Testing the r²SCAN Density Functional for the Thermodynamic Stability of Solids with and without a van der Waals Correction

A central aim of materials discovery is an accurate and numerically reliable description of thermodynamic properties, such as the enthalpies of formation and decomposition. The r²SCAN revision of the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) balances numerical stability with high general accuracy. To assess the r²SCAN description of solid-state thermodynamics, we evaluate the formation and decomposition enthalpies, equilibrium volumes, and fundamental band gaps of more than 1000 solids using r²SCAN, SCAN, and PBE, as well as two dispersion-corrected variants, SCAN+rVV10 and r²SCAN+rVV10. We show that r²SCAN achieves accuracy comparable to SCAN and often improves upon SCAN's already excellent accuracy. Although SCAN+rVV10 is often observed to worsen the formation enthalpies of SCAN and makes no substantial correction to SCAN's cell volume predictions, r²SCAN+rVV10 predicts marginally less accurate formation enthalpies than r²SCAN, and slightly more accurate cell volumes than r²SCAN. The average absolute errors in predicted formation enthalpies are found to decrease by a factor of 1.5 to 2.5 from the GGA level to the meta-GGA level. Smaller decreases in error are observed for decomposition enthalpies. For formation enthalpies r²SCAN improves over SCAN for intermetallic systems. For a few classes of systems-transition metals, intermetallics, weakly bound solids, and enthalpies of decomposition into compounds-GGAs are comparable to meta-GGAs. In total, r²SCAN and r²SCAN+rVV10 can be recommended as stable, general-purpose meta-GGAs for materials discovery.