Heterogeneous Pair Approximation of Methanol Oxidation on TiO2 Reveals Two Reaction Pathways

We propose a novel method to simulate the chemical kinetics of methanol oxidation on the rutile TiO2(110) surface. This method must be able to capture the effects of static disorder (site-to-site variations in the rate constants), as well as dynamic correlation (interdependent probabilities of finding reactants and products next to each other). Combining the intuitions of the mean-field steady state (MFSS) method and the pair approximation (PA), we consider representative pairs of sites in a self-consistent bath of the average pairwise correlation. Pre-averaging over the static disorder in one site of each pair makes this half heterogeneous pair approximation (HHPA) efficient enough to simulate systems of several species and calibrate rate constants. According to the simulated kinetics, a static disorder in the hole transfer steps suffices to reproduce the stretched exponentials in the observed kinetics. The identity of the dominant hole scavenger is found to be temperature-dependent -- the methoxy anion at 80 K and the methanol molecule at 180 K. Moreover, two distinct groups of 5-coordinate titanium (Ti5c) sites emerge -- a high-activity group and a low-activity group -- even though no such division exists in the rate constants. Since the division is quite insensitive to the type of static disorder, the emergence of the two groups might play a significant role in a variety of photocatalytic processes on TiO2.