Exact Static Linear Response of Excited States from Ensemble Density Functional Theory

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Recent advancements in ensemble density functional theory (DFT) have focused on excited electronic energy levels.
• Standard DFT methods often face challenges in accurately describing excited-state properties.

Purpose of the Study:

• To derive the static linear response theory for excited electronic states within the ensemble DFT framework.
• To enable in-principle exact evaluations of excited-state density-density linear response functions.
• To identify exact excited-state corrections to ground-state linear response DFT.

Main Methods:

• Derivation of static linear response theory for ensemble DFT.
• Introduction of individual-state components of the inverse ensemble linear response function.
• Formulation of a working Dyson-type equation for each excited state.
• Analysis of the zero-weight limit of the theory.

Main Results:

• A frequency-independent method for evaluating excited-state density-density linear response functions.
• Emergence of a Dyson-type equation for individual excited states.
• Identification of exact excited-state corrections to ground-state linear response DFT.
• Demonstration that these corrections depend on weight derivatives of the ensemble Hartree-exchange-correlation (Hxc) potential and kernel.

Conclusions:

• The derived theory provides a pathway for exact calculations of excited-state properties.
• Ensemble DFT is crucial for understanding excited-state phenomena.
• The study highlights the significance of weight and density-functional derivatives of the ensemble Hxc energy functional in ensemble DFT.