The kinetics of a diffusion-influenced reaction is described by a time-dependent rate coefficient k(t). In this paper, we implement an algorithm for calculating k(t), introduced by one of us, in the UHBD software package. In the implementation, the electrostatic force exerted on a diffusing substrate by an enzyme is obtained from a finite-difference solution of the Poisson equation. The rate coefficient is obtained by starting the substrate in the active site and monitoring its survival probability using Brownian dynamics simulations. The technique is applied to the binding of superoxide to Cu/Zn superoxide dismutase. The long-time limit of k(t) is found to be in agreement with both the experimental value and that calculated using an algorithm designed specifically for finding k(infinity).