Kinetic Monte Carlo method for simulating reactions in solutions

We present an off-lattice kinetic Monte Carlo method, which is useful to simulate reactions in solutions. We derive the method from first-principles. We assume that diffusion leads to a Gaussian distribution for the position of the particles. This allows us to deal with the diffusion analytically, and we only need to simulate the reactive processes. The rate constants of these reactions can be computed before a simulation is started, and need not be computed on-the-fly as in other off-lattice kinetic Monte Carlo methods. We show how solvent molecules can be removed from the simulations, which minimizes the number of particles that have to be simulated explicitly. We present the relation with the customary macroscopic rate equations, and compare the results of these equations and our method on a variation of the Lotka model.