Density functional theory of interacting closed shell systems. II. The determination of charge densities and the Hellman–Feynman theorem

The density functional formalism and the additive density approximation are used to obtain the nonadditive contribution to the electron density of a set of closed shell atoms in the absence of external fields. It is shown that due to the additive density approximation, the Hellman–Feynman theorem is violated when the force on the nucleus is examined. The reason for this violation is discussed.