Force balance approach for advanced approximations in density functional theories

Area of Science:

• Quantum mechanics
• Computational chemistry
• Materials science

Background:

• Density-functional theory (DFT) is a powerful quantum mechanical method for electronic structure calculations.
• Deriving accurate exchange-correlation potentials is crucial for DFT's predictive power.
• Current methods often face challenges with differentiability, causality, and computational complexity, especially when including vector potentials.

Purpose of the Study:

• To develop a systematic and constructive approach for determining exchange-correlation potentials in DFT.
• To incorporate vector potentials into DFT calculations without relying on energy or action functionals.
• To provide a robust alternative to the optimized-effective-potential (OEP) procedure.

Main Methods:

• The proposed method is based on equations of motion for current quantities, framed as force balance equations.
• This approach is applicable to both ground-state and time-dependent DFT (TDDFT) settings.
• It bypasses the need for differentiability and causality considerations inherent in functional differentiation.

Main Results:

• The method successfully determines exchange-correlation potentials, including those with vector potentials.
• It offers a viable alternative to the OEP procedure, simplifying calculations.
• Straightforward exchange-type approximations are derived, reducing to known approximations (local-density approximation, Slater Xα) for simple systems.

Conclusions:

• The new approach provides a systematic and feasible way to derive exchange-correlation potentials for DFT.
• It effectively handles vector potentials and avoids common issues associated with traditional methods.
• The derived approximations offer practical tools for electronic structure calculations.