Robust Pipek-Mezey Orbital Localization in Periodic Solids.

Area of Science:

• Condensed Matter Physics
• Quantum Chemistry
• Materials Science

Background:

• Boys (maximally-localized) Wannier functions are commonly used.
• Pipek-Mezey (PM) Wannier functions offer formal advantages.
• Efficient calculation methods are needed for complex systems.

Purpose of the Study:

• To describe a robust and efficient method for determining Pipek-Mezey (PM) Wannier functions (WF).
• To demonstrate the solver's performance on various solid-state systems.
• To enhance the applicability of PM WFs in electronic structure theory.

Main Methods:

• Development of a Broyden-Fletcher-Goldfarb-Shanno (BFGS)-based PMWF solver.
• Evaluation of the PM functional and gradient in a periodic linear combination of atomic orbital (LCAO) representation.
• Utilizing Moore-Penrose pseudoinverse projection for atomic charges.
• Implementing an automated "canonicalize phase then randomize" initial guess method.

Main Results:

• The BFGS-based PMWF solver shows dramatically faster convergence compared to steepest ascent and conjugate gradient methods.
• Robust determination of WFs is achieved even in supercells with thousands of atoms.
• The method is effective for various one-, two-, and three-dimensional solids, including those with vanishing band gaps.

Conclusions:

• The developed PMWF solver offers a significant improvement in computational efficiency and robustness.
• This method facilitates reliable Wannier function analysis in complex materials.
• The approach enhances the practical utility of PM WFs in solid-state electronic structure studies.