Sampling the Thermodynamics of Material Interfaces with Markov Chain Monte Carlo and Machine Learning

Material surfaces often differ significantly from the bulk in both structure and composition. Surface structures depend on temperature, the presence of external chemical potentials (oxygen, hydrogen, water) and applied electrical potential. These surface reconstructions are key because they control the performance of the surface in processes like electrochemistry in batteries, electrocatalysis in fuel cells, adsorption on sensors, etc. While electronic structure simulations can accurately predict the energy of a single surface configuration, they are too expensive to investigate all the possible geometrical and compositional transformations that surfaces can undergo. In order to create accurate models of surfaces that can relate surface composition and structure to external conditions, it is necessary to efficiently sample the thermodynamic distributions of states the surface can access. To this end, we propose integrating Markov Chain Monte Carlo (MCMC) sampling with neural network potentials (NNP) trained on electronic simulations data. We demonstrate the validity of our MCMC model with discrete adsorption sites on the well-known Au(110) missing-row reconstruction. Next, as we show in the GaN(0001) surface reconstruction, adding in continuous relaxation leads to better sampling when the atomic spacing changes near the surface. Finally, we evaluated the effectiveness of our combined MCMC-NNP approach on complex oxide surfaces of the SrTiO₃ perovskite.