  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.
