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We have performed calculations on the dissociative chemisorption of H2 on un-reconstructed and reconstructed Au(111) with density functional theory, and dynamics calculations on this process on un-reconstructed Au(111). Due to a very late barrier for dissociation, H2 + Au(111) is a candidate H2-metal system for which the dissociative chemisorption could be considerably affected by the energy transfer to electron-hole pairs. Minimum barrier geometries and potential energy surfaces were computed for six density functionals. The functionals tested yield minimum barrier heights in the range of 1.15-1.6 eV, and barriers that are even later than found for the similar H2 + Cu(111) system. The potential energy surfaces have been used in quasi-classical trajectory calculations of the initial (v,J) state resolved reaction probability for several vibrational states v and rotational states J of H2 and D2. Our calculations may serve as predictions for state-resolved associative desorption experiments, from which initial state-resolved dissociative chemisorption probabilities can be extracted by invoking detailed balance. The vibrational efficacy ηv=0→1 reported for D2 dissociating on un-reconstructed Au(111) (about 0.9) is similar to that found in earlier quantum dynamics calculations on H2 + Ag(111), but larger than found for D2 + Cu(111). With the two functionals tested most extensively, the reactivity of H2 and D2 exhibits an almost monotonic increase with increasing rotational quantum number J. Test calculations suggest that, for chemical accuracy (1 kcal/mol), the herringbone reconstruction of Au(111) should be modeled. [ABSTRACT FROM AUTHOR]