Comparing correlation components and approximations in Hartree-Fock and Kohn-Sham theories via an analytical test...

Area of Science:

• Quantum Chemistry
• Computational Materials Science
• Electronic Structure Theory

Background:

• The Hubbard dimer model provides analytical expressions for Hartree-Fock (HF) and Kohn-Sham (KS) states, enabling direct comparison of correlation energies.
• Understanding correlation energy contributions in different theoretical frameworks is crucial for accurate electronic structure calculations.

Purpose of the Study:

• To rigorously compare individual contributions to correlation energies from HF and KS theories within the Hubbard dimer model.
• To analyze the performance of Liu-Burke and Seidl-Perdew-Levy correlation energy functionals for both HF and KS references.

Main Methods:

• Utilized the asymmetric Hubbard dimer model for explicit analytical expressions of HF and KS states.
• Analyzed correlation energy contributions across the {U, Δv} parameter space.
• Tested Liu-Burke and Seidl-Perdew-Levy functionals against HF and KS correlation energies.

Main Results:

• Observed a sign change in the HF kinetic correlation energy.
• Derived an expression for the traditional correlation energy in a site-occupation function theory spirit.
• Found that tested functionals generally perform better for the HF reference, despite being designed for KS.

Conclusions:

• The Hubbard dimer model highlights potential errors when using strong-interaction ingredients for KS instead of HF references.
• Correlation energy functionals may require re-evaluation for optimal performance across different theoretical references.
• This model offers insights into the fundamental differences between HF and KS correlation energy descriptions.