TY - JOUR

T1 - Asymptotics-based CI models for atoms

T2 - Properties, exact solution of a minimal model for Li to Ne, and application to atomic spectra

AU - Friesecke, Gero

AU - Goddard, Benjamin D.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Atomic spectra

KW - Configuration interaction

KW - Schrödinger equation

KW - Second period

UR - http://www.scopus.com/inward/record.url?scp=79953693319&partnerID=8YFLogxK

U2 - 10.1137/080736648

DO - 10.1137/080736648

M3 - Article

AN - SCOPUS:79953693319

SN - 1540-3459

VL - 7

SP - 1876

EP - 1897

JO - Multiscale Modeling and Simulation

JF - Multiscale Modeling and Simulation

IS - 4

ER -