The temperature and density dependence of the molecular and thermodynamic properties of water is investigated theoretically by means of the ab initio electronic structure theory combined with the reference interaction site model method, so-called RISM-SCF. We consider the autoionization process (H2O + H2O reversible arrow H3O+ + OH-) by regarding H2O, H3O+, and OH- as "solute" molecules in an aqueous solution and evaluate molecular geometry, electronic structure, solvation Structure, and the ionic product of water (pK(w)) of these species as functions of thermodynamic conditions. In our previous paper, we calculated these properties by using essentially the same method in a wide range of density values (0.6-1.4 g/cm(3)). However, the calculation was limited at rather higher density (> 0.6 g/cm(3)) due to the difficulty of convergence, which is inherent to the hypernetted-chain (HNC) closure. The problem is overcome in this study by employing the Kovalenko-Hirata (KH) closure which hybridizes the HNC and the mean-spherical approximation (MSA). Here, we present the results for the thermodynamic range of densities from 0.025 to 1.0 g/cm(3) and for temperatures from 300 to 800 K including the supercritical point.