Molecular hydrogen (H-2) is an excellent alternative fuel. It can be produced from the abundantly present water on earth. Transition-metal oxides are widely used in the environmentally benign photocatalytic generation of H-2 from water, thus actively driving scientific research on the mechanisms for this process. In this study, we investigate the chemical reactions of W3O5- and Mo3O5- clusters with water that shed light on a variety of key factors central to H-2 generation. Our computational results explain why experimentally Mo3O5- forms a unique kinetic trap in its reaction while W3O5- undergoes a facile oxidation to form the lowest-energy isomer of W3O6- and liberates H-2. Mechanistic insights on the reaction pathways that occur, as well as the reaction pathways that do not occur, are found to be of immense assistance to comprehend the hitherto poorly understood pivotal roles of (a) differing metal-oxygen and metal-hydrogen bond strengths, (b) the initial electrostatic complex formed, (c) the loss of entropy when these TMO clusters react with water, and (d) the geometric factors involved in the liberation of H-2.