Construction of Exchange-Correlation Potentials for Strongly Interacting One-Dimensional Systems

Abstract

One-dimensional (1D) systems are useful laboratories aiming further improvement of electronic structure calculations. In order to simulate electron-electron interactions, two types of expressions are commonly considered: soft-Coulomb and exponential. For both cases, in the context of density-functional theory (DFT), 1D systems can be employed to gain insight into the ingredients accurate exchange-correlation (XC) density functionals must incorporate. A question of major interest is the treatment of strongly interacting situations, one of the main modern challenges for DFT. In this manuscript, we propose a generalization of preexisting XC potentials which can be applied to investigate the transition from weak to strong interactions. Specifically, we employ the intriguing behavior of electrons confined in one dimension: the spin-charge separation, for which spin and charge are decoupled to form two independent quasiparticles, spinons, and chargons. By means of Friedel oscillations, our results indicate it is possible to reproduce the weak-strong interaction transition by using a simple strategy we name, from previous works, spin-charge separation correction (SCSC). In addition, SCSC also yields good results in reproducing the constancy of the highest occupied Kohn-Sham eigenvalues upon fractional electron charges.