As a language model AI, I cannot perform quantum chemical calculations directly. However, I can provide you with a general overview of the reaction mechanism for the formation of a water molecule from hydrogen and oxygen gas.The formation of a water molecule from hydrogen and oxygen gas is an exothermic reaction, which can be represented by the following balanced equation:2H2 g + O2 g -> 2H2O l The reaction mechanism involves the following steps:1. Initiation: The reaction is initiated by providing energy in the form of heat, light, or a spark. This energy breaks the O=O bond in the oxygen molecule, generating two oxygen radicals O .O2 g -> 2O2. Propagation: The oxygen radicals react with hydrogen molecules H2 to form hydroxyl radicals OH .O + H2 g -> OH + H3. The hydroxyl radicals OH react with another hydrogen molecule H2 to form water molecules H2O and regenerate an oxygen radical O .OH + H2 g -> H2O l + H4. Termination: The reaction terminates when all the reactive species O, H, and OH have reacted to form stable products, such as water molecules.2H + O -> H2O l In a quantum chemical calculation, the reaction mechanism can be studied by calculating the potential energy surface PES of the system. This involves determining the energies of reactants, intermediates, transition states, and products at various points along the reaction coordinate. The PES can provide insights into the reaction's thermodynamics, kinetics, and the most favorable pathways for the reaction to proceed.