Correct space group determination of 2D materials

Two-dimensional (2D) materials, such as monolayer ${\mathrm{CrI}}_{3}$, are the focus of much attention because of their unique properties and potential applications in various technological fields. Despite their discovery years ago, there remains significant confusion regarding space group assignments, with disparities reported across well-known 2D material databases and publications. Therefore, accurate determination of space groups is crucial for understanding the intrinsic properties of these materials and optimizing their performance. We use first-principles calculations to systematically investigate the space group of monolayer ${\mathrm{CrI}}_{3}$ and other 2D materials reported with disparities. From total energy, geometry optimization, and subsequent lattice dynamics computations, we identify common sources of confusion and propose a methodology to resolve these ambiguities. Our results highlight the necessity of integrating computational analyses with symmetry analysis to achieve a correct space group determination of 2D materials. This approach can be beneficial for, e.g., machine learning algorithms that rely on accurate determination of crystal symmetry to identify material properties.