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Asymptotics-based CI models for atoms: properties, exact solution of a minimal model for Li to Ne, and application to atomic spectra
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Friesecke, Gero and Goddard, Benjamin D. (2009) Asymptotics-based CI models for atoms: properties, exact solution of a minimal model for Li to Ne, and application to atomic spectra. Multiscale Modeling & Simulation, Vol.7 (No.4). pp. 1876-1897. doi:10.1137/080736648 ISSN 1540-3459.
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Official URL: http://dx.doi.org/10.1137/080736648
Abstract
Configuration-interaction (CI) models are approximations to the electronic Schrodinger 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 Schrodinger 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 Schrodinger 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 simulationsin the literature) and facilitate a mathematical understanding of various spectral, chemical, and physical properties of small atoms.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Multiscale Modeling & Simulation | ||||
| Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
| ISSN: | 1540-3459 | ||||
| Official Date: | 2009 | ||||
| Dates: |
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| Volume: | Vol.7 | ||||
| Number: | No.4 | ||||
| Number of Pages: | 22 | ||||
| Page Range: | pp. 1876-1897 | ||||
| DOI: | 10.1137/080736648 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) |
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