Exchange-correlation potentials for inhomogeneous electron systems in two dimensions from exact diagonalization: comparison with the local-spin-density approximation

TL;DR

This paper derives exact exchange-correlation potentials for 2D inhomogeneous electron systems from wave function data and compares them with local-spin-density approximation predictions, providing reference data for functional testing.

Contribution

It introduces a method to obtain exact exchange-correlation potentials from wave function calculations and evaluates the accuracy of the local-spin-density approximation in 2D systems.

Findings

Exact potentials derived from wave functions show deviations from LSDA.

LSDA provides reasonable but imperfect approximations for 2D systems.

Reference data aids in developing better exchange-correlation functionals.

Abstract

We consider electronic exchange and correlation effects in density-functional calculations of two-dimensional systems. Starting from wave function calculations of total energies and electron densities of inhomogeneous model systems, we derive corresponding exchange-correlation potentials and energies. We compare these with predictions of the local-spin-density approximation and discuss its accuracy. Our data will be useful as reference data in testing, comparing and parametrizing exchange and correlation functionals for two-dimensional electronic systems.