Optimized auxiliary functions for robust mitigation of finite-size errors in periodic hybrid density functional theory

TL;DR

This paper introduces optimized auxiliary functions and a fitting approach to systematically reduce finite-size errors in periodic hybrid density functional theory calculations, achieving high accuracy even with sparse k-meshes.

Contribution

It proposes new auxiliary functions and a robust fitting method to improve the convergence of finite-size error correction in hybrid DFT calculations.

Findings

Achieves millihartree-level accuracy in FSE correction.

Demonstrates rapid convergence toward the thermodynamic limit.

Effective for a range of semiconductors and insulators.

Abstract

When calculating properties of periodic systems at the thermodynamic limit (TDL), the dominant source of finite size error (FSE) arises from the long-range Coulomb interaction, and can manifest as a slowly converging quadrature error when approximating an integral in the reciprocal space by a finite sum. The singularity subtraction (SS) method offers a systematic approach for reducing this quadrature error and thus the FSE. In this work, we first investigate the performance of the SS method in the simplest setting, aiming at reducing the FSE in exact exchange calculations by subtracting the Coulomb contribution with a single, adjustable Gaussian auxiliary function. We demonstrate that a simple fitting method can robustly estimate the optimal Gaussian width and leads to rapid convergence toward the TDL. Furthermore, we suggest new forms of the auxiliary function, whose optimal parameters could also be determined through least-squares fitting. For a range of semiconductors and insulators, the proposed auxiliary functions achieve robust, millihartree-level accuracy in hybrid density functional theory calculations, including cases with sparse k-meshes and large basis sets.