Effects of friction and asymmetric inner sphere reorganization energy on the electron transfer reaction rate—Two-dimensional simulations

Molecular dynamic simulations are applied to study inner sphere reorganization effects on outer-sphere electron transfer (ET) reactions. The system studied is assumed to be a complex of the form A(H2O)6. The Hamiltonian describing the one-electron reduction reaction is based on the Schmickler and Koper model [W. Schmickler, M.T.M. Koper, Electrochem. Commun. 1 (1999) 402]. The resulting potential energy is a function of the generalized solvent coordinate and the change in the A–O distance. The first hydration shell in the oxidized and reduced states is described by two harmonic oscillators with frequencies ω1 and ω2. Three cases are studied in the simulations with respect to the frequencies ratio θ = ω2/ω1: 2/3, 1 and 3/2. An effect of different friction parameters applied to the two coordinates and the activation energy on the reaction rate is analyzed and compared for the three cases. A strong decrease in the reaction rate is observed when a very low friction in the inner sphere direction is assumed. The turnover for the three cases is found to increase when θ goes from 2/3 to 3/2, but it corresponds to the friction parameter which is much lower than the barrier frequency. The relation between the saddle point avoidance phenomenon and the reaction rate is qualitatively analyzed.