Insight into the performance of GGA functionals for solid-state calculations

Many exchange-correlation functionals of the generalized gradient approximation GGA are available in the literature. More particularly, during the last few years several research groups have proposed GGA functionals for solids, which very often perform better especially for the lattice constant than the standard GGA functional of Perdew, Burke, and Ernzerhof PBE J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 1996 . The improvement over PBE is not systematic, but trends among the different classes of solids can be observed P. Haas, F. Tran, and P. Blaha, Phys. Rev. B 79, 085104 2009 . A better understanding of the trends obtained with the existing functionals can obviously be very helpful for the construction of more accurate functionals, and in the aim of this we studied the distribution of the Wigner-Seitz radius rs related to the electron density and the reduced density gradient s in a few selected solids and identified the relevant ranges of rs rs 4 and s s 2 in solids. We focus on the variation of the exchange-correlation energy with respect to the unit-cell volume dExc /d , which determines the equilibrium lattice constant and identify the “important regions” in the unit cell, where the differences of dExc /d between two functionals are most pronounced. In metallic systems, these important regions coincide with the spatial separation of semicore and valence electrons, while for semiconductors open structures and insulators inhomogeneous systems the tails of the valence electrons become equally important or even dominate.