Fast Generation of Pipek-Mezey Wannier Functions via the Co-Iterative Augmented Hessian Method.

Area of Science:

• Condensed matter physics
• Computational materials science
• Quantum chemistry

Background:

• Wannier functions (WFs) are crucial for describing localized electronic states in solids.
• Existing methods for WF localization, like the co-iterative augmented Hessian (CIAH) algorithm, face computational scaling challenges, especially with dense k-point sampling.
• Efficient localization of WFs is essential for accurate electronic structure calculations and materials property prediction.

Purpose of the Study:

• To introduce a k-point extension of the CIAH algorithm, named k-CIAH, for efficient Pipek-Mezey (PM) localization of Wannier functions.
• To improve the computational scaling of WF localization methods in k-space.
• To enhance the overall computational efficiency for localizing a large number of orbitals in various solid materials.

Main Methods:

• Developed k-CIAH algorithm, a second-order method for Pipek-Mezey (PM) localization of Wannier functions (WFs).
• Exploited efficient evaluation of the Hessian-vector product for optimized computational scaling.
• Performed benchmark calculations on diverse solid materials (insulators, semiconductors, metals, surfaces) to assess convergence and efficiency.

Main Results:

• k-CIAH achieves O(Nk^2 n^3) scaling in CPU time and memory, outperforming the O(Nk^3 n^3) scaling of Gamma-point CIAH.
• Demonstrated 2-3 fold higher computational efficiency compared to first-order k-space methods and orders of magnitude improvement over Gamma-point CIAH for large orbital localization.
• Validated the quality of PMWFs obtained via k-CIAH through accurate electronic band structures via PMWF-based Wannier interpolation.

Conclusions:

• k-CIAH provides a fast and robust approach for Pipek-Mezey Wannier function optimization.
• The method significantly enhances computational efficiency for electronic structure calculations in condensed matter physics.
• k-CIAH is a valuable tool for accurate materials simulations and property prediction.