### Abstract

Analytic expressions for the large-dimension limit, when renormalized by introducing a suitable effective nuclear charge ζ yield accurate D=3 nonrelativistic energies for ground states of many-electron atoms. Using Hartree-Fock data to estimate ζ, which typically differs from the actual charge Z by ∼1% or less, we find this dimensional renormalization method (denoted DR-0) gives results substantially better than the HF input. Comparison of the 1/Z expansion for the large-D limit with that for D=3 atoms provides expressions for the leading error terms in the renormalized total energy and correlation energy. When configuration mixing occurs in the Z→∞ limit (as for Be and many other atoms), we find the renormalization procedure is markedly improved by including the zeroth-order mixing (denoted DR-1); this contributes a term linear in Z. Including the Z-independent term (DR-2) also improves the accuracy when zeroth-order mixing is absent (e.g., ground-state atoms with N=2, 3, and 7-11) but not otherwise. Correlation energies for atoms and cations with N=2-18 electrons and Z=2-28 are obtained with a mean error of 26% using just the large-D limit or HF input (DR-0); the mean error improves to only 5% when the leading 1/Z term is included (either DR-1 or DR-2). Results much better than the HF approximation are likewise obtained for the ionization potentials and electron affinities of neutral atoms.

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

Pages (from-to) | 4367-4376 |

Number of pages | 10 |

Journal | The Journal of Chemical Physics |

Volume | 100 |

Issue number | 6 |

Publication status | Published - 1 Dec 1994 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of Chemical Physics*,

*100*(6), 4367-4376.

**The 1/Z expansion and renormalization of the large-dimension limit for many-electron atoms.** / Kais, Sabre; Herschbach, Dudley R.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 100, no. 6, pp. 4367-4376.

}

TY - JOUR

T1 - The 1/Z expansion and renormalization of the large-dimension limit for many-electron atoms

AU - Kais, Sabre

AU - Herschbach, Dudley R.

PY - 1994/12/1

Y1 - 1994/12/1

N2 - Analytic expressions for the large-dimension limit, when renormalized by introducing a suitable effective nuclear charge ζ yield accurate D=3 nonrelativistic energies for ground states of many-electron atoms. Using Hartree-Fock data to estimate ζ, which typically differs from the actual charge Z by ∼1% or less, we find this dimensional renormalization method (denoted DR-0) gives results substantially better than the HF input. Comparison of the 1/Z expansion for the large-D limit with that for D=3 atoms provides expressions for the leading error terms in the renormalized total energy and correlation energy. When configuration mixing occurs in the Z→∞ limit (as for Be and many other atoms), we find the renormalization procedure is markedly improved by including the zeroth-order mixing (denoted DR-1); this contributes a term linear in Z. Including the Z-independent term (DR-2) also improves the accuracy when zeroth-order mixing is absent (e.g., ground-state atoms with N=2, 3, and 7-11) but not otherwise. Correlation energies for atoms and cations with N=2-18 electrons and Z=2-28 are obtained with a mean error of 26% using just the large-D limit or HF input (DR-0); the mean error improves to only 5% when the leading 1/Z term is included (either DR-1 or DR-2). Results much better than the HF approximation are likewise obtained for the ionization potentials and electron affinities of neutral atoms.

AB - Analytic expressions for the large-dimension limit, when renormalized by introducing a suitable effective nuclear charge ζ yield accurate D=3 nonrelativistic energies for ground states of many-electron atoms. Using Hartree-Fock data to estimate ζ, which typically differs from the actual charge Z by ∼1% or less, we find this dimensional renormalization method (denoted DR-0) gives results substantially better than the HF input. Comparison of the 1/Z expansion for the large-D limit with that for D=3 atoms provides expressions for the leading error terms in the renormalized total energy and correlation energy. When configuration mixing occurs in the Z→∞ limit (as for Be and many other atoms), we find the renormalization procedure is markedly improved by including the zeroth-order mixing (denoted DR-1); this contributes a term linear in Z. Including the Z-independent term (DR-2) also improves the accuracy when zeroth-order mixing is absent (e.g., ground-state atoms with N=2, 3, and 7-11) but not otherwise. Correlation energies for atoms and cations with N=2-18 electrons and Z=2-28 are obtained with a mean error of 26% using just the large-D limit or HF input (DR-0); the mean error improves to only 5% when the leading 1/Z term is included (either DR-1 or DR-2). Results much better than the HF approximation are likewise obtained for the ionization potentials and electron affinities of neutral atoms.

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M3 - Article

VL - 100

SP - 4367

EP - 4376

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 6

ER -