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Quantifying the effects of the self-interaction error in DFT: when do the delocalized states appear?
Marcus Lundberg1, Per E M Siegbahn
1Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91, Stockholm, Sweden. marc@physto.se
The Journal of Chemical Physics
|June 25, 2005
Summary
The self-interaction error in density-functional theory artificially stabilizes delocalized states, particularly in systems with odd electrons. This study quantifies this error in radical dissociations and transition-metal dimers, finding it decreases with system size and fragment distance.
Area of Science:
- Computational Chemistry
- Quantum Chemistry
- Materials Science
Background:
- The self-interaction error (SIE) in density-functional theory (DFT) inaccurately stabilizes delocalized electronic states.
- This error is pronounced in systems with an odd number of electrons, such as carbocation radicals, leading to significant errors in calculated binding energies.
Purpose of the Study:
- To investigate and quantify the impact of SIE on the delocalization of electronic states in various chemical systems.
- To compare the SIE in dissociating radicals versus mixed-valence transition-metal dimers.
- To establish criteria for when delocalization is artificially favored by DFT.
Main Methods:
- Energy differences between localized and delocalized states were calculated using the B3LYP functional.
- Calculations were performed for dissociating radical systems (e.g., H2+, C12H26+) and a mixed-valence Mn(III,IV) dimer.
- Solvent effects and varying fragment distances were considered.
Main Results:
- The SIE in radical dissociation decreases with increasing system size, from 55 kcal/mol for H2+ to 15 kcal/mol for C12H26+.
- Solvent corrections and asymmetric reaction pathways reduce the impact of SIE.
- For a Mn(III,IV) dimer, the localized state is more stable by 22 kcal/mol, with SIE causing artificial delocalization at larger metal-metal distances (error of 10 kcal/mol at dissociation).
Conclusions:
- The SIE can lead to significant errors in DFT calculations, particularly for systems prone to electronic delocalization.
- Delocalization is often avoided in practice due to energetic costs (70-80 kcal/mol) or geometric/ligand effects.
- Careful consideration of SIE is crucial for accurate DFT predictions, especially in complex systems like charge-transfer complexes and metalloenzymes.