Local functional derivative of the total energy and the shell structure in atoms and molecules

The full and local Thomas–Fermi–Dirac energy functional derivatives are evaluated at Hartree–Fock densities for several atoms and molecules. These functions are interpreted as local chemical potentials and related mainly to kinetic energy functional derivatives. They are able to reveal the shell structure of atoms, and the resulting radial extrema are compared with the ones obtained from the radial density, the average electrostatic potential, and the Laplacian of the density. Correlation between the values of the local potentials and chemical reactivity in molecules is suggested.