We report ab initio density functional theory calculations for the metal-free phthalocyanine (H2Pc) and zinc phthalocyanine (ZnPc) molecules adsorbed on rutile titania TiO2(110) stoichiometric and reduced surface. The hybrid nanostructures that combine titania surfaces with organic molecules help to improve the applications for both the titania surface and the organic molecule. We determine the atomic structures for all possible adsorption sites through total energy calculations and atomic structure optimizations. We find that the surface oxygen atoms play a crucial role in determining the best adsorption position and adsorption energies. Charge transfer occurs from the phthalocyanine to the surface. The electronic structure of the hybrid system indicates the appearance of surface states in the energy gap of the bare surface. We univocally determined that these new states involve N atoms and are originated only from the surface atoms with no bulk contribution.