The optimized effective potential (OEP) yields eigenfunctions which minimize the expectation value of the Hartree-Fock Hamiltonian (in this case with an added local-density-approximation correlation energy functional). Using an approximate OEP, which yields Ge eigenvalues and total energies to within a few meV of the exact OEP, we find the Ge indirect gap close to the experimental value and the direct gap somewhat too large. The cohesive energy is 1.2 eV less than the experimental value from which we conclude that standard correlation energy density functionals are inadequate for covalently bonded systems.

• Received 1 July 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.3660