Stretched or noded orbital densities and self-interaction correction in density functional theory.

Area of Science:

• Quantum Chemistry
• Computational Materials Science
• Electronic Structure Theory

Background:

• Semilocal density functionals often fail for one-electron densities with nodes or lobes.
• The Perdew-Zunger (PZ) self-interaction correction (SIC) aims to correct these errors, improving accuracy for one-electron systems and stretched bonds.

Purpose of the Study:

• To investigate the limitations of the PZ SIC when applied to many-electron systems.
• To explore the impact of orbital localization (real vs. complex) on PZ SIC accuracy.
• To assess the need for generalized self-interaction correction methods.

Main Methods:

• Calculations were performed on one-electron densities and many-electron molecules.
• The PZ SIC was applied to standard generalized gradient approximations (GGAs) and meta-GGAs, including the Strongly Constrained and Appropriately Normed (SCAN) meta-GGA.
• Minimization of PZ total energy was explored over both real and complex localized orbitals.

Main Results:

• Minimization over real orbitals can lead to noded orbital densities and energy errors in many-electron systems.
• Minimization over complex orbitals reduces but does not eliminate SIC errors in atomization energies.
• PZ SIC improves energy barriers for GGAs and meta-GGAs but often worsens atomization energies.

Conclusions:

• PZ SIC introduces errors related to nodality of localized orbitals, increasing with complexity from atoms to molecules.
• Existing PZ SIC limitations suggest the necessity for generalized self-interaction correction approaches.
• The SCAN meta-GGA is a promising candidate for generalized SIC due to its inherent self-interaction-free correlation component.