This computational study is motivated by the apparent conflict between an experiment on dissociation of H-2 and D-2 on Pt(111), which suggests a rather corrugated potential energy surface (PES) for the H-2/Pt(111) system, and an experiment showing only weak nonzero-order diffraction of HD scattering from Pt(111). In the calculations we have used density functional theory (DFT) within the generalized gradient approximation (GGA), including scalar relativistic effects and modelling the Pt(111) surface as a slab. We have found that the H-2/Pt(111) PES is both energetically and geometrically corrugated. We have also found that there are reaction paths without or with very low barriers leading to dissociation of H-2 on the Pt(111) surface, but that there are other reaction paths with substantial barriers. By performing extensive calculations on H interacting with a Pt(111) surface we have shown that a DFT/GGA approach that includes scalar relativistic effects is capable of describing the interaction between a hydrogen atom and a Pt(111) surface in a way that is, for the most part, consistent with experiments.