Comparison of local density functionals based on electron gas and finite systems

Abstract

Article:Entwistle, M. T., Casula, Michele and Godby, R. W. orcid.org/0000-0002- 1012-4176 (2018) Comparison of local density functionals based on electron gas and finite systems. A widely used approximation to the exchange-correlation functional in density functional theory is the local density approximation (LDA), typically derived from the properties of the homogeneous electron gas (HEG). We previously introduced a set of alternative LDAs constructed from one-dimensional systems of one, two, and three electrons that resemble the HEG within a finite region. We now construct a HEG-based LDA appropriate for spinless electrons in one dimension and find that it is remarkably similar to the finite LDAs. As expected, all LDAs are inadequate in low-density systems where correlation is strong. However, exploring the small but significant differences between the functionals, we find that the finite LDAs give better densities and energies in high-density exchange-dominated systems, arising partly from a better description of the self-interaction correction.

Insights from exact exchange-correlation kernels

“…with more than two electrons) excitations that are notoriously not present in the Kohn-Sham response 125155-7 function [21]. Therefore, there are a great deal more eigenvalues that must pass through zero in the interacting response function, and moreover, these eigenvalues that cross zero are connected to the excitations that require them to do so-an account of the precise conditions under which this occurs is given in the Supplemental Material using a two-state model, see also [66].…”

“…The atom of Sec. III is considered, and in particular the optimal gauge is found in order to match the RPA, f RPA xc = 0, with the adiabatic LDA used in this work, f ALDA xc [66]. As discussed in Sec.…”

Accurate total energies from the adiabatic-connection fluctuation-dissipation theorem

“…[n] is constructed is parameterized at each value of λ with reference to both the HEG and one-dimensional slab systems [80] (see supplemental material for details regarding this parameterization).…”

Exact exchange-correlation potentials for calculating the fundamental gap with a fixed number of electrons

“…Next we calculate the IP within the N -centered approach employing the LDA to the xc energy, which neglects the weight dependence entirely. Our LDA to the xc energy was parameterized from the 1D homogeneous electron gas [74]. The LDA does not capture PPLB's discontinuous shift, ∆, in the xc potential.…”