Correcting basis-set errors due to the absence of the electron-electron cusp using an adiabatic correction
Abstract
This article proposes an analytical method to address the slow convergence of electronic structure calculations caused by the inability of finite one-particle basis sets to describe the electron-electron cusp. An equivalence is established between a calculation using a finite basis set with the physical Coulomb interaction and a calculation using a complete basis set with a model interaction (specifically, the error-function screened Coulomb potential characterized by a range-separation parameter μ). By leveraging the adiabatic connection formalism, a simple, parameter-free correction formula is derived. It depends only on the on-top pair density and a locally defined range-separation parameter (μ) derived from the basis set itself. This `adiabatic connection based basis-set error correction' (ABC) is derived from the asymptotic expansion of the wave function at large μ for small inter-electronic distances. Therefore it is applicable to both ground and excited states without the restriction imposed by the Hohenberg-Kohn theorem. Numerical tests illustrate that the method achieves chemical accuracy using smaller basis sets than typically required.
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BibTeX
@misc{scemama2026correcting,
title = {{Correcting basis-set errors due to the absence of the electron-electron cusp using an adiabatic correction}},
author = {Anthony Scemama and Andreas Savin},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2606.07350},
eprint = {2606.07350},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.07350},
}
RIS
TY - UNPB
TI - Correcting basis-set errors due to the absence of the electron-electron cusp using an adiabatic correction
AU - Anthony Scemama
AU - Andreas Savin
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2606.07350
UR - https://arxiv.org/abs/2606.07350
AB - This article proposes an analytical method to address the slow convergence of electronic structure calculations caused by the inability of finite one-particle basis sets to describe the electron-electron cusp. An equivalence is established between a calculation using a finite basis set with the physical Coulomb interaction and a calculation using a complete basis set with a model interaction (specifically, the error-function screened Coulomb potential characterized by a range-separation parameter μ). By leveraging the adiabatic connection formalism, a simple, parameter-free correction formula is derived. It depends only on the on-top pair density and a locally defined range-separation parameter (μ) derived from the basis set itself. This `adiabatic connection based basis-set error correction' (ABC) is derived from the asymptotic expansion of the wave function at large μ for small inter-electronic distances. Therefore it is applicable to both ground and excited states without the restriction imposed by the Hohenberg-Kohn theorem. Numerical tests illustrate that the method achieves chemical accuracy using smaller basis sets than typically required.
ER -