With a view to a better understanding of the influence of atomic quantum delocalization effects on the phase behavior of water, path integral simulations have been undertaken for almost all of the known ice phases using the TIP4P/2005 model in conjunction with the rigid rotor propagator proposed by Muser and Berne [Phys. Rev. Lett. 77, 2638 (1996)]. The quantum contributions then being known, a new empirical model of water is developed (TIP4PQ/2005) which reproduces, to a good degree, a number of the physical properties of the ice phases, for example, densities, structure, and relative stabilities.