Assessment of the Tao-Mo nonempirical semilocal density functional in applications to solids and surfaces

Recently, Tao and Mo developed a semilocal exchange-correlation density functional. The exchange part of this functional is derived from a density-matrix expansion corrected to reproduce the fourth-order gradient expansion of the exchange energy in the slowly-varying-density limit, while the correlation part is based on the Tao-Perdew-Staroverov-Scuseria (TPSS) correlation functional, with a modification for the low-density limit. In the present paper, the Tao-Mo (TM) functional is assessed by computing various properties of solids and jellium surfaces. This includes 22 lattice constants and bulk moduli, 30 band gaps, seven cohesive energies, and jellium surface exchange and correlation energies for the density parameter $r_s$ in the range from 2 to 3 bohr. Our calculations show that the TM approximation can yield consistently high accuracy for most properties considered here, with mean absolute errors (MAEs) of 0.025 Å for lattice constants, 7.0 GPa for bulk moduli, 0.08 eV/atom for cohesive energies, and $35\mathrm{erg}/\mathrm{c}{\mathrm{m}}^2$ for surface exchange-correlation energies. The MAE in band gaps is larger than that of TPSS, but slightly smaller than the errors of the local spin-density approximation, Perdew-Burke-Ernzerhof generalized gradient approximation, and revised TPSS. However, band gaps are still underestimated, particularly for large-gap semiconductors, compared to the Heyd-Scuseria-Ernzerhof nonlocal screened hybrid functional.

Figure 1

Performance of various density functionals for lattice constants of 22 solids. The references used are ZPE-corrected experimental values at 0 K. All values are from Table 2.

Figure 2

Performance of various density functionals for bulk moduli of 22 solids at 0 K. All values are from Table 3.

Figure 3

Performance of various density functionals for cohesive energies of solids. All values are from Table 5.