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Photocatalysis induced by sunlight is one of the most promising approach toenvironmental protection, solar energy conversion and sustainable production offuels. The computational modeling of photocatalysis is a rapidly expendingfield which requires to adapt and further develop the available theoreticaltools. The coupled transfer of proton and electron is an important reactionduring photocatalysis. In this work, we present the first step of ourmethodology development in which we apply existing kinetic theory of suchcoupled transfer to a model system, namely, methanol photo-dissociation onrutile TiO$_2$(110) surface, with the help of high-level first-principlescalculations. Moreover, we adapt the Stuchebrukhov-Hammes-Schiffer kinetictheory, where we use the Georgievskii-Stuchebrukhova vibronic coupling, tocalculate the rate constant of the proton coupled electron transfer reactionfor a particular pathway. In particular, we propose a modified expression tocalculate the rate constant which enforces the near-resonance condition for thevibrational wavefunction during proton tunneling.

Theoretical study of kinetics of proton coupled electron transfer in photocatalysis