Surface structure determination by exhaustive search of asymmetric unit

Determining surface structures is a substantial challenge due to the limitations of experimental techniques and the complexity of theoretical models. In this work, we use a method called the exhaustive search of asymmetric unit (ESAU), designed to identify surface structures through a detailed analysis of the asymmetric unit. This method employs two main strategies: narrowing the research area by focusing on a smaller, unique segment rather than the entire unit cell, and transforming the infinite possibilities of atomic positions into discrete, manageable units. These strategies allow us to systematically enumerate all potential surface structures. Employing the ESAU method, we have successfully replicated a variety of known surface structures, including two-dimensional materials on substrates, and have also uncovered some previously unknown structures. Importantly, the ESAU method shows significant promise not only in utilizing experimental data but also in predicting surface and crystal structures without prior experimental evidence. Our results affirm that the ESAU approach provides a comprehensive and efficient tool for uncovering material structures, paving the way for more in-depth studies on the properties and behaviors of materials.