Gradient-corrected correlation with nearly exact Kohn-Sham exchange: Calculations for Si and Ge

We have constructed a pseudopotential that reduces the errors inherent in ordinary pseudopotentials when used together with nonlocal,exchange potentials. Using the very accurate approximation of Krieger, Li, and lafrate to the exact Kohn-Sham exchange potential together with correlation in the local-density approximation (LDA) both with and without the generalized gradient correction of Perdew and Wang, we calculated the electronic and physical properties of Si and Ge. The gradient collections result in a large reduction of the indirect energy gaps, worsening agreement with experiment. They also reduce the total energy of both of the atoms and both of the crystals, resulting in increases of the Si and Ge cohesive energies which improve their agreement with experiment. In addition we have studied the effect of adding gradient corrections when the valence electrons see a Hartree-Fock potential from the core electrons and LDA exchange and correlation among themselves.