High-density limit of the Perdew-Burke-Ernzerhof generalized gradient approximation and related density functionals

We point out a simplifying but mildly inconsistent assumption of the Perdew-Burke-Ernzerhof (PBE) correlation functional, which should be corrected when evaluating the high-density limit of the PBE energy for nonsinglet systems under uniform density scaling. The discussion also concerns high-density limits of all density functionals that use PBE as an ingredient, including the Tao-Perdew-Staroverov-Scuseria (TPSS) approximation. We revisit the nonrelativistic correlation energies of isoelectronic atomic ions in the limit of infinite nuclear charge and explain small discrepancies between the PBE and TPSS values of these limits existing in the literature.

Figure 1

Functions $\gamma \left(\zeta \right)$ and $\omega \left(\zeta \right)$ of Eq. (12) in hartree units. The limiting values are $\gamma \left(0\right)=\gamma \left(1\right)=0.031091$, $\omega \left(0\right)=0.046644$, $\omega \left(1\right)=0.051198$.