Performance comparison of $r^2\mathrm{SCAN}$ and SCAN metaGGA density functionals for solid materials via an automated, high-throughput computational workflow

Computational materials discovery efforts utilize hundreds or thousands of density functional theory calculations to predict material properties. Historically, such efforts have performed calculations at the generalized gradient approximation (GGA) level of theory due to its efficient compromise between accuracy and computational reliability. However, high-throughput calculations at the higher metaGGA level of theory are becoming feasible. The strongly constrained and appropriately normed (SCAN) metaGGA functional offers superior accuracy to GGA across much of chemical space, making it appealing as a general-purpose metaGGA functional, but it suffers from numerical instabilities that impede its use in high-throughput workflows. The recently developed ${\mathrm{r}}^2\mathrm{SCAN}$ metaGGA functional promises accuracy similar to SCAN in addition to more robust numerical performance. However, its performance compared to SCAN has yet to be evaluated over a large group of solid materials. In this paper, we compared ${\mathrm{r}}^2\mathrm{SCAN}$ and SCAN predictions for key properties of approximately 6000 solid materials using a newly developed high-throughput computational workflow. We find that ${\mathrm{r}}^2\mathrm{SCAN}$ predicts formation energies more accurately than SCAN and PBEsol for both strongly and weakly bound materials and that ${\mathrm{r}}^2\mathrm{SCAN}$ predicts systematically larger lattice constants than SCAN. We also find that ${\mathrm{r}}^2\mathrm{SCAN}$ requires modestly fewer computational resources than SCAN and offers significantly more reliable convergence. Thus, our large-scale benchmark confirms that ${\mathrm{r}}^2\mathrm{SCAN}$ has delivered on its promises of numerical efficiency and accuracy, making it a preferred choice for high-throughput metaGGA calculations.

Figure 1

Automated workflow for metaGGA calculations. The input structure is relaxed using a GGA functional to construct an initial guess of the charge density. A high $k$-point density is used in this step. The output charge density from the GGA optimization is used as the initial guess in the subsequent metaGGA optimization using either ${\mathrm{r}}^2\mathrm{SCAN}$ or SCAN. The band gap estimated from the GGA calculation is used to refine the $k$-point density for the metaGGA optimization, where metals have the highest $k$-point density and semiconductors or nonmetals have lower $k$-point density. Automated error correction routines adjust settings and restart calculations that fail for well-defined reasons, improving reliability.

Figure 2

Changes in (a) formation energy, (b) band gap, (c) cell volume, and (d) formation electron localization function ($\mathrm{\Delta }{\mathrm{ELF}}_f$; see Sec. S5 of the Supplemental Material [32]) when computed in ${\mathrm{r}}^2\mathrm{SCAN}$ vs SCAN. Note that the $y$ axis is logarithmic. Dashed and dotted vertical lines represent the median differences and two-sided 95th percentile differences, respectively, across both material categories.

Figure 3

Mean absolute error compared to experiment in (a) formation energy ($n=986$ materials), (b) cell volume ($n=4974$ materials), and (c) band-gap ($n=582$ materials) computed with ${\mathrm{r}}^2\mathrm{SCAN}$, SCAN, or PBEsol.

Figure 4

(a) Relative computational performance of ${\mathrm{r}}^2\mathrm{SCAN}$ compared to SCAN (blue) or PBEsol (orange), demonstrating that computational time required for ${\mathrm{r}}^2\mathrm{SCAN}$ is smaller than SCAN but larger than PBEsol. Each variable is plotted as the ratio of the value in the ${\mathrm{r}}^2\mathrm{SCAN}$ calculation divided by the value in the corresponding SCAN or PBEsol calculation. Dashed lines inside each violin represent the quartiles of the distribution. (b) Completion rate of calculations carried out using each density functional.