Machine Learning Study of Surface Reconstructions of the Cu$_{2}$O(111) Surface

TL;DR

This study uses machine learning force fields and advanced simulations to systematically explore and identify the most stable surface reconstructions of Cu$_{2}$O(111) under various conditions, providing new insights into their stability.

Contribution

The paper develops on-the-fly machine-learned force fields to efficiently investigate surface reconstructions of Cu$_{2}$O(111) under different chemical environments, revealing stable structures and their dependence on computational methods.

Findings

Nanopyramidal and Cu-deficient structures are most stable under oxidizing conditions.

Two nanopyramidal reconstructions are stable under reducing conditions.

Stability of some structures varies with the choice of computational functional.

Abstract

The atomic structure of the most stable reconstructed surface of cuprous oxide (Cu$_{2}$O)(111) surface has been a longstanding topic of debate. In this study, we develop on-the-fly machine-learned force fields (MLFFs) to systematically investigate the various reconstructions of the Cu$_{2}$O(111) surface under stoichiometric as well as O- and Cu-deficient or rich conditions, focusing on both ($\sqrt{3}$$\times$$\sqrt{3}$)R30{\deg} and (2$\times$2) supercells. By utilizing parallel tempering simulations supported by MLFFs, we confirm that the previously described nanopyramidal and Cu-deficient (1$\times$1) structures are the lowest energy structures from moderately to strongly oxidizing conditions. In addition, we identify two promising nanopyramidal reconstructions at highly reducing conditions, a stoichiometric and a Cu-rich one. Surface energy calculations performed using spin-polarized PBE, PBE+U, r$^{2}$SCAN, and HSE06 functionals show that the previously known Cu-deficient configuration and nanopyramidal configurations are at the convex hull (and, thus, equilibrium structures) for all functionals, whereas the stability of the other structures depends on the functional and is therefore uncertain. Our findings demonstrate that on-the-fly trained MLFFs provide a simple, efficient, and rapid approach to explore the complex surface reconstructions commonly encountered in experimental studies, and also enhance our understanding of the stability of Cu$_{2}$O(111) surfaces.