  We present a simplified computational scheme in order to calculate the
effects of electron correlations on the energy bands of diamond and silicon. By
adopting a quasiparticle picture we compute first the relaxation and
polarization effects around an electron set into a conduction band Wannier
orbital. This is done by allowing the valence orbitals to relax within a
self-consistent field (SCF) calculation. The diagonal matrix element of the
Hamiltonian leads to a shift of the center of gravity of the conduction band
while the off-diagonal matrix elements result in a small reduction of the
conduction-electron band width. This calculation is supplemented by the
computation of the loss of ground state correlations due to the blocked Wannier
orbital into which the added electron has been placed. The same procedure
applies to the removal of an electron, i.e., to the valence bands. But the
latter have been calculated previously in some detail and previous results are
used in order to estimate the energy gap in the two materials. The numerical
data reported here shows that the methods works, in principle, but that also
some extension of the scheme is necessary to obtain fully satisfactory results.
