The one-electron self-interaction error in 74 density functional approximations: a case study on hydrogenic mono- and...

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• The self-interaction error (SIE) is a fundamental challenge in Density Functional Theory (DFT), affecting the accuracy of Density Functional Approximations (DFAs).
• Understanding the one-electron SIE is crucial for developing more reliable computational methods.

Purpose of the Study:

• To conduct a comprehensive investigation of the one-electron SIE in various DFAs.
• To analyze the relationship between SIE, nuclear charge, and basis sets.
• To identify factors contributing to and mitigating the one-electron SIE.

Main Methods:

• Analysis of the one-electron SIE using two decomposition schemes: functional/density-driven errors and exchange/correlation/one-electron components.
• Systematic study of hydrogenic analogues and diatomic molecules at dissociation.
• Investigation of the impact of atomic-orbital basis sets and van-der-Waals dispersion terms on SIE.
• Analysis of over 250,000 data points.

Main Results:

• A linear relationship between SIE and nuclear charge was observed for mononuclear systems and diatomics, with notable exceptions.
• "Self-dispersion" was identified in DFAs with London-dispersion terms.
• Range-separated DFAs were found to be insufficient for eliminating the one-electron SIE universally.
• DFAs designed to be SIE-free for simple systems often exhibit larger errors for heavier systems.
• Robust, widely-used DFAs show moderate one-electron SIE, while nearly SIE-free DFAs perform poorly in applications.

Conclusions:

• The one-electron SIE remains a significant issue, with current DFAs often exhibiting error cancellation or compensating for fundamental deficiencies.
• Future DFA development requires addressing the persistent one-electron SIE to improve fundamental accuracy.
• Insights from this extensive analysis can guide the creation of new DFAs or SIE correction methods.