Here we use the extensive datasets of CCSD(T) energies for 2, 3 and 4-b interactions that we recently reported and used to develop the q-AQUA potential, which we remind the reader is truncated at the 4-b level. Thus, q-AQUA is a fully ab initio MB water potential. These datasets are used to fit the difference potentials ∆V n-b , n = 2, 3, 4, where we use the well-known TTM3-F as the polarizable FF for water. Details of these fits and fast gradient evaluation are given below. Standard tests of the new potential, denoted q-AQUApol, are also provided. These are diffusion Monte Carlo calculations of the dissociation energies of the water dimer and trimer, the energies of the hexamer isomers, the water radial distribution functions, the temperature dependence of the density at 1 atm, the tetrahedral order parameter and the triplet OOO angular distribution. The new potential is shown to be slight improvement over the already highly accurate q-AQUA potential for the hexamer energies. Significant improvements are seen for these energies as well as for the temperature dependence of the density compared to the MB-pol potential.