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

TL;DR

The paper addresses the challenge of identifying stable surface reconstructions of Cu$_{2}$O(111) under varying stoichiometries by developing on-the-fly ML force fields and applying parallel tempering to exhaustively sample configurations. It demonstrates that MLFFs can reproduce known structures and reveal Cu-rich nanopyramidal motifs under reducing conditions, while enabling efficient computation of surface energies across multiple exchange-correlation functionals. The results show CuD and Py-CuD/Py-ST-derived motifs lie on the convex hull under relevant μ$_O$, with PBE+U providing the closest alignment to experiment; standard functionals struggle to capture Cu$^{2+}$ energetics, highlighting the need for U or hybrids. Overall, the approach offers a fast, unbiased pathway to map complex oxide surface reconstructions with implications for catalysis and nanoparticle tip stability, and the accompanying data are openly available for reuse.

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}$)R30° and (2$\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.

Figures (5)

• Figure 1: Crystal structure of the bulk-terminated stoichiometric Cu$_{2}$O(111) surface: (a) Side view and (b) Top view, with atom color codes provided in the top right corner. Darker spheres represent atoms on the surface layer, while lighter spheres indicate atoms beneath the surface layer. For better visualization, the sphere sizes of Cu and O atoms below the surface layer have been enlarged. Navy blue and ocean blue spheres denote coordinatively unsaturated and saturated Cu atoms, respectively, while maroon and red spheres represent the coordinatively unsaturated and saturated O atoms, respectively. Panel (c) and (d) depict the comparison of energies $E$ and forces $F$ from the training dataset, computed using machine-learned force fields (MLFF) and first-principles (FP) calculations, respectively.
• Figure 2: Atomic structures of the ($\sqrt{3}$×$\sqrt{3}$)R30° Cu$_{2}$O(111) surface showing (a) the bulk-truncated stoichiometric termination after relaxation (ST), (b) a 6-atom Cu cluster (Cu$_\mathrm{6}$-ST), (c) a 4-atom Cu cluster (Cu$_\mathrm{4}$-ST), and (d) a stoichiometric nanopyramidal configuration (Py-ST). All representations include the subsurface layer, with light blue and red spheres representing Cu and O atoms, respectively. For (b) and (d), the left panels display the top view, while the upper and lower right panels show the side view and the space-filling model of the respective configurations, respectively. In (b), (c), and (d) red-green circles highlight the formation of the Cu cluster and nanopyramid, respectively. Atom color code follows that of Figure \ref{['figure1']}.
• Figure 3: Atomic structures of the ($\sqrt{3}$×$\sqrt{3}$)R30° Cu$_{2}$O(111) surface showing (a) Cu-deficient surface (CuD), (b) oxygen vacancy stoichiometric surface (ST-O$_\mathrm{v_{ss}}$), (c) oxygen vacancy Cu-deficient surface (CuD-O$_\mathrm{v_{ss}}$), (d) Cu-deficient nanopyramidal reconstruction (Py-CuD), and (e) oxygen vacancy nanopyramidal configuration (Py-O$_\mathrm{v_{ss}}$). For (d) and (e), the left panels display the top view, while the upper and lower right panels show the side view and the space-filling model of the nanopyramidal configuration, respectively. In (b), (c), and (e), the subsurface oxygen vacancy is highlighted by a red-green circle, while in (d), the same marker indicates the formation of the nanopyramid. The atom color coding corresponds to that of Figure \ref{['figure1']}.
• Figure 4: Atomic structures for the (2×2) Cu$_{2}$O(111) surface, showing (a) a stoichiometric nanopyramidal configuration (Py-ST$_\mathrm{(2\times2)}$), (b) a Cu-deficient nanopyramidal configuration (Py-CuD$_\mathrm{(2\times2)}$), and (c) a 6-atom Cu cluster arrangement (Cu$_\mathrm{6}$-CuD$_\mathrm{(2\times2)}$). For (a), the layer beneath the subsurface is also shown. The left panels display the top view, while the upper and lower right panels show the side view and the space-filling model of the respective configurations, respectively. In the left panel of (a), the red-green circle highlights the formation of an oxygen vacancy. In the right panels of (a), (b), and (c), the same marker denotes the formation of a nanopyramid and a Cu cluster. The atom color coding corresponds to that of Figure \ref{['figure1']}.
• Figure 5: Surface energies of various possible reconstructions of Cu$_{2}$O(111) surface for ($\sqrt{3}$×$\sqrt{3}$)R30° and (2 $\times$ 2) supercells, as a function of oxygen chemical potential calculated using spin-polarized PBE, PBE+U, r$^{2}$SCAN, and HSE06 functionals with mixed PAW potentials ($\text{O}_{h}$ for O$_{2}$ molecule and $\text{O}_{s}$ for bulk CuO and Cu$_{2}$O). Dashed red and blue lines in the PBE and HSE06 plots represent the surface energies of CuD and Py-CuD without spin-polarization. The most stable structures across different functionals, Py-ST, CuD, Py-CuD, and Py-O$_\mathrm{v_{ss}}$, correspond to Figure \ref{['figure2']}(d), \ref{['figure3']}(a), \ref{['figure3']}(d), and \ref{['figure3']}(e), respectively. Vertical black and red lines indicate the bulk transitions, from Cu$_{2}$O $\rightarrow$ CuO and Cu → Cu$_{2}$O, respectively.