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PreprintCC BY 4.0arXiv

Fourier Transform-Based Computation of Two-Electron Four-Center Coulomb Repulsion Integrals

  • William Chen
  • Lior Silberman
  • Ury Segal
  • Chen Greif
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Abstract

We present a Fourier-based method for evaluating two-electron four-center Coulomb repulsion integrals over Slater-type orbitals. Spherical Fourier-Bessel coefficients of the convolution factors are precomputed and reused. Since the spherical part of the integral can be evaluated directly, there remains only a one-dimensional quadrature problem in the radial direction. For the ten reference integrals reported here, the largest absolute discrepancy is 1.7×10−9. A preliminary resident-cache benchmark computes approximately 4.2×105 unique integrals per second on an NVIDIA V100 at the contraction stage.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026fourier,
  title = {{Fourier Transform-Based Computation of Two-Electron Four-Center Coulomb Repulsion Integrals}},
  author = {William Chen and Lior Silberman and Ury Segal and Chen Greif},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12608},
  eprint = {2610.12608},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12608},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Fourier Transform-Based Computation of Two-Electron Four-Center Coulomb Repulsion Integrals
AU  - William Chen
AU  - Lior Silberman
AU  - Ury Segal
AU  - Chen Greif
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12608
UR  - https://arxiv.org/abs/2610.12608
AB  - We present a Fourier-based method for evaluating two-electron four-center Coulomb repulsion integrals over Slater-type orbitals. Spherical Fourier-Bessel coefficients of the convolution factors are precomputed and reused. Since the spherical part of the integral can be evaluated directly, there remains only a one-dimensional quadrature problem in the radial direction. For the ten reference integrals reported here, the largest absolute discrepancy is 1.7×10^−9. A preliminary resident-cache benchmark computes approximately 4.2×10^5 unique integrals per second on an NVIDIA V100 at the contraction stage.
ER  -