Abstract
We study for the first time the effect of the dependence of meta generalized gradient approximation (MGGA) for the exchange-correlation energy on its input, the kinetic energy density, through the dimensionless inhomogeneity parameter, α, that characterizes the extent of orbital overlap. This leads to a simple MGGA exchange functional, which interpolates between the single-orbital regime, where α = 0, and the slowly varying density regime, where α ≈ 1, and then extrapolates to α → ∞. When combined with a variant of the Perdew-Burke-Ernzerhof GGA correlation, the resulting MGGA performs equally well for atoms, molecules, surfaces, and solids.
Highlights
Require only a single integral over real space and so are practical even for large molecules or unit cells
As in the revised Tao-Perdew-Staroverov-Scuseria meta generalized gradient approximation (MGGA),6 to distinguish the single-orbital regions from the orbital-overlap regions
The revised Tao-Perdew-Staroverov-Scuseria (revTPSS) enhancement factor is thought to be accurate for small s around α ≈ 1
Summary
The supposed correlation between s and α in the intershell regions of a solid suggests that monotonically decreasing α-dependence of an enhancement factor has qualitatively the same effect as monotonically increasing s-dependence does for these regions. The second observation concerns the variations of the lattice constants of the set of 20 solids (SL20) (Ref. 23) and the atomization energies of the AE6 molecule set in response to changes of the α dependence of the enhancement factor. The alleviation, from LSDA to Fx0int and to Fxint, of the overestimation in the atomization energies and of the underestimation in the lattice constants, suggests that the built-in monotonically increasing s-dependence and monotonically decreasing α-dependence in the enhancement factors reduce the preference of LSDA towards compact systems. Error statistics of lattice constants (Å) of the SL20 solids and atomization energies (kcal/mol) of the AE6 set. See the text for the definitions of Fx0int , Fx int, and Fxint
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