Exact Exchange-Correlation Functional for the Infinitely Stretched Hydrogen Molecule

TL;DR

This paper derives an exact exchange-correlation functional for the infinitely stretched hydrogen molecule, providing insights into its energy and potential with correct asymptotic behavior, advancing density functional theory accuracy.

Contribution

It introduces a closed-form exchange-correlation functional for the dissociated hydrogen molecule based on its exact wave function, enabling precise energy and potential calculations.

Findings

Functional is exact for dissociated hydrogen molecule

Yields correct dissociation energy

Potential exhibits correct -1/r asymptotic behavior

Abstract

The exchange-correlation hole density of the infinitely stretched (dissociated) hydrogen molecule can be cast into a closed analytical form by using its exact wave function. This permits to obtain an explicit exchange-correlation energy functional of the electron density which allows for its functional derivation to yield the corresponding Kohh-Sham effective exchange-correlation potential. We have shown that this exchange-correlation functional is exact for the dissociated hydrogen molecule, yields its dissociation energy correctly, and its corresponding exchange-correlation potential has the correct $-1/r$ asymptotic behavior.