A flexible and scalable scheme for mixing computed formation energies from different levels of theory

Phase stability predictions are central to computational materials discovery efforts and have been made possible by large databases of computed properties from high-throughput density functional theory (DFT) calculations. Such databases now contain millions of calculations at the generalized gradient approximation (GGA) level of theory, representing an enormous investment of computational resources. Although it is now feasible to carry out large numbers of calculations using more accurate methods, such as meta-GGA functionals, recomputing the entirety of a database with a higher-fidelity method is impractical and would not effectively leverage the value embodied in existing calculations. Instead, we propose in this work a general procedure by which higher-fidelity, low-coverage calculations (e.g., meta-GGA calculations for selected chemical systems) can be combined with lower-fidelity, high-coverage calculations (e.g., an existing database of GGA calculations) in a robust and scalable manner to yield improved phase stability predictions. We demonstrate our scheme using legacy GGA(+\textit{U}) calculations and new r$^2$SCAN meta-GGA calculations from the Materials Project and illustrate its application to solid and aqueous phase stability. We discuss practical considerations for constructing mixed phase diagrams and present guidelines for prioritizing high-fidelity calculations for maximum benefit.