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Oxides containing metals or metalloids from the p block of the periodic table (e.g., In, Sn, Sb, Pb, and Bi) are of technological interest as transparent conductors and light absorbers for solar-energy conversion due to the tunability of their electronic conductivity and optical absorption. Comparatively, these oxides have found limited applications in hydrogen photoelectrolysis, primarily due to their high electronegativity, which impedes electron transfer for reducing protons into hydrogen. We have shown recently that inserting s-block cations into p-block metal oxides is effective at lowering electronegativities while affording further control of band gaps. Here, we explain the origins of this dual tunability by demonstrating the mediator role of s-block cations in modulating orbital hybridization while not contributing to frontier electronic states. From this result, we carry out a comprehensive computational study of 109 ternary oxides of s- and p-block metal elements as candidate photocatalysts for solar hydrogen generation. We down-select the most desirable materials using band gaps and band edges obtained from Hubbard-corrected density-functional theory, with Hubbard parameters computed entirely from first principles, evaluate the stability of these oxides in aqueous conditions, and characterize experimentally four of the remaining materials, synthesized with high phase uniformity, to validate and further develop the computational models. We thus propose nine oxide semiconductors, including CsIn_{3}O_{5}, Sr_{2}In_{2}O_{5}, and KSbO_{2}, which, to the extent of our literature review, have not been previously considered as water-splitting photocatalysts.