Kohn-Sham calculations with the exact functional

TL;DR

This paper demonstrates self-consistent Kohn-Sham calculations using the exact exchange-correlation functional, employing the density matrix renormalization group method for one-dimensional systems, and explores convergence and spin-dependence.

Contribution

It introduces a practical approach to perform Kohn-Sham calculations with the exact functional for 1D systems, revealing convergence behaviors and spin-related issues.

Findings

Successful self-consistent calculations with the exact functional

Analysis of convergence for weakly and strongly correlated systems

Insights into spin-dependent densities and functional ill-definition

Abstract

As a proof of principle, self-consistent Kohn--Sham calculations are performed with the exact exchange-correlation functional. Finding the exact functional for even one trial density requires solving the interacting Schr\"odinger equation many times. The density matrix renormalization group method makes this possible for one-dimensional, real-space systems of more than two interacting electrons. We illustrate and explore the convergence properties of the exact KS scheme for both weakly and strongly correlated systems. We also explore the spin-dependent generalization and densities for which the functional is ill defined.