The shell model for the exchange-correlation hole in the strong-correlation limit

Area of Science:

• Quantum Chemistry
• Condensed Matter Physics
• Computational Materials Science

Background:

• Density functional theory (DFT) relies on accurate approximations for exchange-correlation functionals.
• The strong-correlation (SC) limit is crucial for developing accurate DFT functionals via adiabatic connection interpolation.
• Existing models like the non-local radius (NLR) model have limitations in reproducing the SC limit of the homogeneous electron gas.

Purpose of the Study:

• To introduce an improved "shell model" for the exchange-correlation hole and energy in the SC limit of DFT.
• To address the shortcomings of the NLR model in accurately describing strongly correlated electron systems.
• To provide efficient implementation strategies for the shell model and related quantities.

Main Methods:

• Development of the "shell model" approximation, refining the NLR model.
• Utilizing the spherically averaged electron density ρ(r,u) as a starting point.
• Derivation of analytical integrals for normalization and energy density of underlying holes.
• Demonstration of efficient computational implementation for ρ(r,u), NLR, and shell models.

Main Results:

• The shell model successfully remedies the NLR model's failure to reproduce the SC limit of the homogeneous electron gas.
• Efficient computational methods are presented for calculating the electron density and model energies.
• Analytical integrals simplify the computation of hole normalization and energy density.

Conclusions:

• The shell model offers a significant improvement over the NLR model for DFT in the strong-correlation regime.
• Efficient implementation strategies pave the way for practical application of the shell model.
• The developed model enables the construction of more accurate adiabatic connection interpolations for improved DFT functionals.