Here we present a thorough density functional theory study, including and excluding dispersive forces interaction description, on the adsorption and dissociation of H-2 molecule on the low-index Miller Cu (111), (100), and (110) surfaces and two different surface Cu nanorows, all displaying a different number of surface nearest neighbors, nn. The computational setup has been optimized granting an accuracy below 0.04 eV. Surface and nanorow energies-for which a new methodology to extract them is presented-are found to follow the nn number. However, the adsorption strength is found not to. Thus, the adsorption energies seem to be governed by a particular orbital <-> band interaction rather than by the simple nn surface saturation. The van der Waals (vdW) forces are found to play a key role in the adsorption of H-2, and merely an energetic adjustment on chemisorbed H adatoms. Neither clear trends are observed for H-2 and H adsorption energies, and H-2 dissociation energy with respect nn, and nor Bronsted-Evans-Polanyi, making H-2 adsorption and dissociation a trend outlier compared to other cases. H-2 is found to adsorb and dissociate on Cu(100) surface. On the Cu(111) surface, the rather small H-2 adsorption energy would prevent H-2 dissociation, regardless if it is thermodynamically driven. On Cu(110) surface, the H-2 dissociation process would be endothermic and achievable if adsorption energy is released on surpassing the dissociation energy barrier. On low-coordinated sites on Cu nanorows, vdW plays a key role in the H-2 dissociation process, which otherwise is found to be endothermic. Indeed, dispersive forces turn the process markedly exothermic. Nanoparticle Cu systems must display Cu(100) surfaces or facets in order to dissociate H-2, vital in many hydrogenation processes. (C) 2015 Elsevier B.V. All rights reserved.