the inversion point.We find that when the model parameters are finely tuned, ET between donorand acceptor becomes reversible. Then, large amplitude electronic oscillations,associated with large amplitude and collective phonon oscillations at the samefrequency, are spontaneously generated. This system is a coherent electron–phononoscillator (CEPO) which cannot be confused with a standard normal mode. Theacceptor which does not capture the electron may play the role of a catalyst. Thuswhen the catalyst is finely tuned with the donor in order to form a CEPO, itmay trigger an irreversible and ultrafast electron transfer at low temperaturebetween the donor and an extra acceptor, while in the absence of a catalyst, ETcannot occur. Such a trimer system may be regulated by small perturbations andbehaves as a molecular transistor. We illustrate this idea by explicit numericalsimulations on trimer models of the type donor–catalyst–acceptor. We discussthe relevance of our approach for understanding the ultrafast electron transferexperimentally observed in biosystems such as the photosynthetic reaction centre.