The Coulomb singularity corrections in plane-wave electronic structure calculations: Implementation and benchmarking

Y Yexuan Lin (Hefei National Research Center for Physical Sciences at the Microscale, and Hefei National Laboratory, University of Science and Technology of China 1 , Hefei, Anhui 230026,) S Sheng Chen (Beijing Frontier Research Center for Biological Structures, State Key Laboratory of Membrane Biology, Tsinghua-Peking Joint Center for Life Sciences, School of Life Sciences, Tsinghua University, Beijing, China.) L Linhao Wang (Hefei National Research Center for Physical Sciences at the Microscale, and Hefei National Laboratory, University of Science and Technology of China 1 , Hefei, Anhui 230026,) X Xilin Yin (State Key Laboratory of Precision and Intelligent Chemistry, and Department of Chemical Physics, University of Science and Technology of China 2 , Hefei, Anhui 230026,) Z Zhaolong Luo (Hefei National Research Center for Physical Sciences at the Microscale, and Hefei National Laboratory, University of Science and Technology of China 1 , Hefei, Anhui 230026,) W Wentiao Wu (Hefei National Research Center for Physical Sciences at the Microscale, and Hefei National Laboratory, University of Science and Technology of China 1 , Hefei, Anhui 230026,) X Xinhui Cui (Hefei National Research Center for Physical Sciences at the Microscale, and Hefei National Laboratory, University of Science and Technology of China 1 , Hefei, Anhui 230026,) X Xinming Qin (Hefei National Research Center for Physical Sciences at the Microscale, and Hefei National Laboratory, University of Science and Technology of China 1 , Hefei, Anhui 230026,) W Wei Hu J Jinlong Yang (State Key Laboratory of Precision and Intelligent Chemistry, School of Chemistry and Materials Science, and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM))

Abstract

The Kohn–Sham density functional theory (DFT) is a fundamental tool for investigating the electronic structures of molecules and solids. For periodic systems, the singularity problem does not arise in pure DFT calculations. However, when DFT is combined with the Hartree–Fock method and other wave function methods to improve accuracy, the long-range nature of the Coulomb potential 1/r leads to cumbersome interactions and introduces a 1/G2 singularity at the Γ point in reciprocal space. Handling these divergence singularities is crucial for enhancing both the accuracy and efficiency of calculations in periodic systems, particularly in various computational methods such as hybrid functionals, random phase approximation (RPA), second-order Møller–Plesset perturbation theory, GW approximation, and time-dependent density functional theory. In this study, we conduct detailed comprehensive calculations and comparisons of various approaches, including spherical truncation, Wigner–Seitz truncation, screened Coulomb potentials, auxiliary functions, and the probe charge method, to address this singularity problem in plane-wave calculations within periodic boundary conditions. In the context of plane-wave-based RPA and GW calculations, we pioneeringly implement the Wigner–Seitz truncation scheme and systematically investigate its convergence and accuracy through both supercell expansion and k-point sampling. Our results reveal optimal correction strategies tailored to different systems and computational methods, providing valuable guidance for future developments in the field.

Article Details

Volume / Issue Vol. 164, Issue 3
Published January 21, 2026
ISSN 0021-9606
Publisher American Institute of Physics

Journal Info

The Journal of Chemical Physics

American Institute of Physics

ISSN: 0021-9606 Physical Sciences

Authors (10)

Y

Yexuan Lin

Hefei National Research Center for Physical Sciences at the Microscale, and Hefei National Laboratory, University of Science and Technology of China 1 , Hefei, Anhui 230026,

S

Sheng Chen

Beijing Frontier Research Center for Biological Structures, State Key Laboratory of Membrane Biology, Tsinghua-Peking Joint Center for Life Sciences, School of Life Sciences, Tsinghua University, Beijing, China.

L

Linhao Wang

Hefei National Research Center for Physical Sciences at the Microscale, and Hefei National Laboratory, University of Science and Technology of China 1 , Hefei, Anhui 230026,

X

Xilin Yin

State Key Laboratory of Precision and Intelligent Chemistry, and Department of Chemical Physics, University of Science and Technology of China 2 , Hefei, Anhui 230026,

Z

Zhaolong Luo

Hefei National Research Center for Physical Sciences at the Microscale, and Hefei National Laboratory, University of Science and Technology of China 1 , Hefei, Anhui 230026,

W

Wentiao Wu

Hefei National Research Center for Physical Sciences at the Microscale, and Hefei National Laboratory, University of Science and Technology of China 1 , Hefei, Anhui 230026,

X

Xinhui Cui

Hefei National Research Center for Physical Sciences at the Microscale, and Hefei National Laboratory, University of Science and Technology of China 1 , Hefei, Anhui 230026,

X

Xinming Qin

Hefei National Research Center for Physical Sciences at the Microscale, and Hefei National Laboratory, University of Science and Technology of China 1 , Hefei, Anhui 230026,

W

Wei Hu

J

Jinlong Yang

State Key Laboratory of Precision and Intelligent Chemistry, School of Chemistry and Materials Science, and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM)