Fragment-based Treatment of Delocalization and Static Correlation Errors in Density-Functional Theory

TL;DR

This paper introduces a fragment-based approach using partition density-functional theory to effectively address delocalization and static correlation errors in density-functional theory, improving accuracy in bond-stretching calculations.

Contribution

The authors demonstrate that PDFT with simple local and semi-local functionals can avoid common DFT errors, providing a new framework for treating fractional charges and spins.

Findings

Less than 3% dissociation-energy errors in H2 and H2+

Key features in the KS potential are captured by the method

Effective potentials show correct features around bond midpoints

Abstract

One of the most important open challenges in modern Kohn-Sham (KS) density-functional theory (DFT) is the correct treatment of fractional electron charges and spins. Approximate exchange-correlation (XC) functionals struggle to do this in a systematic way, leading to pervasive delocalization and static correlation errors. We demonstrate how these errors, which plague density-functional calculations of bond-stretching processes, can be avoided by employing the alternative framework of partition density-functional theory (PDFT), even with simple local and semi-local functionals for the fragments. Our method is illustrated with explicit calculations on the two paradigm systems exhibiting delocalization and static-correlation, stretched H$_2^+$ and H$_2$. We find in both cases our scheme leads to dissociation-energy errors of less than 3%. The effective KS potential corresponding to our self-consistent solutions display key features around the bond midpoint; these are known to be present in the exact KS potential, but are absent from most approximate KS potentials and are essential for the correct description of electron dynamics.