[Paper Review] DC-DFT for Open Shells: How to Deal with Spin Contamination

Hayoung Yu, Suhwan Song+3 more|arXiv (Cornell University)|Jul 20, 2023

Advanced Chemical Physics StudiesPhysics and Astronomy3 citations

TL;DR

This paper investigates spin contamination in unrestricted Hartree-Fock (UHF) densities within density-corrected DFT (DC-DFT) for open-shell systems. It demonstrates that using restricted open-shell HF (ROHF) densities instead of UHF densities significantly reduces mean absolute errors—especially in spin-contaminated cases—improving accuracy across GGA, meta-GGA, and hybrid functionals, with reductions up to a factor of 2 in error for DC-DFT functionals.

ABSTRACT

Density functional theory (DFT) is widely used to predict chemical properties, but its accuracy is limited by functional approximations and their approximate self-consistent densities. Density-corrected DFT (DC-DFT) is the study of the errors due to densities and Hartree-Fock DFT (HF-DFT) uses HF densities to improve energetics. With increasing use of HF-DFT, the question of how to address strong spin contamination in the HF calculation becomes increasingly important. We compare two different open-shell HF densities across 13 different DFT functionals and two DC-DFT methods. For significant spin contamination, ROHF densities outperform UHF densities by as much as a factor of 3, depending on the energy functional, and ROHF-DFT improves over self-consistent DFT for most of the tested functionals. We refine the DC(HF)-DFT algorithm, recommending ROHF-DFT in cases of severe spin contamination.

Motivation & Objective

• To address the issue of spin contamination in unrestricted Hartree-Fock (UHF) densities when applied in density-corrected DFT (DC-DFT) for open-shell systems.
• To evaluate whether restricted open-shell HF (ROHF) densities offer more accurate energetics than UHF densities in the presence of spin contamination.
• To assess the performance of various density functional approximations (DFA) when paired with ROHF vs. UHF densities in spin-contaminated and spin-uncontaminated cases.
• To provide practical guidance for applying DC-DFT in open-shell systems by identifying conditions under which ROHF densities yield superior results.
• To extend the applicability of HF-DFT and DC-DFT to challenging open-shell systems such as radicals and transition metal complexes with significant spin contamination.

Proposed method

• The study evaluates self-consistent (sc), UHF, and ROHF densities using the GMTKN55 database, classifying reactions as spin-contaminated (Δ⟨Ŝ²⟩ > 0.1) or spin-uncontaminated.
• It applies the DC-DFT framework to decompose total error into functional error (ΔEF) and density-driven error (ΔED), isolating the impact of density quality.
• For each functional, the weighted total mean absolute deviation (WTMAD-2) is computed for sc-, UHF-, and ROHF-DFT results on open-shell subsets.
• The analysis uses a density sensitivity threshold of 2 kcal/mol (based on Sim et al.) to distinguish density-sensitive from insensitive cases.
• The study compares performance across 13 functionals: 4 GGAs, 4 meta-GGAs, 5 hybrids, and 2 fully HF-DFT functionals (HF-r²SCAN-DC4 and BL1p).
• All calculations use the Ahlrichs def2-QZVPPD basis set and the Simulations of Chemistry Framework with custom Python codes for CUHF.

Experimental results

Research questions

• RQ1 Does replacing UHF densities with ROHF densities in DC-DFT reduce errors in open-shell systems with significant spin contamination?
• RQ2 How does the performance of UHF vs. ROHF densities vary across different types of functionals (GGA, meta-GGA, hybrid, DC-DFT) in spin-contaminated cases?
• RQ3 To what extent does spin contamination degrade the accuracy of DC-DFT when using UHF densities, and can ROHF densities mitigate this?
• RQ4 Are there functional-specific trends in error reduction when using ROHF densities instead of UHF in spin-contaminated systems?
• RQ5 Can the use of ROHF densities in DC-DFT be reliably recommended for open-shell systems, even when spin contamination is present?

Key findings

• For spin-contaminated cases, using ROHF densities reduced WTMAD-2 errors by up to a factor of 2 compared to UHF densities, especially for DC-DFT functionals like HF-r²SCAN-DC4.
• In spin-contaminated cases, the WTMAD-2 error for UBL1p reached 25.42 kcal/mol, but dropped to 5.40 kcal/mol with ROBL1p, demonstrating a dramatic improvement.
• For the hybrid functional PBE0, UHF-DFT yielded a WTMAD-2 of 13.07 kcal/mol in spin-contaminated cases, while ROHF-DFT reduced it to 5.24 kcal/mol.
• In spin-uncontaminated cases, ROHF-DFT showed only slightly higher errors than UHF-DFT (e.g., 6.13 vs. 5.20 kcal/mol for PBE), indicating minimal penalty for using ROHF in non-contaminated systems.
• The double-hybrid functional BL1p suffered most severely from spin contamination in UHF, but ROHF-DFT reduced its spin-contaminated error from 25.42 to 5.40 kcal/mol.
• The study confirms that spin contamination in UHF densities leads to large density-driven errors (ΔED), and replacing UHF with ROHF densities effectively suppresses these errors in open-shell systems.