One-electron self-interaction error and its relationship to geometry and higher orbital occupation

Area of Science:

• Computational Chemistry and Physics
• Quantum Mechanics
• Materials Science

Background:

• Density Functional Theory (DFT) is widely used in computational chemistry and physics.
• The self-interaction error (SIE) is an unphysical artifact in DFT that negatively affects calculation accuracy.
• Understanding and mitigating SIE is crucial for reliable DFT predictions.

Purpose of the Study:

• To analyze the one-electron SIE in DFT calculations.
• To investigate how geometric and electronic factors influence SIE.
• To provide insights for developing more accurate DFT approximations.

Main Methods:

• In-depth analysis of the one-electron SIE.
• Replication of delocalization effects using simple geometries.
• Visualization of SIE effects.
• Examination of SIE in two- and three-dimensional molecular shapes.
• Analysis of SIE in systems with electrons occupying higher-lying atomic orbitals.

Main Results:

• The SIE increases dramatically with the number of nuclei in linear arrangements.
• Molecular shape significantly impacts the SIE, with 2D and 3D shapes exhibiting greater errors.
• The exchange functional is a primary contributor to SIE, with some error compensation from one-electron errors.
• Functional and density errors were observed, with potential links between density errors and unequal electron delocalization.
• SIE increases for electrons in higher-lying atomic orbitals, affecting excited states and some DFAs.

Conclusions:

• The erratic behavior of SIE in simple systems highlights the need for robust Density Functional Approximations (DFAs).
• The developed test systems can serve as benchmarks for future DFT development.
• This work provides critical insights for improving the accuracy of DFT calculations, particularly for excited states.