Correlated electronic structure models suggested by the large-dimension limit

Abstract

We describe three simple models for electronic structure in many-electron atoms and ions. Each model is parametrized by the spatial dimensionality D, which is ordinarily set to 3. All procedures are motivated by the solution for D → ∞, a classical limit which can be solved exactly either with or without electron correlation. Each model modifies the D → ∞ limit treatment to reflect important finite-D effects, but retains the classical character of the limit; the modifications, in order of increasing realism, are designated post-scaling, pre-scaling, and pre-structuring. The three models yield pointlike electronic structures somewhat reminiscent of pre-quantal atomic models. However, all electronic positions have components outside the D-dimensional physical subspace, a feature which significantly enhances the ability of a localized structure to represent the true solution and to model it quantitatively. Specific calculations reported are total and correlation energies for atoms with Z ≤ 92 (computed by post-scaling and pre-scaling), correlation corrections to ionization potentials and electron affinities for Z ≤ 54 (post-scaling), and the asymptotic behavior of correlation energies for Z → ∞ (post-scaling).