Free energy calculation of water addition coupled to reduction of aqueous $RuO4−$

Free energy calculations were carried out for water addition coupled reduction of aqueous ruthenate, $RuO4−+H2O+e−→[RuO3(OH)2]2−$⁠, using Car-Parrinello molecular dynamics simulations. The full reaction is divided into the reduction of the tetrahedral monoanion, $RuO4−+e−→RuO42−$⁠, followed by water addition, $RuO42−+H2O→[RuO3(OH)2]2−$⁠. The free energy of reduction is computed from the fluctuations of the vertical energy gap using the $MnO4−+e−→MnO42−$ reaction as reference. The free energy for water addition is estimated using constrained molecular dynamics methods. While the description of this complex reaction, in principle, involves multiple reaction coordinates, we found that reversible transformation of the reactant into the product can be achieved by control of a single reaction coordinate consisting of a suitable linear combination of atomic distances. The free energy difference of the full reaction is computed to be $−0.62eV$ relative to the normal hydrogen electrode. This is in good agreement with the experimental value of $−0.59eV$⁠, lending further support to the hypothesis that, contrary to the ruthenate monoanion, the dianion is not tetrahedral but forms a trigonal-bipyramidal dihydroxo complex in aqueous solution. We construct an approximate two-dimensional free energy surface using the coupling parameter for reduction and the mechanical constraint for water addition as variables. Analyzing this surface we find that in the most favorable reaction pathway the reduction reaction precedes water addition. The latter takes place via the protonated complex $[RuO3(OH)]−$ and subsequent transport of the created hydroxide ion to the fifth coordination site of Ru.