Finite-Temperature Thermodynamics of Cu(100) Oxidation: Missing-Row Reconstruction, Defect States, and Order-Disorder Transition from Nested Sampling

Metal surfaces undergo structural, compositional, and morphological changes in response to their chemical environment. Tuning the surfaces' function and stability for a given application correspondingly necessitates an understanding of how this surface evolution couples to external conditions. Here, we demonstrate the feasibility of nested sampling simulations to obtain this coupling at first-principles predictive quality. By exploring the full configuration space, nested sampling estimates the partition function and gives direct access to desired thermodynamic ensemble averages at any temperature without prior knowledge. Computational feasibility is achieved through machine-learned interatomic potentials, an efficient GPU implementation of the sampling algorithm and bespoke sampling moves. Applied to the early oxidation of Cu(100), the approach successfully predicts the experimentally observed, complex $(2\sqrt{2}\times\sqrt{2})$R45$^\circ$-O missing-row reconstruction. The full access to the partition function enables a detailed characterization of the temperature-dependent surface evolution, mapping the emergence of defect states and the order-disorder transition of the reconstructed surface.