Asymptotics-based CI models for atoms: properties, exact solution of a minimal model for Li to Ne, and application to atomic spectra

TL;DR

This paper introduces asymptotics-based CI models for atoms that accurately approximate eigenvalues and eigenstates in the large nuclear charge limit, solved exactly for Li to Ne, and validated against experimental data.

Contribution

The paper presents a new class of CI models derived from asymptotic analysis that reproduce atomic eigenvalues and eigenstates in the large nuclear charge limit, with exact solutions for Li to Ne.

Findings

Energy levels closely match experimental data.

Models provide insight into atomic spectral and physical properties.

Comparable accuracy to larger numerical simulations.

Abstract

Configuration-Interaction (CI) models are approximations to the electronic Schr\"odinger equation which are widely used for numerical electronic structure calculations in quantum chemistry. Based on our recent closed-form asymptotic results for the full atomic Schr\"odinger equation in the limit of fixed electron number and large nuclear charge, we introduce a class of CI models for atoms which reproduce, at fixed finite model dimension, the correct Schr\"odinger eigenvalues and eigenstates in this limit. We solve exactly the ensuing minimal model for the second period atoms, Li to Ne. The energy levels and eigenstates are in remarkably good agreement with experimental data (comparable to that of much larger scale numerical simulations in the literature), and facilitate a mathematical understanding of various spectral, chemical and physical properties of small atoms.