Quantifying Density Errors in DFT

TL;DR

This paper emphasizes that the energy functional is the most relevant measure of density errors in DFT, and introduces practical methods to estimate and address these errors without relying on arbitrary density measures.

Contribution

It proposes using the energy functional as a universal measure of density errors and provides practical techniques to estimate and mitigate density-driven errors in DFT calculations.

Findings

Energy functional is a universal measure of density errors.

Practical estimation of density errors is possible without exact densities.

Adjusting exchange-mixing is often unnecessary in large error cases.

Abstract

We argue that any general mathematical measure of density error, no matter how reasonable, is too arbitrary to be of universal use. However the energy functional itself provides a universal relevant measure of density errors. For the self-consistent density of any Kohn-Sham calculation with an approximate functional, the theory of density-corrected density functional theory (DC-DFT) provides an accurate, practical estimate of this ideal measure. We show how to estimate the significance of the density-driven error even when exact densities are unavailable. In cases with large density errors, the amount of exchange-mixing is often adjusted, but we show this is unnecessary. Many chemically relevant examples are given.