The calculations for GaAs are performed with a third kind of optical potential. The self-energy is assumed as a function of the local charge density in a way similar to the procedure applied by the LDA for the exchange and correlation in the ground state. The imaginary part of the self-energy is calculated as a function of the local charge density. The function is fitted to well known results for the homogenous electron gas. Therefore the optical potential depends only on one position and the energy.
Several choices are possible for such a function.
For a valence density functional Fig. 3 shows the charge density and the resulting optical potential for two energies. Shown is a cut in direct space with the vacuum at the top of the images. Dark shades belong to high charge density and high damping. The optical potential from the local density functional shows more structure than the charge itself.