Calculation of Berry curvature using non-orthogonal atomic orbitals

Area of Science:

• Condensed Matter Physics
• Materials Science
• Computational Chemistry

Background:

• Calculating Berry curvature is crucial for understanding electronic properties in materials.
• Non-orthogonal numerical atomic orbital (NAO) bases are commonly used but computationally intensive.
• Existing methods may not fully account for basis set characteristics.

Purpose of the Study:

• To derive a complete formula for Berry curvature on non-orthogonal NAO bases.
• To develop an efficient computational approach using orbital contraction.
• To validate the formula and investigate corrections to existing theories.

Main Methods:

• Derivation of the full Berry curvature formula for non-orthogonal NAO bases.
• Implementation of an orbital contraction method to reduce basis set size.
• Benchmarking calculations for ferroelectric BaTiO3 and bcc Fe, including anomalous Hall conductivity.

Main Results:

• The derived formula accurately calculates Berry curvature on non-orthogonal NAO bases.
• Orbital contraction significantly enhances computational efficiency with minimal accuracy loss.
• Calculations for BaTiO3 and Fe show excellent agreement with established methods.
• Identified and quantified correction terms to the Kubo formula for Berry curvature.

Conclusions:

• The developed formula and method provide an efficient and accurate tool for Berry curvature calculations.
• Orbital contraction is a viable strategy for large NAO basis sets.
• Correction terms to the Kubo formula are significant for reduced basis sets and warrant consideration.