Self-consistent Hartree-Fock calculation of exchange effects in a weakly inhomogeneous electron gas
An exact calculation is given for the function Bx(n) which enters the Hohenberg-Kohn-Sham expansion, in powers of ▿n(r), of the echange energy of an inhomogeneous eletron gas. The calculation is made for arbitrary inter-particle interaction. It is shown that the gradient expansion does not exist, in the case of Coulomb interaction, unless correlations are taken into account.
