Exchange-Correlation Potentials and Energy Densities through Orbital Averaging and Aufbau Integration

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Density Functional Theory (DFT) relies on accurate approximations for exchange-correlation (XC) potentials and energy densities.
• Developing accurate XC functionals is crucial for predicting molecular and material properties.

Purpose of the Study:

• To derive accurate exchange-correlation potentials and energy densities using a novel inversion procedure.
• To provide benchmark data for the development of improved XC functionals.

Main Methods:

• Orbital-averaged (OA) Kohn-Sham (KS) inversion procedure.
• Utilizing reference densities from full configuration interaction (FCI) calculations.
• Employing an aufbau path integral for energy density calculations.

Main Results:

• Accurate derivation of exchange-correlation potentials (v) and energy densities (e) for integer and fractional electron counts.
• Captured key features of v, including -1/r decay and step discontinuities.
• Achieved good agreement between calculated energy densities and total energies (E).

Conclusions:

• The developed workflow provides FCI-derived KS quantities (v, e, step contributions).
• This approach can significantly contribute to creating more accurate XC functionals.
• It bridges the gap between wavefunction accuracy and DFT computational efficiency.