Kohn-Sham equations with functionals from the strictly-correlated regime: investigation with a spectral...

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Density Functional Theory (DFT) relies on Kohn-Sham (KS) equations, which are computationally intensive.
• Functionals based on the strictly-correlated electrons (SCE) regime pose convergence challenges.
• Solving KS equations for strong interactions requires advanced numerical methods.

Purpose of the Study:

• To adapt a spectral renormalization method from nonlinear optics for solving KS equations.
• To address the convergence difficulties associated with SCE-based functionals.
• To enable calculations with advanced functionals, including zero-point energy (ZPE) and interaction-strength interpolation.

Main Methods:

• Re-adaptation of a spectral renormalization method.
• Simultaneous computation of eigenvalues and electron density.
• Utilization of randomized initial guesses for improved convergence.
• Ease of implementation for practical application.

Main Results:

• Successful convergence of KS equations with functionals incorporating the ZPE term.
• First-time convergence for interaction-strength interpolation functionals combining SCE and ZPE terms.
• Demonstration of a robust and efficient numerical approach.

Conclusions:

• The spectral renormalization method offers a viable solution for challenging DFT calculations.
• This work paves the way for studying quantum systems with strong long-range interactions.
• Future research can explore localization properties in low-dimensional systems with varying statistics and potentials.