We have developed a potential energy function for the interaction of H, CH3, and CH4 with crystalline Ni surfaces and the dissociation reaction of CH4 on such surfaces. The potential is based on the embedded diatomics-in-molecules (EDIM) formalism, and it involves mixing the semiempirical diatomics-in-molecules (DIM) valence bond method for the covalent part of the system (CH4) with the embedded atom method (EAM) for the metal. A new molecular modeling technique is developed to accomplish this, and it employs a physically motivated mapping of electron density into an effective interatomic distance. The EDIM potential energy surface is calibrated against experimental findings and ab initio electronic structure calculations for CH3 and CH4 adsorbed on Ni(111), and it reproduces the best available binding geometries, energies, and frequencies quite well. Based on the behavior of the methyl torsion mode for CH3 in the 3-fold hollow site, our results indicate that the minimum energy orientation for this site has the H atoms staggered with respect to the three Ni atoms that form the hollow site. This differs from the prediction of previous calculations, and we present a possible explanation for this discrepancy. Finally, we calculated the barrier height for dissociative chemisorption of methane to produce CH3 and H, and we obtained 13.8 kcal/mol, which is within the range of estimates obtained from experiment.