Global and local curvature in density functional theory

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Electronic structure methods require energy linearity with fractional electron changes, indicating a derivative discontinuity at integer occupations.
• Semi-local approximations in Density Functional Theory (DFT) exhibit convex global curvature, signaling self-interaction error and electron delocalization.
• Existing functional tuning strategies prioritize piecewise linearity for improved optical property predictions.

Purpose of the Study:

• To investigate the effectiveness of Hubbard U-augmented DFT (DFT+U) in correcting energy linearity deviations in real systems.
• To determine if DFT+U can simultaneously address global and local energy curvature issues.
• To analyze the factors influencing DFT+U efficiency across various transition metal complexes and ligand strengths.

Main Methods:

• Applied DFT+U calculations to 27 octahedral transition metal complexes.
• Systematically varied transition metals (Sc-Cu) and ligand strengths (CO, NH3, H2O).
• Utilized an atomic projection framework to analyze delocalization errors and their visibility to DFT+U.

Main Results:

• DFT+U corrections were shown to minimize, and never worsen, deviations from energy linearity.
• The efficiency of DFT+U varied significantly based on the transition metal and ligand strength.
• Identified specific cases where DFT+U could not fully correct delocalization errors.

Conclusions:

• DFT+U is a valuable tool for improving the linearity of energy calculations in electronic structure methods.
• Global and local energy curvatures are distinct quantities that can exhibit opposing behaviors with changing ligand field strength.
• The study provides insights into the conditions under which DFT+U is most effective and its limitations.