An accurate expression for the rates of diffusion-influenced bimolecular reactions with long-range reactivity

By using the recently developed method for solving the Fredholm integral equations of the second kind, we derive a very accurate expression for the steady-state rate constant of diffusion-influenced bimolecular reactions involving long-range reactivity. We consider the general case in which the reactants interact via an arbitrary central potential and hydrodynamic interaction. The rate expression becomes exact in the two opposite limits of small and large reactivity, and also performs very well in the intermediate regime.