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

James Mitroy, Michael Bromley, K Ratnavelu

    Research output: Contribution to journalArticleResearchpeer-review

    Abstract

    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.
    Original languageEnglish
    Pages (from-to)907-920
    Number of pages14
    JournalInternational Journal of Quantum Chemistry
    Volume107
    Issue number4
    DOIs
    Publication statusPublished - 2007

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    Ground state
    ground state
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    Extrapolation
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    configuration interaction
    extrapolation

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    Mitroy, James ; Bromley, Michael ; Ratnavelu, K. / Convergence of an s-wave calculation of the he ground state. In: International Journal of Quantum Chemistry. 2007 ; Vol. 107, No. 4. pp. 907-920.
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    abstract = "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.",
    keywords = "Electron absorption, Extrapolation, Helium, Optimization, Basis set convergence, Configuration interaction, Laguerre-type orbitals, Electron energy levels",
    author = "James Mitroy and Michael Bromley and K Ratnavelu",
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    Convergence of an s-wave calculation of the he ground state. / Mitroy, James; Bromley, Michael; Ratnavelu, K.

    In: International Journal of Quantum Chemistry, Vol. 107, No. 4, 2007, p. 907-920.

    Research output: Contribution to journalArticleResearchpeer-review

    TY - JOUR

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

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    AU - Bromley, Michael

    AU - Ratnavelu, K

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    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

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