Confronting surface hopping molecular dynamics with Marcus theory for a molecular donor-acceptor system

We investigate the performance of fewest switches surface hopping (SH) in describing electron transfer (ET) for a molecular donor-acceptor system. Computer simulations are carried out for a wide range of reorganisation energy (lambda), electronic coupling strength (H-ab) and driving force using our recently developed fragment orbital-based SH approach augmented with a simple decoherence correction. This methodology allows us to compute SH ET rates over more than four orders of magnitude, from the sub-picosecond to the nanosecond time regime. We find good agreement with semi-classical ET theory in the non-adiabatic ET regime. The correct scaling of the SH ET rate with electronic coupling strength is obtained and the Marcus inverted regime is reproduced, in line with previously reported results for a spin-boson model. Yet, we find that the SH ET rate falls below the semi-classical ET rate in the adiabatic regime, where the free energy barrier is in the order of k(B)T in our simulations. We explain this by first signatures of non-exponential population decay of the initial charge state. For even larger electronic couplings (H-ab = lambda/2), the free energy barrier vanishes and ET rates are no longer defined. At this point we observe a crossover from ET on the vibronic time scale to charge relaxation on the femtosecond time scale that is well described by thermally averaged Rabi oscillations. The extension of the analysis from the non-adiabatic limit to large electronic couplings and small or even vanishing activation barriers is relevant for our understanding of charge transport in organic semiconductors.