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

Abstract

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.

Zinc Titanium Nitride Semiconductor toward Durable Photoelectrochemical Applications

“…Figure a shows a selected Pourbaix region for ZnTiN 2 calculated using data from the Materials Project , (complete diagrams with multiple ionic concentrations are given in Figure S5). These diagrams are built from a combination of r 2 SCAN meta generalized gradient approximation (GGA) and PBE GGA DFT calculations using the computational Pourbaix formalism of Persson et al and the DFT mixing scheme of Kingsbury et al (see 4. Experimental Section).…”

“…S3). These diagrams are built from a combination of r 2 SCAN metaGGA and PBE GGA DFT calculations using the computational Pourbaix formalism of Persson et al 61 and the DFT mixing scheme of Kingsbury et al 62 (see Methods). Including metaGGA calculations is beneficial because SCAN (on which r 2 SCAN is based) was shown to predict ternary nitride formation enthalpies in the nitrogen-rich region of the phase diagram more accurately than GGA.…”

“…Our electrochemical stability calculations (Pourbaix diagrams) are built from a combination of PBE GGA DFT calculations retrieved from the Materials Project database and regulated-restored strongly-constrained and appropriately normed (r 2 SCAN) metaGGA calculations calculated using the workflow detailed in Kingsbury et al 90 We used the Materials Project DFT mixing scheme 62 to combine these two sets of calculations and create a solid phase diagram of the Zn-N-Ti-O-H chemical system, from which we constructed Pourbaix diagrams using the computational formalism of Persson et al 61 The mixing scheme allowed us to build the convex energy hull from higher-level metaGGA calculations by recomputing only the stable phases and phases close to the hull with r 2 SCAN (170 calculations total) instead of the entire Zn-N-Ti-O-H chemical system (more than 500 total phases according to the Materials Project Database). For two stable phases where the large number of sites made r 2 SCAN structure optimizations impractical (Ti 3 Zn 22 and Ti 20 H 2 N 17 , with 100 and 39 sites, respectively) we employed single point calculations, as suggested in Kingsbury et al 62 The stability predictions of this mixed Pourbaix diagram were qualitatively similar to those obtained from a pure GGA phase diagram constructed without any r 2 SCAN calculations, but predicted a slightly larger region of decomposition to Ti3Zn2O8 and/or ZnO (see Figure S3).…”

“…This material has been theoretically predicted to be stable with a cation-ordered wurtzite-derived crystal structure compatible with wurtzite GaN, 59 with other independent computational studies supporting these theoretical predictions. 30,31 Materials Project Pourbaix stability calculations 7,[60][61][62] indicate that ZnTiN2 will decompose to stable oxides such as ZnO and TiO2 in near-neutral pH aqueous environments. These ZnO and TiO2 decomposition products are not only electrochemically stable under the operating conditions, but are also utilized in other applications as transparent conducting oxides with good electrical charge transport and wide optical band gaps.…”

Co-design of zinc titantium nitride semiconductor towards durable photoelectrochemical applications

“…Our electrochemical stability calculations (Pourbaix diagrams) are built from a combination of PBE GGA DFT calculations retrieved from the Materials Project database and regulated-restored strongly-constrained and appropriately normed (r 2 SCAN) metaGGA calculations calculated using the workflow detailed in Kingsbury et al 90 We used the Materials Project DFT mixing scheme 62 to combine these two sets of calculations and create a solid phase diagram of the Zn-N-Ti-O-H chemical system, from which we constructed Pourbaix diagrams using the computational formalism of Persson et al 61 The mixing scheme allowed us to build the convex energy hull from higher-level metaGGA calculations by recomputing only the stable phases and phases close to the hull with r 2 SCAN (170 calculations total) instead of the entire Zn-N-Ti-O-H chemical system (more than 500 total phases according to the Materials Project Database). For two stable phases where the large number of sites made r 2 SCAN structure optimizations impractical (Ti3Zn22 and Ti20H2N17, with 100 and 39 sites, respectively) we employed single point calculations, as suggested in Kingsbury et al 62 The stability predictions of this mixed Pourbaix diagram were qualitatively similar to those obtained from a pure GGA phase diagram constructed without any r 2 SCAN calculations, but predicted a slightly larger region of decomposition to Ti3Zn2O8 and/or ZnO (see Figure S3).…”