Extended Brownian dynamics. III. Three-dimensional diffusion

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Abstract
An improved version of the ‘‘extended Brownian dynamics’’ algorithm recently proposed [J. Chem. Phys. 78, 2713 (1983)] is given. This work represents the conclusion of an analysis of a Monte Carlo approach to diffusion. The algorithm suggested here and in the previous paper is a procedure for solving the full three-dimensional Smoluchowski diffusion equation, including general force and reaction terms and boundary conditions. The method is most suited for the investigation of diffusion-controlled systems with asymmetric geometries. In this paper a general overview of the Monte Carlo approach is presented. A slight modification to the one-dimensional algorithm introduced earlier is given and the extensions necessary to treat three-dimensional diffusion are discussed. The procedure is then applied to three-dimensional free diffusion and diffusion in a Coulomb force and the reaction yields for these processes are presented and compared with other numerical and analytic results. A summary of the Monte Carlo method is given and comments concerning the advantages and difficulties of the algorithm are made.