The diffusion of a sorbate molecule in a zeolite can be studied using transition-state theory. In this application, and other applications of transition-state theory, finding all local minima and saddle points of the potential energy surface is a critical computational step. A new strategy is described here for locating stationary points on a potential energy surface. The methodology is based on interval analysis, and provides a mathematical and computational guarantee that all stationary points will be found. The technique is demonstrated using potential energy surfaces arising in the use of transition-state theory to study the diffusion of three sorbates, xenon, methylene, and sulfur hexafluoride, at infinite dilution in silicalite. (C) 2004 American Institute of Physics.