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The rate coefficients of adsorption, desorption, Eley-Rideal (ER) and Langmuir-Hinshelwood (LH) reactions are determined for heterogeneous recombination of atomic oxygen on the a-Al2O3 surface in the 500-2000 K temperature range from the first-principle calculations on alumina clusters. These parameters are used to calculate recombination coefficients at the conditions that model the experiments at MESOX facility. Crossover from the ER-mediated to LH-mediated regime is found to occur at ca. 1100 K. Good agreement with the measurements in the 1000-1400 K temperature range attests the first-principle cluster modeling combined with the statistical methods for rate coefficient calculations as a simple and adequate approach for preliminary characterization of the prospective thermal protection coverages.