The ionic product of water (pK(w)) has been calculated in a wide range of temperature (0-600 degrees C) and density (0.6-1.4 g/cm(3)) by means of ab initio electronic structure theory combined with the extended reference interaction site model in statistical mechanics for molecular liquids (RISM-SCF/MCSCF). 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 geometries, electronic structure, solvation structure, and free energy components of these species as functions of thermodynamical conditions. The results for pK(w) obtained from the theory have shown a monotonical decrease with increasing density at all the temperatures investigated, in good accord with the experimental observation. The behavior is determined essentially by the difference in solvation free energies, Delta mu(H3O+) + Delta mu(OH-) - 2 Delta mu(H2O), associated with the reaction. The Delta mu(OH-) shows the density dependence, which is entirely different from that of the other species and which gives rise to the observed behavior for Delta log K-w. It is shown through analyses of the electronic structure of the "solutes" that the distinct density dependence of Delta mu(OH-) has the origin in its rather "soft" electronic cloud interacting with solvent polarization.