Connections between variation principles at the interface of wave-function and density-functional theories.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Many-Body Theory

Background:

• The Kohn-Sham (KS) approach is central to density functional theory (DFT) for electronic structure calculations.
• Accurate determination of the KS effective potential is crucial for the reliability of DFT predictions.
• Existing methods for KS potential determination have limitations regarding electron interaction strengths and system states.

Purpose of the Study:

• To analyze and extend a recently proposed variation principle for KS effective potentials.
• To investigate the applicability of this principle to arbitrary electron-interaction strengths and mixed states.
• To compare the new variation principle with Lieb's convex-conjugate functional.

Main Methods:

• Examination and extension of Gidopoulos's variation principle.
• Comparison with Lieb's convex-conjugate functional for potential determination.
• Numerical implementation and validation within a unified framework.

Main Results:

• The Gidopoulos variation principle is successfully extended to arbitrary electron-interaction strengths and mixed states.
• A direct mathematical relationship is established between Gidopoulos's variation principle and Lieb's functional.
• Numerical results confirm the equivalence of the information obtained from both approaches.

Conclusions:

• The extended Gidopoulos variation principle offers a robust method for determining KS potentials.
• The intrinsic link between the two functionals provides deeper theoretical insight into DFT.
• The findings facilitate more accurate and versatile electronic structure calculations.