Competition of memory, potential-shape and inertial effects on pair-reaction dynamics in water

When described by a one-dimensional reaction coordinate, pair-reaction rates in a solvent depend, in addition to the potential barrier height and the friction coefficient, also on the potential shape, the effective mass and the friction relaxation spectrum, but a rate theory that accurately accounts for all these effects does not exist. We extract all parameters and in particular the friction memory function from molecular dynamics (MD) simulations of two prototypical pair reactions in water, the dissociation of NaCl and of two methane molecules. The memory exhibits multiple time scales and, for NaCl, pronounced oscillatory components. Simulations of the resulting generalized Langevin equation by Markovian embedding techniques accurately reproduce the pair-reaction kinetics from MD simulations and thereby enable us to investigate the relative importance of memory, mass and potential-shape effects. Neglect of memory slows down reactions by roughly a factor of two, neglect of mass accelerates reactions by a similar factor, the harmonic approximation of the potential shape gives rise to acceleration. This partial error cancellation explains why Kramers theory, which neglects memory effects and approximates the potential as a double parabola, describes reaction rates better than more sophisticated theories. In essence, all three effects, friction memory, inertia and the nonharmonic potential shape, are important to quantitatively describe pair-reaction kinetics in water.