### Abstract

By combining Hartree–Fock results for nonrelativistic ground‐state energies of N‐electron atoms with analytic expressions for the large‐dimension limit, we have obtained a simple renormalization procedure. For neutral atoms, this yields energies typically threefold more accurate than the Hartree–Fock approximation. Here, we examine the dependence on Z and N of the renormalized energies E(N, Z) for atoms and cations over the range Z, N = 2 → 290. We find that this gives for large Z = N an expansion of the same form as the Thomas–Fermi statistical model, E → Z^{7/2}(C_{0} + C_{1}Z^{−1/3} + C_{2}Z^{−2/3} + C_{3}Z^{−3/3} + ⃛), with similar values of the coefficients for the three leading terms. Use of the renormalized large‐D limit enables us to derive three further terms. This provides an analogous expansion for the correlation energy of the form δE δZ^{4/3}(δC_{3} + δC_{5}Z^{−2/3} + δC_{6}Z^{−3/3} + ⃛); comparison with accurate values of δE available for the range Z ⩽ 36 indicates the mean error is only about 10%. Oscillatory terms in E and δE are also evaluated. © 1994 John Wiley & Sons, Inc.

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

Pages (from-to) | 657-674 |

Number of pages | 18 |

Journal | International Journal of Quantum Chemistry |

Volume | 49 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1994 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics
- Physical and Theoretical Chemistry

### Cite this

*International Journal of Quantum Chemistry*,

*49*(5), 657-674. https://doi.org/10.1002/qua.560490511

**Large‐Z and ‐N dependence of atomic energies from renormalization of the large‐dimension limit.** / Kais, Sabre; Sung, Stella M.; Herschbach, Dudley R.

Research output: Contribution to journal › Article

*International Journal of Quantum Chemistry*, vol. 49, no. 5, pp. 657-674. https://doi.org/10.1002/qua.560490511

}

TY - JOUR

T1 - Large‐Z and ‐N dependence of atomic energies from renormalization of the large‐dimension limit

AU - Kais, Sabre

AU - Sung, Stella M.

AU - Herschbach, Dudley R.

PY - 1994

Y1 - 1994

N2 - By combining Hartree–Fock results for nonrelativistic ground‐state energies of N‐electron atoms with analytic expressions for the large‐dimension limit, we have obtained a simple renormalization procedure. For neutral atoms, this yields energies typically threefold more accurate than the Hartree–Fock approximation. Here, we examine the dependence on Z and N of the renormalized energies E(N, Z) for atoms and cations over the range Z, N = 2 → 290. We find that this gives for large Z = N an expansion of the same form as the Thomas–Fermi statistical model, E → Z7/2(C0 + C1Z−1/3 + C2Z−2/3 + C3Z−3/3 + ⃛), with similar values of the coefficients for the three leading terms. Use of the renormalized large‐D limit enables us to derive three further terms. This provides an analogous expansion for the correlation energy of the form δE δZ4/3(δC3 + δC5Z−2/3 + δC6Z−3/3 + ⃛); comparison with accurate values of δE available for the range Z ⩽ 36 indicates the mean error is only about 10%. Oscillatory terms in E and δE are also evaluated. © 1994 John Wiley & Sons, Inc.

AB - By combining Hartree–Fock results for nonrelativistic ground‐state energies of N‐electron atoms with analytic expressions for the large‐dimension limit, we have obtained a simple renormalization procedure. For neutral atoms, this yields energies typically threefold more accurate than the Hartree–Fock approximation. Here, we examine the dependence on Z and N of the renormalized energies E(N, Z) for atoms and cations over the range Z, N = 2 → 290. We find that this gives for large Z = N an expansion of the same form as the Thomas–Fermi statistical model, E → Z7/2(C0 + C1Z−1/3 + C2Z−2/3 + C3Z−3/3 + ⃛), with similar values of the coefficients for the three leading terms. Use of the renormalized large‐D limit enables us to derive three further terms. This provides an analogous expansion for the correlation energy of the form δE δZ4/3(δC3 + δC5Z−2/3 + δC6Z−3/3 + ⃛); comparison with accurate values of δE available for the range Z ⩽ 36 indicates the mean error is only about 10%. Oscillatory terms in E and δE are also evaluated. © 1994 John Wiley & Sons, Inc.

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U2 - 10.1002/qua.560490511

DO - 10.1002/qua.560490511

M3 - Article

VL - 49

SP - 657

EP - 674

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

IS - 5

ER -