We present a new parametrization for the embedded-diatomics-in-molecules (EDIM) potential energy function that is significantly more accurate than the previous one for the interactions of two H atoms with a Ni surface or with a third H atom. Thus, it can be used to study lateral interactions of H2 with H, and it is also parametrized for a system of three H atoms on a Ni surface. In addition, the metal atom parameters are independent of which layer the metal atom is in so there is no ambiguity in studying reactions at steps or kinks. We apply canonical variational transition state theory with semiclassical transmission coefficients to investigate the dynamics of the dissociative chemisorption of gas-phase H2 molecules on both single-crystal-face and stepped Ni(100) surfaces. We also consider the effect of additional H atoms, and we compre results for clean and partially covered surfaces. We find that classical transition-state recrossing and quantal tunneling effects are very important in the dissociation of H2 on the clean Ni(100) surface. The presence of a step on the metal surface is found to increase the rate of chemisorption significantly, while somewhat decreasing the kinetic isotope effect (KIE). Conversely, the presence of adsorbed H atoms is found to decrease (poison) the chemisorption rate, although it increases the KIE. The results are consistent with experimental observations. Finally, the exchange reaction on Ni(100) is found to proceed most favorably by a two-step mechanism consisting of dissociative chemisorption of H2 followed by recombination with a coadsorbed H atom.