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

G. Friesecke, B.D. Goddard

Research output: Contribution to journalArticlepeer-review

Abstract

Configuration-interaction (CI) models are approximations to the electronic Schrödinger 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 Schrödinger equation in the limit of fixed electron number and large nuclear charge [SIAM J. Math. Anal., 41 (2009), pp. 631-664], we introduce a class of CI models for atoms which reproduce, at fixed finite model dimension, the correct Schrödinger eigenvalues and eigenstates in this limit. We solve exactly the ensuing minimal model for the second period atoms, Li to Ne, except for optimization of eigenvalues with respect to orbital dilation parameters, which is carried out numerically. 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.
Original languageEnglish
Pages (from-to)1876-1897
Number of pages22
Journal Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
Volume7
Issue number4
DOIs
Publication statusPublished - 1 Jan 2009

Fingerprint

Dive into the research topics of 'Asymptotics-based CI models for atoms: Properties, exact solution of a minimal model for Li to Ne, and application to atomic spectra'. Together they form a unique fingerprint.

Cite this