Density sensitivity of empirical functionals

TL;DR

This paper discusses how density-driven errors affect empirical density functionals in DFT and shows that using Hartree-Fock densities can significantly improve accuracy without extra computational cost.

Contribution

It demonstrates the importance of density correction in DFT and highlights the benefits of using HF densities over self-consistent densities for better results.

Findings

Using HF densities reduces errors in noncovalent interaction energies.

Range-separated hybrids with HF densities are less affected by density-driven errors.

Density correction improves accuracy in small water cluster binding energies.

Abstract

Empirical fitting of parameters in approximate density functionals is common. Such fits conflate errors in the self-consistent density with errors in the energy functional, but density-corrected DFT (DC-DFT) separates these two. We illustrate with catastrophic failures of a toy functional applied to $H_2^+$ at varying bond lengths, where the standard fitting procedure misses the exact functional; Grimme's D3 fit to noncovalent interactions, which can be contaminated by large density errors such as in the WATER27 and B30 datasets; and double-hybrids trained on self-consistent densities, which can perform poorly on systems with density-driven errors. In these cases, more accurate results are found at no additional cost, by using Hartree-Fock (HF) densities instead of self-consistent densities. For binding energies of small water clusters, errors are greatly reduced. Range-separated hybrids with 100\% HF at large distances suffer much less from this effect.