Ensemble Density Functional Theory: Insight from the Fluctuation-Dissipation Theorem.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Density functional theory (DFT) is a powerful tool for calculating electronic structures.
• Generalizing DFT to excited states is crucial for understanding electronic excitations but faces fundamental challenges.
• Existing methods struggle to adapt ground-state DFT approximations for excited-state calculations.

Purpose of the Study:

• To develop a robust framework for calculating excitation energies using low-cost DFT approximations.
• To overcome fundamental issues hindering the adaptation of ground-state DFT approximations for excited states.
• To provide a versatile approach for ensemble density functional approximations.

Main Methods:

• Generalization of density functional theory to mixtures of ground and excited states.
• Utilization of a fluctuation dissipation theorem (FDT) to guide the development of key functionals.
• Adaptation of existing exchange energy approximations with a rigorous, excited-state-specific Hartree term.

Main Results:

• The fluctuation dissipation theorem (FDT) effectively prevents fundamental issues in excited-state DFT.
• Existing exchange energy approximations are successfully adapted for excited states.
• The framework provides insights into ground-statelike and ensemble-only correlations.

Conclusions:

• A comprehensive and versatile framework for ensemble density functional approximations is established.
• This approach facilitates the use of low-cost DFT approximations for determining excitation energies.
• The study paves the way for significant advancements in computational chemistry and materials science.