Local density approximations from finite systems

Abstract

The local density approximation (LDA) constructed through quantum Monte Carlo calculations of the homogeneous electron gas (HEG) is the most common approximation to the exchange-correlation functional in density functional theory. We introduce an alternative set of LDAs constructed from slablike systems of one, two and three electrons that resemble the HEG within a finite region, and illustrate the concept in one dimension. Comparing with the exact densities and Kohn-Sham potentials for various test systems, we find that the LDAs give a good account of the self-interaction correction, but are less reliable when correlation is stronger or currents flow.

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

“…The refined form for the xc energy density in the three finite LDAs has now been increased from the four-parameter fit in Ref. [27] to a seven-parameter fit 5 in this paper: 5 We have significantly increased the precision of the calculations for the slab systems in order to do this. The numerical difference between the new seven-parameter fits and original four-parameter fits is less than 1% in ε xc across the density range used in constructing the LDAs (except in the very low-density region n<0.06 a.u.).…”

“…Due to the initial parametrization of ε xc (n) focusing on the plateau regions of the slabs (i.e., ignoring the inhomogeneous regions at the edges), we used a refinement process [27]i n order to fulfill this requirement. The refined form for the xc energy density in the three finite LDAs has now been increased from the four-parameter fit in Ref.…”

“…[27] we chose a set of finite locally homogeneous systems in order to mimic the HEG, which we referred to as "slabs" (Fig. 1).…”

“…[27] we solved the Hartree-Fock equations to find the exact exchange energy density ε x for a fully spin-polarized [ζ = 1 where ζ ≡ (N ↑ − N ↓ )/N ] 1D HEG of density n consisting of an infinite number of electrons interacting via the softened Coulomb repulsion u(x − x ′ ) = (|x − x ′ |+1) −1 :…”

“…In a previous paper [27], we introduced a set of LDAs which, in contrast to the traditional HEG LDA, were constructed from systems of one, two, and three electrons which resembled the HEG within a finite region. Illustrating our approach in one dimension (1D), we found that the three LDAs were remarkably similar to one another.…”