Analysis of atomic Pauli potentials and their large-Z limit

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Modeling Pauli energy without orbitals is a key challenge in orbital-free density functional theory (OF-DFT).
• The Pauli potential, representing the response of Pauli kinetic energy to density changes, is crucial for OF-DFT accuracy.
• Understanding atomic Pauli potential behavior under scaling is vital for developing accurate OF-DFT functionals.

Purpose of the Study:

• To analyze the behavior of the Pauli potential in non-relativistic neutral atoms under Lieb-Simon scaling.
• To investigate the convergence of the Pauli potential towards the Thomas-Fermi limit.
• To identify new constraints for improving orbital-free density functional theory functionals.

Main Methods:

• Mathematical analysis of the near-nuclear region of atomic potentials.
• Calculation of the exact orbital-dependent Pauli potential for closed-shell atoms up to Z = 976 using the Levy-Ouyang approach.
• Investigation of atomic Pauli potential behavior under Lieb-Simon scaling.

Main Results:

• The atomic Pauli potential does not converge smoothly to the Thomas-Fermi limit but exhibits distinct regional behaviors.
• Near the nucleus, the potential approaches a constant value related to occupied eigenvalue differences.
• A transition region in the outer core shows unexpected deviations from Thomas-Fermi and gradient expansion potentials.

Conclusions:

• The study provides insights into the semi-classical description of Pauli statistics.
• Findings offer new constraints for developing improved orbital-free density functional theory functionals.
• The non-smooth convergence highlights the complexity of modeling Pauli energy in OF-DFT.