### Abstract

By augmenting Hartree-Fock (HF) results for nonrelativistic ground-state energies of N-electron atoms by analytic expressions for the D -→ ∞ limit derived by Loeser, we obtain a simple renormalization procedure which substantially enhances accuracy. A renormalized nuclear charge, Z _{∞}, is found which renders the dimensionally scaled energy at D → ∞ a good approximation to that for D = 3 with the actual Z. The renormalized charge is readily evaluated by comparing the HF energy (or any other input approximation) with its D → ∞ limit. For atoms with any N or Z, the computations are elementary, requiring little more than solution of a quartic equation. With only HF input in addition to the D →; ∞ limit, the renormalization procedure yields about 2/3 or more of the correlation energy, for neutral atoms with N = Z = 2 → 86. Further improvements in the method seem feasible, but will require better means to incorporate shell-structure in the large-D limit.

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

Pages (from-to) | 5184-5196 |

Number of pages | 13 |

Journal | The Journal of Chemical Physics |

Volume | 99 |

Issue number | 7 |

Publication status | Published - 1 Dec 1993 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of Chemical Physics*,

*99*(7), 5184-5196.

**Atomic energies from renormalization of the large-dimension limit.** / Kais, Sabre; Sung, Stella M.; Herschbach, Dudley R.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 99, no. 7, pp. 5184-5196.

}

TY - JOUR

T1 - Atomic energies from renormalization of the large-dimension limit

AU - Kais, Sabre

AU - Sung, Stella M.

AU - Herschbach, Dudley R.

PY - 1993/12/1

Y1 - 1993/12/1

N2 - By augmenting Hartree-Fock (HF) results for nonrelativistic ground-state energies of N-electron atoms by analytic expressions for the D -→ ∞ limit derived by Loeser, we obtain a simple renormalization procedure which substantially enhances accuracy. A renormalized nuclear charge, Z ∞, is found which renders the dimensionally scaled energy at D → ∞ a good approximation to that for D = 3 with the actual Z. The renormalized charge is readily evaluated by comparing the HF energy (or any other input approximation) with its D → ∞ limit. For atoms with any N or Z, the computations are elementary, requiring little more than solution of a quartic equation. With only HF input in addition to the D →; ∞ limit, the renormalization procedure yields about 2/3 or more of the correlation energy, for neutral atoms with N = Z = 2 → 86. Further improvements in the method seem feasible, but will require better means to incorporate shell-structure in the large-D limit.

AB - By augmenting Hartree-Fock (HF) results for nonrelativistic ground-state energies of N-electron atoms by analytic expressions for the D -→ ∞ limit derived by Loeser, we obtain a simple renormalization procedure which substantially enhances accuracy. A renormalized nuclear charge, Z ∞, is found which renders the dimensionally scaled energy at D → ∞ a good approximation to that for D = 3 with the actual Z. The renormalized charge is readily evaluated by comparing the HF energy (or any other input approximation) with its D → ∞ limit. For atoms with any N or Z, the computations are elementary, requiring little more than solution of a quartic equation. With only HF input in addition to the D →; ∞ limit, the renormalization procedure yields about 2/3 or more of the correlation energy, for neutral atoms with N = Z = 2 → 86. Further improvements in the method seem feasible, but will require better means to incorporate shell-structure in the large-D limit.

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M3 - Article

VL - 99

SP - 5184

EP - 5196

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 7

ER -