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

Sabre Kais, Dudley R. Herschbach

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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 languageEnglish
Pages (from-to)4367-4376
Number of pages10
JournalThe Journal of Chemical Physics
Issue number6
Publication statusPublished - 1 Dec 1994
Externally publishedYes


ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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