Calculation of the lattice constant of solids with semilocal functionals

The exchange-correlation functionals of the generalized gradient approximation (GGA) are still the most used for the calculations of the geometry and electronic structure of solids. The PBE functional [J. P. Perdew et al., Phys. Rev. Lett. 77, 3865 (1996)], the most common of them, provides excellent results in many cases. However, very recently other GGA functionals have been proposed and compete in accuracy with the PBE functional, in particular for the structure of solids. We have tested these GGA functionals, as well as the local-density approximation (LDA) and TPSS (meta-GGA approximation) functionals, on a large set of solids using an accurate implementation of the Kohn-Sham equations, namely, the full-potential linearized augmented plane-wave and local orbitals method. Often these recently proposed GGA functionals lead to improvement over LDA and PBE, but unfortunately none of them can be considered as good for all investigated solids.

Figure 1

(Color online) Relative error (in percent) in the calculated lattice constants with respect to the ZPAE-corrected experimental values (see Table ).

Figure 2

(Color online) Relative error (in percent) in the calculated lattice constants with respect to the ZPAE-corrected experimental values (see Table ). For each functional, the solids have been ordered such that the relative error goes in the direction of the positive values from bottom to top.

Figure 3

(Color online) Total energy of graphite vs the lattice constant $c$ (the interlayer distance is $c/2$). The in-plane lattice constant $a$ was kept fixed at the experimental value $\left(2.464\text{Å}\right)$ for all values of $c$. The minima for the AM05 and TPSS functionals are either much larger than $15\text{Å}$ or absent. The vertical dashed line represents the experimental lattice constant $\left(c_0=6.71\text{Å}\right)$.