A classical Lennard-Jones potential is derived from a fit to the ab initio energies obtained from an all-electron mixed-basis calculation for methane in zeolite LTA. The potential predicts the heat of adsorption, adsorption isotherm, and self-diffusivity of methane in excellent agreement with experiment. This study suggests, for the first time, that ab initio energies-in addition to experimental data-can form a good basis for derivation of accurate classical potentials between organic and inorganic elements.