A simple model to calculate total and ionization energies of any atom

An earlier-proposed atomic geometrical model is used to estimate the inter-electronic repulsion in multi-electronic atoms. The model allows calculation of the energies for each shell. The resulting total energies of all atoms in the periodic table differ by less than 1% from Hartree–Fock calculations, except for He, where the difference is 1.8%. However, compared to the experimental total energy values for the first 36 elements, the largest difference is 1.04% for Ne. In this simplified model, the first ionization energies of the alkali metals and alkaline earths proved to be somewhat poor. A modification of the model is proposed to improve these ionization energies, keeping a very good agreement with the experimental average shell energies and with the Hartree–Fock calculations for the total energies.