Hartree and Exchange in Ensemble Density Functional Theory: Avoiding the Nonuniqueness Disaster

Area of Science:

• Quantum mechanics
• Computational chemistry
• Theoretical physics

Background:

• Ensemble density functional theory (EDFT) offers efficient and accurate calculations for quantum system excitations.
• The practical applicability of EDFT is limited by the need for improved functionals.
• Developing robust functionals is key to expanding EDFT's domain.

Purpose of the Study:

• Introduce a novel, guaranteed single-valued Hartree-exchange ensemble density functional, E_{Hx}[n].
• Provide a unifying framework for existing specialized expressions of E_{Hx}[n].
• Establish a clear and practical description for Hartree and exchange interactions in ensemble systems.

Main Methods:

• Define E_{Hx}[n] using the right derivative of the universal ensemble density functional.
• Express E_{Hx}[n] via block eigenvalues of a specific matrix.
• Demonstrate how literature expressions for E_{Hx}[n] fit into this unified picture.

Main Results:

• A guaranteed single-valued Hartree-exchange ensemble density functional, E_{Hx}[n], is presented.
• E_{Hx}[n] is shown to be expressible using block eigenvalues.
• Existing specialized expressions for E_{Hx}[n] are unified under this new framework.

Conclusions:

• The introduced E_{Hx}[n] functional offers a practical and clear description for Hartree and exchange in ensemble systems.
• This work unifies various approaches to calculating E_{Hx}[n], simplifying its application.
• The development promises to broaden the practical applicability of ensemble density functional theory.