[en] A semi-classical density functional (SCD) approach have been applied to the smoothly varying part of the Hartree-Fock (HF) binding energy in atoms of the first part of the periodic table. A comparison with the Thomas-Fermi-Schwinger (TFS) model shows that there are tiny differences between E_SCD and E_TFS consisting mainly in opposite drifts of the curves δE_SCD(Z) and δE_TFS(Z) with respect to the baseline. These drifts correspond to a non-oscillating term proportional to Z which is over-estimated in E_SCD but is missing in E_TFS. In the HF energy variation there exists a term proportional to Z³ and Z⁴ in addition to those coming from SCD and TFS models. The minima of both curves δE_SCD(Z) and δE_TFS(Z) are slightly shifted relative to the points of filling the shells and subshells in the periodic table. It is suggested that the resemblance of the HF energy third derivative to the curve of the first-ionization energies may connect the shell effects to electrons near the Fermi surface. 2 figs., 13 refs