Benchmark tests of a strongly constrained semilocal functional with a long-range dispersion correction

The strongly constrained and appropriately normed (SCAN) semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] obeys all 17 known exact constraints for meta-generalized-gradient approximations (meta-GGAs), and it includes some medium-range correlation effects. Long-range London dispersion interactions are still missing, but they can be accounted for via an appropriate correction scheme. In this study, we combine SCAN with an efficient London dispersion correction and show that lattice energies of simple organic crystals can be improved with the applied correction by 50%. The London-dispersion corrected SCAN meta-GGA outperforms all other tested London-dispersion corrected meta-GGAs for molecular geometries. Our method yields mean absolute deviations (MADs) for main group bond lengths that are consistently below 1 pm, rotational constants with MADs of 0.2%, and noncovalent distances with MADs below 1%. For a large database of general main group thermochemistry and kinetics ($\sim 800$ chemical species), one of the lowest weighted mean absolute deviations for long-range corrected meta-GGA functionals is achieved. Noncovalent interactions are of average quality, and hydrogen bonded systems in particular seem to suffer from overestimated polarization related to the self-interaction error of SCAN. We also discuss some consequences of numerical sensitivity encountered for meta-GGAs.

Figure 1

Mean absolute deviations of various methods for different bond distances separated into light main group bonds (LMGB35), heavy main group bonds (HMGB11), and transition-metal complexes (TMC32). For SCAN, we show both the plain functional (gray bar) and the dispersion-corrected variant in order to highlight the influence of the long-range correction.

Figure 2

Normal distribution of the relative errors in the computed rotational constants $B_e$ for the ROT34 benchmark set with various theoretical methods. HF and MP2 results are taken from Ref. [73]. The inset shows the molecules of this set.

Figure 3

Lattice energy of the (a) benzene and (b) oxalic acid $\alpha$ crystal based on constrained volume optimizations (TPSS-D3 level) with single-point evaluations of various dispersion-corrected DFAs. For each method, the cross shows the position of the energy minimum, and the arrow indicates the effect of the added dispersion correction.

Figure 4

Weighted mean absolute deviations (WTMADs) for the three categories (basic properties, reaction energies, and noncovalent interactions) of the large GMTKN30 database composed of 30 individual benchmark sets given in Table 4 [28, 96]. For SCAN, we show both the plain functional (gray bar) and the dispersion-corrected variant in order to highlight the influence of the long-range correction.