A new ab initio pair potential for water was generated by fitting 2510 interaction energies computed by the use of symmetry-adapted perturbation theory (SAPT). The new site-site functional form, named SAPT-5s, is simple enough to be applied in molecular simulations of condensed phases and at the same time reproduces the computed points with accuracy exceeding that of the elaborate SAPT-pp functional form used earlier [J. Chem. Phys. 107, 4207 (1997)]. SAPT-5s has been shown to quantitatively predict the water dimer spectra, see the following paper (paper II). It also gives the second virial coefficient in excellent agreement with experiment. Features of the water dimer potential energy surface have been analyzed using SAPT-5s. Average values of powers of the intermolecular separation-obtained from the ground-state rovibrational wave function computed in the SAPT-5s potential-have been combined with measured values to obtain a new empirical estimate of the equilibrium O-O separation equal to 5.50 +/-0.01 bohr, significantly shorter than the previously accepted value. The residual errors in the SAPT-5s potential have been estimated by comparison to recent large-scale extrapolated ab initio calculations for water dimer. This estimate-together with the dissociation energy D-0 computed from SAPT-5s-leads to a new prediction of the limit value of D-0 equal to 1165 +/- 54 cm(-1), close to but significantly more accurate than the best empirical value.