Energies of isoelectronic atomic ions from a successful metageneralized gradient approximation and other density functionals

We show that the poor performance of approximate Kohn-Sham (KS) density functional theory for highly charged atomic ions is improved dramatically by ensuring that (i) the exchange functional recovers the correct leading term in the Z expansion of the exchange energy (Z is the nuclear charge) and (ii) the correlation functional is bounded under uniform scaling of the density to the high-density limit—i.e., lim_λ→∞E_c^KS[n_λ]>−∞, where n_λ(r)=λ³n(λr). The performance of several density functionals (BLYP, BP86, VS98, HCTH/407, PBE, PKZB, and TPSS) is compared for the 4-, 10-, and 18-electron atomic series spanning values of Z from 4 to 28. Especially accurate results are obtained with the nonempirical metageneralized gradient approximation of Tao, Perdew, Staroverov, and Scuseria (TPSS). High-Z limits of selected exchange and correlation functionals are evaluated and compared with the exact values.