### Abstract

^{7/2}+ B/N

^{8/2}+ …, where N is the number of Laguerre basis functions. The electron–electron δ‐function expectation converges as Δδ

^{N}≈ A/N

^{5/2}+ B/N

^{6/2}+ …, and the variational limit for the ℓ = 0 basis is estimated as 0.1557637174(2) a(0)(3). It was seen that extrapolation of the energy to the variational limit is dependent on the basis dimension at which the exponent in the Laguerre basis was optimized. In effect, it may be best to choose a nonoptimal exponent if one wishes to extrapolate to the variational limit. An investigation of the natural orbital asymptotics revealed the energy converged as ΔE

^{N}≈ A/N

^{6 }+ B/N

^{7}+ …, while the electron–electron δ‐function expectation converged as Δδ

^{N}≈ A/N

^{4}+ B/N

^{5}+ …. The asymptotics of expectation values other than the energy showed fluctuations that depended on whether N was even or odd.

Original language | English |
---|---|

Pages (from-to) | 907-920 |

Number of pages | 14 |

Journal | International Journal of Quantum Chemistry |

Volume | 107 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2007 |

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### Cite this

*International Journal of Quantum Chemistry*,

*107*(4), 907-920. https://doi.org/10.1002/qua.21217

}

*International Journal of Quantum Chemistry*, vol. 107, no. 4, pp. 907-920. https://doi.org/10.1002/qua.21217

**Convergence of an s-wave calculation of the he ground state.** / Mitroy, James; Bromley, Michael; Ratnavelu, K.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Convergence of an s-wave calculation of the he ground state

AU - Mitroy, James

AU - Bromley, Michael

AU - Ratnavelu, K

PY - 2007

Y1 - 2007

N2 - The configuration interaction (CI) method using a large Laguerre basis restricted to ℓ = 0 orbitals is applied to the calculation of the He ground state. The maximum number of orbitals included was 60. The numerical evidence suggests that the energy converges as ΔEN ≈ A/N7/2 + B/N8/2 + …, where N is the number of Laguerre basis functions. The electron–electron δ‐function expectation converges as ΔδN ≈ A/N5/2 + B/N6/2 + …, and the variational limit for the ℓ = 0 basis is estimated as 0.1557637174(2) a(0)(3). It was seen that extrapolation of the energy to the variational limit is dependent on the basis dimension at which the exponent in the Laguerre basis was optimized. In effect, it may be best to choose a nonoptimal exponent if one wishes to extrapolate to the variational limit. An investigation of the natural orbital asymptotics revealed the energy converged as ΔEN ≈ A/N6 + B/N7 + …, while the electron–electron δ‐function expectation converged as ΔδN ≈ A/N4 + B/N5 + …. The asymptotics of expectation values other than the energy showed fluctuations that depended on whether N was even or odd.

AB - The configuration interaction (CI) method using a large Laguerre basis restricted to ℓ = 0 orbitals is applied to the calculation of the He ground state. The maximum number of orbitals included was 60. The numerical evidence suggests that the energy converges as ΔEN ≈ A/N7/2 + B/N8/2 + …, where N is the number of Laguerre basis functions. The electron–electron δ‐function expectation converges as ΔδN ≈ A/N5/2 + B/N6/2 + …, and the variational limit for the ℓ = 0 basis is estimated as 0.1557637174(2) a(0)(3). It was seen that extrapolation of the energy to the variational limit is dependent on the basis dimension at which the exponent in the Laguerre basis was optimized. In effect, it may be best to choose a nonoptimal exponent if one wishes to extrapolate to the variational limit. An investigation of the natural orbital asymptotics revealed the energy converged as ΔEN ≈ A/N6 + B/N7 + …, while the electron–electron δ‐function expectation converged as ΔδN ≈ A/N4 + B/N5 + …. The asymptotics of expectation values other than the energy showed fluctuations that depended on whether N was even or odd.

KW - Electron absorption

KW - Extrapolation

KW - Helium

KW - Optimization

KW - Basis set convergence

KW - Configuration interaction

KW - Laguerre-type orbitals

KW - Electron energy levels

U2 - 10.1002/qua.21217

DO - 10.1002/qua.21217

M3 - Article

VL - 107

SP - 907

EP - 920

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

IS - 4

ER -