A nonadiabatic theory for electron transfer and application to ultrafast catalytic reactions

We propose a general formalism which extends those used for the standard theory of electron transfer (ET) in chemistry but also becomes equivalent to it far from the inversion point. Our model yields different results essentially in the vicinity of the inversion point when the energy barrier for ET is small. In that regime, the electronic frequencies become of the order of the phonon frequencies and the process of electron tunnelling is nonadiabatic because it is strongly coupled to the phonons. The consequence of nonadiabaticity is that the effective electron dynamics becomes nonlinear and that there is energy dissipation through the phonon bath. 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 donor and acceptor becomes reversible. Then, large amplitude electronic oscillations, associated with large amplitude and collective phonon oscillations at the same frequency, are spontaneously generated. This system is a coherent electron-phonon oscillator (CEPO) which cannot be confused with a standard normal mode. The acceptor which does not capture the electron may play the role of a catalyst. Thus when the catalyst is finely tuned with the donor in order to form a CEPO, it may trigger an irreversible and ultrafast electron transfer at low temperature between the donor and an extra acceptor, while in the absence of a catalyst, ET cannot occur. Such a trimer system may be regulated by small perturbations and behaves as a molecular transistor. We illustrate this idea by explicit numerical simulations on trimer models of the type donor-catalyst-acceptor. We discuss the relevance of our approach for understanding the ultrafast electron transfer experimentally observed in biosystems such as the photosynthetic reaction centre