Reactive trajectories of the Ru2^+/3+ self-exchange reaction and the connection to Marcus' theory

Outer sphere electron transfer between two ions in aq. soln. is a rare event on the time scale of first principles mol. dynamics simulations. We have used transition path sampling to generate an ensemble of reactive trajectories of the self-​exchange reaction between a pair of Ru²⁺ and Ru³⁺ ions in water. To distinguish between the reactant and product states, we use as an order parameter the position of the maximally localised Wannier center assocd. with the transferring electron. This allows us to align the trajectories with respect to the moment of barrier crossing and compute statistical avs. over the path ensemble. We compare our order parameter with two typical reaction coordinates used in applications of Marcus theory of electron transfer: the vertical gap energy and the solvent electrostatic potential at the ions.