Smoothed truncated Coulomb potential for periodic Gaussian-basis Hartree--Fock exchange
Abstract
Truncated Coulomb (TC) potentials reduce finite-size errors and accelerate thermodynamic-limit convergence in periodic Hartree--Fock (HF) calculations, but their use with Gaussian basis sets is complicated by the evaluation of electron repulsion integrals (ERIs), particularly for nonspherical truncation domains and all-electron calculations. We introduce the smoothed truncated Coulomb (sTC) potential as a systematically improvable approximation to a parent TC potential. A real-space Gaussian convolution smooths the sharp truncation boundary, and a single dimensionless parameter, η, controls the width of the smoothing window, which can be tightened to systematically approach the TC reference. The smoothing by sTC enables a dual-space algorithm for evaluating periodic Gaussian-basis ERIs that requires neither a large plane-wave basis nor new molecular integral kernels and is applicable to both pseudopotential and all-electron calculations, including the important Wigner--Seitz-cell truncation boundaries. Benchmarks spanning insulating, semiconducting, layered, metallic, and molecular-crystal systems show that sTC-based HF closely reproduces TC results in pseudopotential calculations and extends TC-quality calculations to all-electron settings. Across these systems, sTC substantially improves thermodynamic-limit convergence relative to the probe-charge Ewald method while remaining practical for all-electron calculations in which direct TC-based calculations are computationally challenging.
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BibTeX
@misc{yang2026smoothed,
title = {{Smoothed truncated Coulomb potential for periodic Gaussian-basis Hartree--Fock exchange}},
author = {Gengzhi Yang and Aamy Bakry and Hong-Zhou Ye},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.00203},
eprint = {2609.00203},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00203},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Smoothed truncated Coulomb potential for periodic Gaussian-basis Hartree--Fock exchange
AU - Gengzhi Yang
AU - Aamy Bakry
AU - Hong-Zhou Ye
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2609.00203
UR - https://arxiv.org/abs/2609.00203
AB - Truncated Coulomb (TC) potentials reduce finite-size errors and accelerate thermodynamic-limit convergence in periodic Hartree--Fock (HF) calculations, but their use with Gaussian basis sets is complicated by the evaluation of electron repulsion integrals (ERIs), particularly for nonspherical truncation domains and all-electron calculations. We introduce the smoothed truncated Coulomb (sTC) potential as a systematically improvable approximation to a parent TC potential. A real-space Gaussian convolution smooths the sharp truncation boundary, and a single dimensionless parameter, η, controls the width of the smoothing window, which can be tightened to systematically approach the TC reference. The smoothing by sTC enables a dual-space algorithm for evaluating periodic Gaussian-basis ERIs that requires neither a large plane-wave basis nor new molecular integral kernels and is applicable to both pseudopotential and all-electron calculations, including the important Wigner--Seitz-cell truncation boundaries. Benchmarks spanning insulating, semiconducting, layered, metallic, and molecular-crystal systems show that sTC-based HF closely reproduces TC results in pseudopotential calculations and extends TC-quality calculations to all-electron settings. Across these systems, sTC substantially improves thermodynamic-limit convergence relative to the probe-charge Ewald method while remaining practical for all-electron calculations in which direct TC-based calculations are computationally challenging.
ER -