Generalized local-density approximation and one-dimensional finite uniform electron gases

Abstract

We explicitly build a generalized local-density approximation (GLDA) correlation functional based on one-dimensional (1D) uniform electron gases (UEGs). The fundamental parameters of the GLDA -a generalization of the widely-known local-density approximation (LDA) used in density-functional theory (DFT) -are the electronic density ρ and a newly-defined two-electron local parameter called the hole curvature η. The UEGs considered in this study are finite versions of the conventional infinite homogeneous electron gas and consist of n electrons on an infinitely thin wire with periodic boundary conditions. We perform a comprehensive study of these finite UEGs at high, intermediate and low densities using perturbation theory and quantum Monte Carlo calculations. We show that the present GLDA functional yields accurate estimates of the correlation energy for both weakly and strongly correlated one-dimensional systems and can be easily generalized to higher-dimensional systems.

The uniform electron gas

“…The first two coefficients of the low‐density energy expansion of 1‐jellium can be found in Fogler's work . The present authors have also given an alternative, simpler derivation using uniformly spaced electrons on a ring . Both constructions lead to where Li 3 is the trilogarithm function and the energy expansion is …”

“…Lee and Drummond have published accurate DMC data for the range 1 ≤ r s ≤ 20. The present authors have published DMC data at higher and lower densities in order to parametrize a generalized version of the LDA . The DMC data for 1‐jellium are reported in Table .…”

“…51 The present authors have also given an alternative, simpler derivation using uniformly spaced electrons on a ring. 55,96 Both constructions lead to…”

“…The present authors have published DMC data at higher and lower densities in order to parametrize a generalized version of the LDA. 55,56,96 The DMC data for 1-jellium are reported in Table 6. Using the 'robust' interpolation proposed by Cioslowski 136 and the high-and low-density expansions (47) and (58), the correlation energy of 1jellium calculated with the HF energy given by (19) can be approximated by…”

Natural occupation numbers in two-electron quantum rings

“…11 From this perspective, these new finite UEGs are not merely toy-models but pave a tremendously promising path for the improvement of DFT. 12,13 Therefore, it is important to better understand the properties of such prototype models.…”