The catalytic activity toward H-2 dissociation of several Au nanoparticles of different shape, supported on stoichiometric and reduced TiO2 surfaces, has been investigated by means of periodic DF calculations. Gold nanoparticles become positively charged when supported on stoichiometric TiO2 and negatively charged when adsorbed on the reduced surface, although this finding does not appear to be relevant for H-2 dissociation activity. It is shown that Au atoms active for H-2 dissociation must be neutral or with a net charge close to zero, and be located at corner or edge low coordinated positions and not directly bonded to the support. The particles with the largest number of potentially active sites for H-2 dissociation are 2L isomers consisting of at least one bottom layer of gold atoms in contact with the support and therefore inactive, and one top layer with low coordinated gold atoms on which H-2 is adsorbed and activated. The presence of O-vacancy defects in reduced surfaces preferentially stabilizes the most active 2L particles, while less active 1L isomers are the most stable on the stoichiometric surfaces.