A promising vanadium-based photo-catalyst (InVO4) has been proposed recently by our group. This catalyst has been shown to be active in the visible light range, up to a wavelength of about 600 nm, and is able to promote the decomposition of water. In this paper, we focus on its electronic structure, computed via first principles calculations, in order to figure out analogies and differences with similar systems (InNbO4, InTaO4 and BiVO4) that have already been reported to act as photo-catalysts. An attempt is made to address the problem of the wavelength dependency of the photo catalytic activity of the InMO4 (M = V, Nb, Ta) family and how this is related to the crystal structure. Finally, by using an ab initio molecular dynamics approach, we inspect the relaxation/reconstruction phenomena occurring at the exposed surface of the InVO4 catalyst induced by the absorption of a water molecule, that represents a crucial step in the catalysis reaction.