[Paper Review] Testing the r$^2$SCAN density functional for the thermodynamic stability of solids with and without a van der Waals correction

Manish Kothakonda, Aaron D. Kaplan+7 more|arXiv (Cornell University)|Aug 4, 2022

nanoparticles nucleation surface interactions4 citations

TL;DR

This study evaluates the r2SCAN density functional and its dispersion-corrected variant r2SCAN+rVV10 for predicting thermodynamic stability in over 1,000 solids. It demonstrates that r2SCAN achieves accuracy comparable to SCAN with improved numerical stability, while r2SCAN+rVV10 provides slightly more accurate cell volumes and maintains formation enthalpy accuracy, making both functionals reliable for high-throughput materials discovery.

ABSTRACT

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 r$^2$SCAN 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 r$^2$SCAN description of solid-state thermodynamics, we evaluate the formation and decomposition enthalpies, equilibrium volumes, and fundamental bandgaps of more than 1,000 solids using r$^2$SCAN, SCAN, and PBE, as well as two dispersion-corrected variants, SCAN+rVV10 and r$^2$SCAN+rVV10. We show that r$^2$SCAN achieves accuracy comparable to SCAN and often improves upon SCAN's already excellent accuracy. Whereas SCAN+rVV10 is often observed to worsen the formation enthalpies of SCAN, and makes no substantial correction to SCAN's cell volume predictions, r$^2$SCAN+rVV10 predicts marginally less-accurate formation enthalpies than r$^2$SCAN, and slightly more-accurate cell volumes than r$^2$SCAN. 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 r$^2$SCAN 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, r$^2$SCAN and r$^2$SCAN+rVV10 can be recommended as stable, general-purpose meta-GGAs for materials discovery.

Motivation & Objective

• To assess the thermodynamic accuracy of the r2SCAN meta-GGA functional for solids compared to SCAN, PBE, and their dispersion-corrected variants.
• To evaluate the impact of the rVV10 dispersion correction on r2SCAN and SCAN in predicting formation and decomposition enthalpies, equilibrium volumes, and bandgaps.
• To determine whether r2SCAN offers improved numerical stability and predictive accuracy over SCAN for diverse solid-state systems.
• To identify system-specific performance trends, particularly for transition metals, intermetallics, and weakly-bound solids.
• To provide a recommendation for general-purpose use of r2SCAN and r2SCAN+rVV10 in high-throughput materials discovery workflows.

Proposed method

• Calculated formation and decomposition enthalpies, equilibrium volumes, and fundamental bandgaps for 1,015 solids (934 binary and 81 ternary compounds) using r2SCAN, SCAN, PBE, SCAN+rVV10, and r2SCAN+rVV10.
• Employed the rVV10 dispersion correction with b=11.95 for r2SCAN+rVV10 and b=15.7 for SCAN+rVV10 to account for long-range van der Waals interactions.
• Used experimental data from Isaacs et al. for reference formation enthalpies and structural parameters.
• Compared mean absolute errors (MAEs) in formation and decomposition enthalpies, cell volumes, and bandgaps across functionals.
• Analyzed error distributions using violin plots and assessed performance across material classes (e.g., oxides, transition metals, intermetallics, weakly-bound solids).
• Evaluated the influence of the meta-GGA’s non-local kinetic energy density (τ) on magnetic moments and bandgaps in metals and narrow-gap semiconductors.

Experimental results

Research questions

• RQ1 How does r2SCAN compare to SCAN and PBE in predicting formation and decomposition enthalpies of solids?
• RQ2 What is the effect of the rVV10 dispersion correction on r2SCAN’s accuracy in predicting thermodynamic properties compared to SCAN+rVV10?
• RQ3 Does r2SCAN improve numerical stability over SCAN while maintaining high accuracy in solid-state thermodynamics?
• RQ4 For which classes of materials (e.g., transition metals, intermetallics, layered solids) do GGAs outperform meta-GGAs in formation enthalpy prediction?
• RQ5 How accurate are r2SCAN and r2SCAN+rVV10 in predicting fundamental bandgaps, particularly in narrow-gap insulators and metals?

Key findings

• The average absolute error in formation enthalpies decreased by a factor of 1.5 to 2.5 from GGA (PBE) to meta-GGA (r2SCAN) levels.
• r2SCAN achieved formation enthalpy accuracy comparable to SCAN and improved upon it for intermetallic systems.
• r2SCAN+rVV10 predicted marginally less accurate formation enthalpies than r2SCAN but slightly more accurate equilibrium cell volumes.
• For decomposition enthalpies, the reduction in error from GGA to meta-GGA was smaller than for formation enthalpies, with all functionals achieving errors below 30 meV/atom for Type 2 decompositions.
• r2SCAN and r2SCAN+rVV10 showed improved numerical stability over SCAN, with r2SCAN+rVV10 providing a more compatible dispersion correction due to its lower b-parameter (11.95) compared to SCAN+rVV10 (15.7).
• r2SCAN sometimes overestimated bandgaps in narrow-gap insulators, consistent with trends in other meta-GGAs like TASK, while both r2SCAN and SCAN underestimated bandgaps in wide-gap insulators.