Optimized Auxiliary Functions for Robust Mitigation of Finite-Size Errors in Periodic Hybrid Density Functional...

Area of Science:

• Computational materials science
• Quantum chemistry
• Solid-state physics

Background:

• Finite size errors (FSE) are a major challenge in calculating properties of periodic systems.
• The long-range Coulomb interaction is the dominant source of FSE, leading to slow convergence in reciprocal space integration.
• The singularity subtraction (SS) method provides a systematic way to reduce these errors.

Purpose of the Study:

• To investigate the performance of the SS method for reducing FSE in exact exchange calculations.
• To develop and test new auxiliary functions for the SS method.
• To achieve robust, high accuracy in hybrid density functional theory (DFT) calculations.

Main Methods:

• Applying the SS method with a single, adjustable Gaussian auxiliary function.
• Developing a fitting method to estimate optimal Gaussian parameters for rapid convergence.
• Proposing new auxiliary function forms with parameters determined by least-squares fitting.

Main Results:

• A simple fitting method robustly estimates optimal Gaussian width, enabling rapid convergence to the thermodynamic limit.
• New auxiliary functions, optimized via least-squares fitting, achieve millihartree-level accuracy.
• The method demonstrates effectiveness for semiconductors and insulators, even with sparse k-meshes and large basis sets.

Conclusions:

• The SS method, enhanced with optimized Gaussian auxiliary functions, effectively mitigates finite size errors in periodic calculations.
• This approach offers a reliable and accurate pathway for materials property prediction using hybrid DFT.
• The developed techniques are broadly applicable to various materials and computational conditions.