Quantitative Electron Delocalization in Solids from Maximally Localized Wannier Functions.

Area of Science:

• Solid-state chemistry
• Quantum chemistry
• Materials science

Background:

• Electron delocalization is fundamental to chemical bonding, resonance, and aromaticity.
• Current methods for quantifying electron delocalization in solids, like maximally localized Wannier functions, offer only qualitative insights and are limited by arbitrary choices.
• Quantitative methods, such as Bader's delocalization indices, are informative but computationally expensive.

Purpose of the Study:

• To develop a fast and accurate method for calculating electron localization and delocalization indices in periodic solids.
• To enable quantitative analysis of chemical bonding in complex solid-state systems.

Main Methods:

• A novel approach combining grid-based atomic integration and maximally localized Wannier functions within the plane-wave/pseudopotential approximation.
• Grid-based integration facilitates rapid calculation of atomic overlap integrals.
• Maximally localized Wannier functions are used to efficiently discard distant overlaps, significantly reducing computational cost.

Main Results:

• The new method dramatically accelerates the calculation of localization and delocalization indices for solids containing dozens of atoms, completing in hours on a desktop computer.
• The approach was successfully applied to various systems, including simple and molecular solids, polymeric nitrogen, different ice phases, and ammonia under pressure.
• Demonstrated the ability to quantitatively describe chemical bonding in solids.

Conclusions:

• This work presents a significant advancement in the quantitative assessment of chemical bonding in solids.
• The developed method provides a computationally efficient pathway for analyzing electron delocalization, paving the way for deeper understanding of material properties.
• Enables quantitative description of chemical bonding in solids, particularly under pressure.