A novel model is derived for electrochemical solar water splitting processes by semiconductors, which is the first derivation of band gap restricted thermal enhanced solar water splitting efficiencies. The theory combines photodriven charge transfer, with excess subband gap insolation to lower the water potential, providing a process of highly efficient elevated temperature solar electrolysis of water to H-2 fuel. Solar water splitting can provide clean, renewable sources of H-2 fuel. Prior models had indicated only low conversion efficiencies would be attainable. A theoretical basis is developed for solar energy conversion efficiencies in the 50% range as determined for both AM0 and AM1.5 insolation-with contemporary thermodynamic values over a wide range of temperature and pressure conditions. The temperature and pressure consistent for a range of systems with various minimum band gaps, E-g min(T,p), are determined. At these values of T and p a photoelectonic conversion efficiency, eta(photo), yields a solar energy conversion efficiency for water splitting of eta(solar max)(T,p) (1.229 V)eta(photo)/Edegrees(H2O)(T,p(H2O)). At p(H2O) = 1 bar, values of Edegrees(H2O) include 1.229 V (25 degreesC), 1.167 V (100 degreesC), 1.116 V (300 degreesC), 1.034 V (600 degreesC), 0.919 V (1000 degreesC), and 0.771 V (1500 degreesC); at p(H2O) = 500 bar values of Edegrees(H2O) include 1.224 V (25 degreesC), 1.163 V (100 degreesC), 1.007 V (300 degreesC), 0.809 V (600 degreesC), and 0.580 V (1000 degreesC).