Understanding the interaction of multiple types of adsorbate molecules on solid surfaces is crucial to establishing the stability of catalysts under various chemical environments. Computational studies on the high coverage and mixed coverages of reaction intermediates are still challenging, especially for transition-metal compounds. In this work, we present a framework to predict differential adsorption energies and identify low-energy structures under high- and mixed-adsorbate coverages on oxide materials. The approach uses Gaussian process machine-learning models with quantified uncertainty in conjunction with an iterative training algorithm to actively identify the training set. The framework is demonstrated for the mixed adsorption of CH<sub>x</sub>, NH<sub>x</sub> and OH<sub>x</sub> species on the oxygen vacancy and pristine rutile TiO<sub>2</sub>(110) surface sites. The results indicate that the proposed algorithm is highly efficient at identifying the most valuable training data, and is able to predict differential adsorption energies with a mean absolute error of ~0.3 eV based on <25% of the total DFT data. The algorithm is also used to identify 76% of the low-energy structures based on <30% of the total DFT data, enabling construction of surface phase diagrams that account for high and mixed coverage as a function of the chemical potential of C, H, O, and N. Furthermore, the computational scaling indicates the algorithm scales nearly linearly (N<sup>1.12</sup>) as the number of adsorbates increases. This framework can be directly extended to metals, metal oxides, and other materials, providing a practical route toward the investigation of the behavior of catalysts under high-coverage conditions.
Stochastic quantization at finite chemical potential
