Local-Density Correlation Functional from the Force-Balance Equation

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Time-dependent density-functional theory (TDDFT) offers a path to approximate functionals.
• Deriving practical correlation functionals via the force-balance equation remains challenging.
• Existing methods lack systematic improvement for correlation functionals.

Purpose of the Study:

• To derive an analytical correlation-energy functional for ground-state calculations.
• To utilize the force-balance equation within TDDFT.
• To establish a foundation for systematically improvable correlation functionals.

Main Methods:

• Starting with the Colle-Salvetti correlated wave function.
• Applying the force-balance equation to derive the functional.
• Comparing the new functional against the local-density approximation (LDA).

Main Results:

• An analytical correlation-energy functional was successfully derived.
• The new functional demonstrated enhanced performance for atomic systems compared to LDA.
• A slight decrease in performance was observed for solid systems.

Conclusions:

• The force-balance equation provides a viable route for deriving correlation functionals.
• The derived functional offers a promising starting point for future improvements.
• Systematic enhancement of the force-based correlation functional is feasible.