We construct a rigid-body (five-dimensional) potential-energy surface for the water-hydrogen complex using scaled perturbation theory (SPT). An analytic fit of this surface is obtained, and, using this, two minima are found. The global minimum has C-2v symmetry, with the hydrogen molecule acting as a proton donor to the oxygen atom on water. A local minimum with C-s symmetry has the hydrogen molecule acting as a proton acceptor to one of the hydrogen atoms on water, where the OH bond and H-2 are in a T-shaped configuration. The SPT global minimum is bound by 1097 muE(h) (E(h)approximate to4.359 744x10(-18) J). Our best estimate of the binding energy, from a complete basis set extrapolation of coupled-cluster calculations, is 1076.1 muE(h). The fitted surface is used to calculate the second cross virial coefficient over a wide temperature range (100-3000 K). Three complementary methods are used to quantify quantum statistical mechanical effects that become significant at low temperatures. We compare our results with experimental data, which are available over a smaller temperature range (230-700 K). Generally good agreement is found, but the experimental data are subject to larger uncertainties. (C) 2004 American Institute of Physics.