Comprehensive sampling of coverage effects in catalysis by leveraging generalization in neural network models†

Sampling high-coverage configurations and predicting adsorbate–adsorbate interactions on surfaces are highly relevant to understand realistic interfaces in heterogeneous catalysis. However, the combinatorial explosion in the number of adsorbate configurations among diverse site environments presents a considerable challenge in accurately estimating these interactions. Here, we propose a strategy combining high-throughput simulation pipelines and a neural network-based model with the MACE architecture to increase sampling efficiency and speed. By training the models on unrelaxed structures and energies, which can be quickly obtained from single-point DFT calculations, we achieve excellent performance for both in-domain and out-of-domain predictions, including generalization to different facets, coverage regimes and low-energy configurations. From this systematic understanding of model robustness, we exhaustively sample the configuration phase space of catalytic systems without active learning. In particular, by predicting binding energies for over 14 million structures within the neural network model and the simulated annealing method, we predict coverage-dependent adsorption energies for CO adsorption on six Cu facets (111, 100, 211, 331, 410 and 711) and the co-adsorption of CO and CHOH on Rh(111). When validated by targeted post-sampling relaxations, our results for CO on Cu correctly reproduce experimental interaction energies reported in the literature, and provide atomistic insights on the site occupancy of steps and terraces for the six facets at all coverage regimes. Additionally, the arrangement of CO on the Rh(111) surface is demonstrated to substantially impact the activation barriers for the CHOH bond scission, illustrating the importance of comprehensive sampling on reaction kinetics. Our findings demonstrate that simplified data generation routines and evaluating generalization of neural networks can be deployed at scale to understand lateral interactions on surfaces, paving the way towards realistic modeling of heterogeneous catalytic processes.