Mapping the influence of symmetry breaking in structure-property relationships of ABO$_3$ perovskites
Perovskite oxides have emerged as an important class of material with promising energy applications owing to their compositional and structural flexibility, which enables stabilization of both low- and high-symmetry phases and gives rise to diverse physical properties. Under ambient conditions, most perovskites adopt low-symmetry structures characterized by octahedral tilting and B-site displacements. Despite their importance, computational studies have largely focused on the ideal cubic phase as modeling these distortions remains challenging. The difficulty stems from the absence of a quantitative framework capable of capturing composition-dependent distortions that can occur through multiple non-equivalent atomic displacement modes, often requiring computationally expensive large supercells to explore the structural landscape. Consequently, the influence of distortions on the stability and properties of low-symmetry perovskites remains insufficiently understood. In this work, we develop an efficient computational framework for the rapid construction and exploration of composition-dependent structural models across both low- and high-symmetry phases. Using $\textit{symmetry constrained templates}$ and $\textit{unconstrained supercell templates}$, we systematically investigate 15 representative compositions to uncover relationships between composition, supercell size and shape, and distortion patterns. Based on these insights, we propose a robust and computationally inexpensive protocol for rapid structural exploration and assess the influence of different distortion modes on key physical properties.