A weight-dependent local correlation density-functional approximation for ensembles.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Density Functional Theory (DFT) is a powerful method for electronic structure calculations.
• Ensemble DFT (eDFT) extends DFT to handle systems with degenerate ground states or for calculating excited states.
• Accurate computation of electronic excitations, especially double excitations, remains a challenge.

Purpose of the Study:

• To develop a novel weight-dependent correlation density-functional approximation for ensembles (eDFT).
• To incorporate information from both ground and excited states for improved excitation energy calculations.
• To extend the local-density approximation for neutral excitations within eDFT.

Main Methods:

• Formulated a local, weight-dependent correlation density-functional approximation for eDFT.
• Incorporated ensemble weight dependence to capture derivative discontinuity contributions.
• Utilized uniform electron gas models (finite and infinite) for functional development.
• Applied the method to compute single and double excitations in 1D many-electron systems.

Main Results:

• The new approximation accurately computes single and double excitations in 1D systems across weak, intermediate, and strong correlation regimes.
• The weight-dependent functional inherently includes derivative discontinuity effects.
• Demonstrated the functional's effectiveness for various correlation strengths.

Conclusions:

• The proposed weight-dependent functional approximation is a significant advancement for eDFT.
• The methodology is general and applicable to 3D systems like molecules and solids.
• This approach offers a promising route for accurate electronic excitation calculations in complex systems.