Machine learning study of surface reconstructions of the Cu 2 O ( 111 ) surface

The atomic structure of the most stable reconstructed surface of cuprous oxide <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mo>(</a:mo> <a:msub> <a:mi>Cu</a:mi> <a:mn>2</a:mn> </a:msub> <a:mi mathvariant="normal">O</a:mi> <a:mo>)</a:mo> <a:mo>(</a:mo> <a:mn>111</a:mn> <a:mo>)</a:mo> </a:mrow> </a:math> 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msub> <c:mi>Cu</c:mi> <c:mn>2</c:mn> </c:msub> <c:mi mathvariant="normal">O</c:mi> <c:mo>(</c:mo> <c:mn>111</c:mn> <c:mo>)</c:mo> </c:mrow> </c:math> surface under stoichiometric as well as O- and Cu-deficient or rich conditions, focusing on both <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mo>(</e:mo> <e:msqrt> <e:mn>3</e:mn> </e:msqrt> <e:mo>×</e:mo> <e:msqrt> <e:mn>3</e:mn> </e:msqrt> <e:mrow> <e:mo>)</e:mo> <e:mi mathvariant="normal">R</e:mi> </e:mrow> <e:msup> <e:mn>30</e:mn> <e:mo>∘</e:mo> </e:msup> </e:mrow> </e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mo>(</g:mo> <g:mn>2</g:mn> <g:mo>×</g:mo> <g:mn>2</g:mn> <g:mo>)</g:mo> </g:mrow> </g:math> supercells. By utilizing parallel tempering simulations supported by MLFFs, we confirm that the previously described nanopyramidal and Cu-deficient <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mo>(</h:mo> <h:mn>1</h:mn> <h:mo>×</h:mo> <h:mn>1</h:mn> <h:mo>)</h:mo> </h:mrow> </h:math> 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 one and a Cu-rich one. Surface energy calculations performed using spin-polarized PBE, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mtext>PBE</i:mtext> <i:mo>+</i:mo> <i:mi>U</i:mi> </i:mrow> </i:math> , <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:msup> <j:mrow> <j:mi mathvariant="normal">r</j:mi> </j:mrow> <j:mn>2</j:mn> </j:msup> <j:mi>SCAN</j:mi> </j:mrow> </j:math> , 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 <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mrow> <l:msub> <l:mi>Cu</l:mi> <l:mn>2</l:mn> </l:msub> <l:mi mathvariant="normal">O</l:mi> <l:mo>(</l:mo> <l:mn>111</l:mn> <l:mo>)</l:mo> </l:mrow> </l:math> surfaces.