  An exchange-correlation energy functional beyond the local density
approximation, based on the exchange-correlation kernel of the homogeneous
electron gas and originally introduced by Kohn and Sham, is considered for
electronic structure calculations of semiconductors and atoms. Calculations are
carried out for diamond, silicon, silicon carbide and gallium arsenide. The
lattice constants and gaps show a small improvement with respect to the LDA
results.
  However, the corresponding corrections to the total energy of the isolated
atoms are not large enough to yield a substantial improvement for the cohesive
energy of solids, which remains hence overestimated as in the LDA.
