Optimized Effective Potential Using The Hylleraas Variational Method
  In electronic structure calculations the optimized effective potential (OEP) is a method that treats exchange interactions exactly using a local potential within density-functional theory (DFT). We present a method using density functional perturbation theory combined with the Hylleraas variational method for finding the OEP by direct minimization which avoids any sum over unoccupied states. The method has been implemented within the plane-wave, pseudopotential formalism. Band structures for zinc blende semiconductors Si, Ge C, GaAs, CdTe and ZnSe, wurtzite semiconductors InN, GaN and ZnO and the rocksalt insulators CaO and NaCl have been calculated using the OEP and compared to calculations using the local density approximation (LDA), a selection of generalized gradient approximations (GGAs) and Hartree-Fock (HF) functionals. The band gaps found with the OEP improve on the calculated results for the LDA, GGAs or HF, with calculated values of 1.16eV for Si, 3.32eV for GaN and 3.48eV for ZnO. The OEP energies of semi-core d-states are also greatly improved compared to LDA. 
Tom W. Hollins, Stewart J. Clark, Keith Refson, Nikitas I. Gidopoulos
cond-mat.mtrl-sci