Ab initio calculations, using a plane-wave, pseudopotential method, of the potential-energy surface for H-2 dissociation on W(100) are presented. The construction and testing of the W pseudopotential an discussed, as are the techniques that ensure the stability and convergence of the energy minimization scheme for large-scale metallic systems. The calculations use a supercell geometry with slabs of W separated by vacuum and H-2 molecules incident on both sides of the slab. The generalized-gradient approximation is used for exchange and correlation. Calculations on the ban W(100) slab show that the equilibrium structure has the outer layers relaxed by 9% towards the center of the slab, consistent with the experimentally determined surface structure. The most favorable adsorption site for atomic H is found to be at the bridge, with the hollow and top sites being 0.4 eV and 0.7 eV higher in energy, respectively. Two-dimensional potential-energy surfaces for H-2 dissociation are presented for a number of high-symmetry dissociation pathways with the molecular axis both parallel and perpendicular to the surface. The calculations show that there is no energy barrier to dissociation over much of the surface. There is no sign of the precursor state that has been used to interpret molecular-beam experiments on the H-2/W(100) system. An alternative interpretation, based on molecular steering, is advanced.