Recently, a derivative of the heptazine (tris-triazine) molecule, trianisole-heptazine (TAHz), was synthesized and was shown to catalyze the oxidation of water to hydroxyl radicals under 365 nm LED light in a homogeneous reaction (E. J. Rabe et al., J. Phys. Chem. Lett. 2018, 9, 6257-6261). The possibility of water photo-oxidation with a precisely defined molecular catalyst in neat solvents opens new perspectives for clarifying the fundamental reaction mechanisms involved in water oxidation photocatalysis. In the present work, the effects of chemical substituents on the three CH positions of Hz on the photocatalytic reactivity were explored with wave function-based ab initio electronic-structure calculations for hydrogen-bonded complexes of Hz and three selected Hz derivatives (TAHz, trichloro-Hz, and tricyano-Hz) with a water molecule. While anisole is an electron-donating substituent, Cl is a weakly electron-withdrawing substituent and CN is a strongly electron-withdrawing substituent. It is shown that the barrier for the photoinduced abstraction of an H atom from the water molecule is raised (lowered) by electron-donating (electron-withdrawing) substituents. The highly mobile and reactive hydroxyl radicals generated by water oxidation can recombine with the reduced chromophore radicals to yield photohydrates. The effect of substituents on the thermodynamics of the photohydration reaction was computed. Among the four chromophores studied, TAHz stands out on account of the metastability of its photohydrate, which suggests self-healing of the photocatalyst after oxidation of TAHzH radicals by OH radicals. In addition, the effect of substituents on the H atom photodetachment reaction from the reduced chromophores, which closes the catalytic cycle, has been investigated. The energy of the repulsive 2πσ* state, which drives the photodetachment reaction is lowered (raised) by electron-donating (electron withdrawing) substituents. All four chromophores exhibit inverted S1/T1 gaps. This feature eliminates long-lived triplet states and thus avoids the activation of molecular oxygen to highly reactive singlet oxygen.