A difficulty in the generation and testing of intermolecular interaction potentials has to do with the effects of vibrational motion. For weak modes, the vibrational excursions can be and often are sizable. So, not only do model potentials have to be suitable over a considerable range, they must also be accurate with respect to experimental data that reflects the vibrational averaging (i.e., on-average structures). In this report, we present an explicit interaction potential for the water dimer that has been devised with a systematic treatment of vibrational effects by means of quantum Monte Carlo treatment of the vibrational ground state. The model potential uses intrinsic electrical properties of isolated water and four empirical parameters. An iterative procedure based on matching measured on-average rotational constants to calculated values was used to select the atom-atom Lennard-Jones (empirical) parameters. We present the results of these calculations, including zero point vibrational energies and on-average separations.