Convergence of the partial wave expansion of the He ground state

Michael Bromley, James Mitroy

    Research output: Contribution to journalArticleResearchpeer-review

    Abstract

    The configuration interaction (CI) method, using a very large Laguerre orbital basis, is applied to the calculation of the He ground state. The largest calculations included a minimum of 35 radial orbitals for each ? ranging from 0 to 12, resulting in basis sets in excess of 400 orbitals. The convergence of the energy and electron-electron ?-function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) were investigated in detail. Extrapolations to the limit of infinite angular momentum using expansions of the type ?XJ = AX[J + 1/2] -p + BX[J + 1/2]-p-1 + ..., gave an energy accurate to 10-7 Hartree and a value of ??? accurate to about 0.5%. Improved estimates of ?E? and ???, accurate to 10-8 Hartree and 0.01%, respectively, were obtained when extrapolations to an infinite radial basis were done prior to the determination of the J ? ? limit. Round-off errors were the main impediment to achieving even higher precision, since determination of the radial and angular limits required the manipulation of very small energy and ??? differences. � 2006 Wiley Periodicals, Inc.
    Original languageEnglish
    Pages (from-to)1150-1161
    Number of pages12
    JournalInternational Journal of Quantum Chemistry
    Volume107
    Issue number5
    Publication statusPublished - 2007

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    Angular momentum
    Extrapolation
    elastic waves
    Ground state
    orbitals
    ground state
    Electrons
    configuration interaction
    extrapolation
    angular momentum
    expansion
    energy
    manipulators
    electrons
    estimates

    Cite this

    Bromley, Michael ; Mitroy, James. / Convergence of the partial wave expansion of the He ground state. In: International Journal of Quantum Chemistry. 2007 ; Vol. 107, No. 5. pp. 1150-1161.
    @article{028ba119778c4272b08cd0f63e04503c,
    title = "Convergence of the partial wave expansion of the He ground state",
    abstract = "The configuration interaction (CI) method, using a very large Laguerre orbital basis, is applied to the calculation of the He ground state. The largest calculations included a minimum of 35 radial orbitals for each ? ranging from 0 to 12, resulting in basis sets in excess of 400 orbitals. The convergence of the energy and electron-electron ?-function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) were investigated in detail. Extrapolations to the limit of infinite angular momentum using expansions of the type ?XJ = AX[J + 1/2] -p + BX[J + 1/2]-p-1 + ..., gave an energy accurate to 10-7 Hartree and a value of ??? accurate to about 0.5{\%}. Improved estimates of ?E? and ???, accurate to 10-8 Hartree and 0.01{\%}, respectively, were obtained when extrapolations to an infinite radial basis were done prior to the determination of the J ? ? limit. Round-off errors were the main impediment to achieving even higher precision, since determination of the radial and angular limits required the manipulation of very small energy and ??? differences. � 2006 Wiley Periodicals, Inc.",
    keywords = "Convergence of numerical methods, Error analysis, Extrapolation, Functions, Helium, Basis set convergence, Configuration interactions, Laguerre type orbitals, Partial wave expansion, Ground state",
    author = "Michael Bromley and James Mitroy",
    year = "2007",
    language = "English",
    volume = "107",
    pages = "1150--1161",
    journal = "International Journal of Quantum Chemistry",
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    Convergence of the partial wave expansion of the He ground state. / Bromley, Michael; Mitroy, James.

    In: International Journal of Quantum Chemistry, Vol. 107, No. 5, 2007, p. 1150-1161.

    Research output: Contribution to journalArticleResearchpeer-review

    TY - JOUR

    T1 - Convergence of the partial wave expansion of the He ground state

    AU - Bromley, Michael

    AU - Mitroy, James

    PY - 2007

    Y1 - 2007

    N2 - The configuration interaction (CI) method, using a very large Laguerre orbital basis, is applied to the calculation of the He ground state. The largest calculations included a minimum of 35 radial orbitals for each ? ranging from 0 to 12, resulting in basis sets in excess of 400 orbitals. The convergence of the energy and electron-electron ?-function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) were investigated in detail. Extrapolations to the limit of infinite angular momentum using expansions of the type ?XJ = AX[J + 1/2] -p + BX[J + 1/2]-p-1 + ..., gave an energy accurate to 10-7 Hartree and a value of ??? accurate to about 0.5%. Improved estimates of ?E? and ???, accurate to 10-8 Hartree and 0.01%, respectively, were obtained when extrapolations to an infinite radial basis were done prior to the determination of the J ? ? limit. Round-off errors were the main impediment to achieving even higher precision, since determination of the radial and angular limits required the manipulation of very small energy and ??? differences. � 2006 Wiley Periodicals, Inc.

    AB - The configuration interaction (CI) method, using a very large Laguerre orbital basis, is applied to the calculation of the He ground state. The largest calculations included a minimum of 35 radial orbitals for each ? ranging from 0 to 12, resulting in basis sets in excess of 400 orbitals. The convergence of the energy and electron-electron ?-function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) were investigated in detail. Extrapolations to the limit of infinite angular momentum using expansions of the type ?XJ = AX[J + 1/2] -p + BX[J + 1/2]-p-1 + ..., gave an energy accurate to 10-7 Hartree and a value of ??? accurate to about 0.5%. Improved estimates of ?E? and ???, accurate to 10-8 Hartree and 0.01%, respectively, were obtained when extrapolations to an infinite radial basis were done prior to the determination of the J ? ? limit. Round-off errors were the main impediment to achieving even higher precision, since determination of the radial and angular limits required the manipulation of very small energy and ??? differences. � 2006 Wiley Periodicals, Inc.

    KW - Convergence of numerical methods

    KW - Error analysis

    KW - Extrapolation

    KW - Functions

    KW - Helium

    KW - Basis set convergence

    KW - Configuration interactions

    KW - Laguerre type orbitals

    KW - Partial wave expansion

    KW - Ground state

    M3 - Article

    VL - 107

    SP - 1150

    EP - 1161

    JO - International Journal of Quantum Chemistry

    JF - International Journal of Quantum Chemistry

    SN - 0020-7608

    IS - 5

    ER -