Variational determination of electron density

A method is proposed for calculation of electron charge distributions using a variational principle for energy treated as a functional of the electron density. The method consists of introducing into the functional an effective field, the potential of which is determined by solving a problem slightly different than the given one. The following example is studied: the effective potential is constructed for the electron density of the carbon atom; then the potential is used in calculation of the charge distribution of the positive ion by minimization of the energy. The results obtained in this way are close to the results obtained by the Kohn-Sham method