Representing crystal potential energy surfaces via a stationary-point network

A cornerstone of materials physics is the principle that all properties of crystalline systems are fundamentally determined based on the underlying potential energy surface (PES), which affects the structural stability and structure–property relations. Finding a proper representation of the PES is essential for the implementation of this principle, which has attracted considerable interest over the past decades; however, progress has been impeded by the lack of a firm theoretical basis for effectively exploring the vast configurational space. Here, we introduce a new method for constructing a crystal PES by using a solution landscape with an improved high-index saddle dynamic scheme, in which generalized coordinates are introduced to encode crystals that satisfy translational and rotational invariance. To represent the PES of periodic crystalline structures, we devise an advanced graph-based stationary-point network to visualize and analyze complex PES terrains, with nodes and edges representing stationary points and their connections, respectively. Crystalline GaN and Si are considered as exemplary case studies, and our newly devised approach leads to the discovery of several hidden transition paths with low enthalpy barriers associated with multistep processes; thus, the effectiveness of the approach is validated. Our method combined with the first-principles calculations offers a viable solution to long-standing problems associated with crystal PESs, such as the kinetics of activated processes, materials stability and synthesizability. These findings represent a notable advancement and offer a basis for future research.