Efficiently charting the space of mixed vacancy-ordered perovskites by machine-learning encoded atomic-site information

Vacancy-ordered double perovskites (VODPs) are promising alternatives to three-dimensional lead halide perovskites for optoelectronic applications. Mixing these materials creates a vast compositional space for tunable properties but complicates efficient screening of target candidates. Here, we illustrate the diverse electronic and optical characteristics as well as the nonlinear mixing effects within mixed VODPs. Furthermore, inspired by the observation that all physical properties of mixed systems with limited local environment options can be uniquely determined by the information regarding atomic-site occupation, we developed a method combining data augmentation and a transformer-inspired graph neural network to effectively encodes atomic-site information in mixed systems. This approach accurately predicts band gaps and formation energies for mixed VODPs, achieving Root Mean Square Errors of 21 meV and 3.9 meV/atom, respectively. Trained with samples with up-to three mixed elements and small supercells (<72 atoms), the model not only can be generalized to medium- and high-entropy systems and larger supercells (>200 atoms), but also well reproduces the bandgap bowing effect in Sn-based mixed VODPs.