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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. (English) Zbl 1180.81154

Summary: 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 [the authors, SIAM J. Math. Anal., 41, 631–664 (2009)], 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.

MSC:

81V45 Atomic physics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65Y20 Complexity and performance of numerical algorithms
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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