Excitations and benchmark ensemble density functional theory for two electrons.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Density Functional Theory (DFT) is a powerful tool for electronic structure calculations.
• Ensemble DFT extends standard DFT to systems with degenerate ground states or excited states.
• Accurate calculation of ensemble potentials is crucial for understanding complex electronic behaviors.

Purpose of the Study:

• To develop and apply a new method for extracting ensemble Kohn-Sham potentials.
• To explore the behavior of exact ensemble density functional theory (DFT) in two-electron systems.
• To investigate the impact of separating Hartree energy and choosing degenerate eigenstates.

Main Methods:

• Application of a novel method to extract ensemble Kohn-Sham potentials from accurate excited state densities.
• Systematic analysis of various two-electron systems, including one-dimensional boxes, Hooke's atom, and the Helium atom.
• Derivation of a new approximation: spin eigenstate Hartree-exchange.

Main Results:

• The study provides insights into the behavior of exact ensemble DFT.
• Exact conditions are proven, including signs of correlation energy components and potential's asymptotic behavior.
• Energy components are detailed as a function of weights for diverse two-electron systems and ensembles.

Conclusions:

• The new method offers a pathway to more accurate ensemble potentials.
• The findings contribute to a deeper theoretical understanding of ensemble DFT.
• The research validates theoretical predictions with calculations on various model systems.