Exploring energy landscapes for solid-state systems with variable cells at the extended tight-binding level

The design of novel materials requires a theoretical understanding of dynamical processes in the solid state, including polymorphic transitions and associated pathways. The organization of the potential energy landscape plays a crucial role in such processes, which may involve changes in the periodic boundaries. This study reports the implementation of a general framework for periodic condensed matter systems in our energy landscape analysis software, allowing for variation in both the unit cell and atomic positions. This implementation provides access to basin-hopping global optimization, the doubly nudged elastic band procedure for identifying transition state candidates, the missing connection approach for multi-step pathways, and general tools for the construction and analysis of kinetic transition networks. The computational efficacy of the procedures is explored using the state-of-the-art semiempirical method GFN1-xTB for the first time in this solid-state context. We investigate the effectiveness of this level of theory by characterizing the potential energy and enthalpy landscapes of several systems, including silicon, CdSe, ZnS, and NaCl, and discuss further technical challenges, such as translational permutation of the cell. Despite the expected limitations of the semiempirical method, we find that the resulting energy landscapes provide useful insight into solid-state simulations, which will facilitate detailed analysis of processes such as defect and ion migration, including refinement at higher levels of theory.