APPROXIMATE EXCHANGE ENERGY AS A FUNCTIONAL OF THE ELECTRON-DENSITY - LIGHT-ATOMS

We derive an expression for the exchange energy integral in terms of the density for the case of light atoms containing s and p electrons. We start from an approximate functional form of the density matrix for an electron cloud in the presence of an attractive nucleus. An important restriction to consider is the Pauli principle. A correction factor is included to account for the multipole expansion in an average way. The results we obtain, both for closed and open shells, are within a few percent of the exact exchange integral. © 1980 American Institute of Physics.