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, on the potential shape, the effective
mass, and the friction relaxation spectrum, but a rate theory that
accurately accounts for all of these effects does not exist. After
a review of classical reaction-rate theories, we show how to extract
all parameters of the generalized Langevin equation (GLE) 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 GLE by Markovian embedding techniques accurately reproduce
the pair-reaction kinetics from MD simulations without any fitting
parameters, which confirms the accuracy of the approximative form
of the GLE and of the parameter extraction techniques. By modification
of the GLE parameters, we investigate the relative importance of memory,
mass, and potential shape effects. Neglect of memory slows down NaCl
and methane dissociation by roughly a factor of 2; neglect of mass
accelerates reactions by a similar factor, and the harmonic approximation
of the potential shape gives rise to slight acceleration. This partial
error cancellation explains why Kramers’ theory, which neglects
memory effects and treats the potential shape in harmonic approximation,
describes reaction rates better than more sophisticated theories.
In essence, all three effects, friction memory, inertia, and the potential
shape nonharmonicity, are important to quantitatively describe pair-reaction
kinetics in water.