### Abstract

We develop a systematic way to determine an effective nuclear charge Z _{D}
^{R} such that the Hartree-Fock results will be significantly closer to the exact energies by utilizing the analytically known large-D limit energies. This method yields an expansion for the effective nuclear charge in powers of (1/D), which we have evaluated to the first order. This first order approximation to the desired effective nuclear charge has been applied to two-electron atoms with Z = 2-20, and weakly bound systems such as H^{-}. The errors for the two-electron atoms when compared with exact results were reduced from ∼0.2% for Z = 2 to ∼0.002% for large Z. Although usual Hartree-Fock calculations for H^{-} show this to be unstable, our results reduce the percent error of the Hartree-Fock energy from 7.6% to 1.86% and predicts the anion to be stable. For N-electron atoms (N = 3-18, Z = 3-28), using only the zeroth order approximation for the effective charge significantly reduces the error of Hartree-Fock calculations and recovers more than 80% of the correlation energy.

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

Pages (from-to) | 7472-7478 |

Number of pages | 7 |

Journal | The Journal of Chemical Physics |

Volume | 102 |

Issue number | 19 |

Publication status | Published - 1 Dec 1995 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of Chemical Physics*,

*102*(19), 7472-7478.

**Charge renormalization at the large-D limit for N-electron atoms and weakly bound systems.** / Kais, S.; Bleil, R.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 102, no. 19, pp. 7472-7478.

}

TY - JOUR

T1 - Charge renormalization at the large-D limit for N-electron atoms and weakly bound systems

AU - Kais, S.

AU - Bleil, R.

PY - 1995/12/1

Y1 - 1995/12/1

N2 - We develop a systematic way to determine an effective nuclear charge Z D R such that the Hartree-Fock results will be significantly closer to the exact energies by utilizing the analytically known large-D limit energies. This method yields an expansion for the effective nuclear charge in powers of (1/D), which we have evaluated to the first order. This first order approximation to the desired effective nuclear charge has been applied to two-electron atoms with Z = 2-20, and weakly bound systems such as H-. The errors for the two-electron atoms when compared with exact results were reduced from ∼0.2% for Z = 2 to ∼0.002% for large Z. Although usual Hartree-Fock calculations for H- show this to be unstable, our results reduce the percent error of the Hartree-Fock energy from 7.6% to 1.86% and predicts the anion to be stable. For N-electron atoms (N = 3-18, Z = 3-28), using only the zeroth order approximation for the effective charge significantly reduces the error of Hartree-Fock calculations and recovers more than 80% of the correlation energy.

AB - We develop a systematic way to determine an effective nuclear charge Z D R such that the Hartree-Fock results will be significantly closer to the exact energies by utilizing the analytically known large-D limit energies. This method yields an expansion for the effective nuclear charge in powers of (1/D), which we have evaluated to the first order. This first order approximation to the desired effective nuclear charge has been applied to two-electron atoms with Z = 2-20, and weakly bound systems such as H-. The errors for the two-electron atoms when compared with exact results were reduced from ∼0.2% for Z = 2 to ∼0.002% for large Z. Although usual Hartree-Fock calculations for H- show this to be unstable, our results reduce the percent error of the Hartree-Fock energy from 7.6% to 1.86% and predicts the anion to be stable. For N-electron atoms (N = 3-18, Z = 3-28), using only the zeroth order approximation for the effective charge significantly reduces the error of Hartree-Fock calculations and recovers more than 80% of the correlation energy.

UR - http://www.scopus.com/inward/record.url?scp=0000775704&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000775704&partnerID=8YFLogxK

M3 - Article

VL - 102

SP - 7472

EP - 7478

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 19

ER -