Theory and Applications of Generalized Pipek-Mezey Wannier Functions

Area of Science:

• Computational Chemistry
• Condensed Matter Physics
• Quantum Chemistry

Background:

• Wannier functions are crucial for analyzing electronic structure in materials science and quantum chemistry.
• Existing methods like maximally localized Wannier functions (MLWF) can mix different orbital types (σ and π), hindering chemical interpretation.
• A need exists for localized Wannier functions that preserve the distinction between σ- and π-orbitals, aligning better with chemical intuition.

Purpose of the Study:

• To present the theory and implementation of generalized Pipek-Mezey Wannier functions (PMWF).
• To compare the localization properties and performance of PMWF against traditional MLWF.
• To demonstrate the applicability of PMWF across various dimensionalities and computational frameworks.

Main Methods:

• Developed and implemented the generalized Pipek-Mezey localization criterion for generating Wannier functions.
• Tested the implementation on systems with 1D, 2D, and 3D periodicity, as well as isolated molecules.
• Utilized the Atomic Simulation Environment (ASE) and supported various wavefunction representations (real-space grids, plane waves, LCAO) and the projector-augmented wave (PAW) formalism.

Main Results:

• Generalized Pipek-Mezey Wannier functions (PMWF) are shown to be highly localized and maintain the σ/π orbital distinction.
• PMWF achieve localization comparable to MLWF, as confirmed by comparing their respective objective function values.
• The implementation is versatile, compatible with GPAW, ABINIT, NWChem, and VASP electronic structure codes.

Conclusions:

• The generalized Pipek-Mezey approach provides a robust method for generating chemically intuitive, localized Wannier functions.
• PMWF offer a valuable alternative to MLWF, particularly when preserving the character of σ- and π-orbitals is important.
• The presented implementation facilitates the application of PMWF in diverse computational chemistry and condensed matter studies.