  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 earlier work of Wu et
al. 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. smaller value for reorganization free energy can be explained by
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.
