Nonuniversality of commonly used correlation-energy density functionals

Abstract

The correlation energies of the helium isoelectronic sequence and of Hooke's atom isoelectronic sequence have been evaluated using an assortment of local, gradient and meta-gradient density functionals. The results are compared with the exact correlation energies, showing that while several of the more recent density functionals reproduce the exact correlation energies of the helium isoelectronic sequence rather closely, none is satisfactory for Hooke's atom isoelectronic sequence. It is argued that the uniformly acceptable results for the helium sequence can be explained through simple scaling arguments that do not hold for Hooke's atom sequence, so that the latter system provides a more sensitive testing ground for approximate density functionals. This state of affairs calls for further effort towards formulating correlation-energy density functionals that would be truly universal at least for spherically-symmetric two-fermion systems.

Range separation combined with the Overhauser model: Application to the H2 molecule along the dissociation curve

“…In 35, we have combined the Overhauser equations with the KS equations in a self‐consistent way, recovering full CI total energies within 1 mH for the He isoelectronic series. In 34, we have shown that, unlike all the available correlation functionals 36, the model works equally well for the high‐density limit of the He and the Hooke's atom series. Thus, on one hand, the Overhauser model seems to be a very good candidate to construct short‐range correlation energy functionals.…”

Nonlocal Wigner-like correlation energy density functional: Parametrization and tests on two-electron systems

“…24 Remarkably, we found that it is feasible to choose parameters for the Wigner functional such that the correlation energies for the helium isoelectronic sequence are estimated adequately. 24 Remarkably, we found that it is feasible to choose parameters for the Wigner functional such that the correlation energies for the helium isoelectronic sequence are estimated adequately.…”

“…Attempting to identify such characteristics, we evaluated the expectation values ͗1/r͘, ͗r͘, and ͗r 2 ͘ for both the exact and the Hartree-Fock ground states. 24 To test how well scaling with a screened Z performs, we evaluated ͗1/r͘ / ͑Z − ͒ with the above scaling factors. 2-4, respectively.…”

On THE N-Representability AND UNIVERSALITY OF F[ρ] IN THE HOHENBERG-KOHN-SHAM VERSION OF DENSITY FUNCTIONAL THEORY

“…Some of the acomplishments and shortcomings of this assortement of approximate functionals has been recently reviewed. 18,40 We provide in what follows some arguments showing that the functional F [ρ] is not universal.…”