[Paper Review] A New View on Density Corrected DFT: Can One Get a Better Answer for a Good Reason?

Devin J. Hernandez, Adam Rettig+1 more|arXiv (Cornell University)|Jun 26, 2023

Catalysis and Oxidation Reactions10 citations

TL;DR

The paper analyzes density corrected DFT (DC-DFT) using improved densities from kappa-OOMP2, showing that error cancellation often drives HF-DFT success and that higher-quality densities can degrade low-rung functionals, with implications for SIE and derivative discontinuities.

ABSTRACT

Despite its widespread use, density functional theory (DFT) has several notable areas of failure; perhaps the most well-studied of these failures is self-interaction error (SIE). Density corrected DFT (DC-DFT) was proposed as a potential solution to systems where SIE causes traditional DFT to fail. The Hartree-Fock (HF) density is then used for cases where the DFT energy is suitable but the self-consistent density is erroneous. In this study, we investigate the utility of the higher quality orbital optimized MP2 densities in DC-DFT for barrier heights and halogen bonded complexes. For functionals such as PBE and r$^2$SCAN, find that these densities yield worse results than the HF density due to favorable cancellation between the density-driven and functional-driven errors, confirming a recent study. Error decomposition reveals functional driven error, not density driven error, to be the primary cause of inaccuracy in DFT calculations where SIE is prominent. We therefore advise caution when using HF-DFT, because the only rigorous way to remove large functional-driven errors in lower rungs of Jacob's ladder is by climbing to higher rungs that include exact exchange. We recommend that better functionals be improved by using a better density in SIE-sensitive cases. Examples support the value of this variant of DC-DFT. We also emphasize that DC-DFT potential energy surfaces have first derivative discontinuities at Coulson-Fischer points, in contrast to the second derivative discontinuities in SCF solutions.

Motivation & Objective

• Assess the effectiveness of DC-DFT using HF and kappa-OOMP2 densities across SIE-sensitive problems.
• Decompose total errors into density-driven and functional-driven components to identify the source of inaccuracies.
• Evaluate barrier heights, halogen bonding, and bond-breaking problems to understand when better densities improve or degrade results.
• Investigate derivative behavior and discontinuities in DC-DFT potential energy surfaces at Coulson-Fischer points.

Proposed method

• Compute single-point energies using three densities: self-consistent native density, Hartree-Fock (HF) density, and kappa-OOMP2 (κ-OOMP2) density.
• Evaluate energy with a range of density functionals (SPW92, PBE, r2SCAN, PBE0, B3LYP, ωB97X-V, ωB97M-V) across datasets BH76, SIE4x4, Bauzá halogen bonding set, and SIE-sensitive cases.
• Use κ-OOMP2 as a proxy for the “better” density and decompose errors into density-driven and functional-driven contributions.
• Compare DC-DFT variants (HF-based and κ-OOMP2-based) to self-consistent DFT to assess error cancellation and performance.
• Analyze dipole moments and potential energy surfaces to illustrate non-Hellmann-Feynman contributions in DC-DFT.

Experimental results

Research questions

• RQ1 Does using κ-OOMP2 densities in DC-DFT improve or degrade accuracy across SIE-sensitive problems relative to HF densities?
• RQ2 To what extent do density-driven and functional-driven errors cancel in HF-DFT for different functionals?
• RQ3 How do DC-DFT variants perform on barrier heights (BH76), halogen-bonded complexes ( Bauzá set), and bond-breaking problems (SIE4x4)?
• RQ4 What are the derivative discontinuities in DC-DFT potential energy surfaces at Coulson-Fischer points compared to SCF solutions?
• RQ5 Can κ-OOMP2 densities provide a reliable, affordable proxy for the exact density to analyze error components?

Key findings

• HF-DFT often outperforms self-consistent DFT for barrier heights due to fortuitous error cancellation, especially with low-rung functionals.
• κ-OOMP2 densities improve dipole moments significantly over HF and self-consistent DFT for NSP cases, but degrade HF-DFT performance for low-rung functionals due to loss of error cancellation.
• For BH76 barriers, HF-DFT reduces MAE substantially for PBE and r2SCAN, while κ-OOMP2-DFT can worsen or barely improve results, indicating density-driven errors are not the sole source of inaccuracy.
• Decomposition shows functional-driven error dominates in SIE-sensitive problems; density-driven error from HF can be large, and higher-rung functionals mitigate but do not eliminate this.
• Halogen bonding (Bauzá set) shows HF-DFT often comparable to self-consistent DFT for higher-rung functionals, with κ-OOMP2-DFT offering only modest gains, suggesting less reliance on error cancellation in these cases.
• SIE4x4 bond-breaking problems reveal large functional errors that HF-DFT partially alleviates via density-driven correction, while κ-OOMP2 densities provide limited improvements, highlighting limits of dc-DFT in extreme SIE cases.