Charge constrained density functional molecular dynamics for simulation of condensed phase electron transfer reactions

We present a plane-wave basis set implementation of charge constrained density functional molecular dynamics (CDFT-MD) for simulation of electron transfer reactions in condensed phase systems. Following the earlier work of Wu and Van Voorhis [Phys. Rev. A 72, 024502 (2005)], the density functional is minimized under the constraint that the charge difference between donor and acceptor is equal to a given value. The classical ion dynamics is propagated on the Born-Oppenheimer surface of the charge constrained state. We investigate the dependence of the constrained energy and of the energy gap on the definition of the charge and present expressions for the constraint forces. The method is applied to the Ru2+-Ru3+ electron self-exchange reaction in aqueous solution. Sampling the vertical energy gap along CDFT-MD trajectories and correcting for finite size effects, a reorganization free energy of 1.6 eV is obtained. This is 0.1-0.2 eV lower than a previous estimate based on a continuum model for solvation. The smaller value for the reorganization free energy can be explained by the fact that the Ru-O distances of the divalent and trivalent Ru hexahydrates are predicted to be more similar in the electron transfer complex than for the separated aqua ions.