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. In the exchange-only case, this is commonly called exact exchange. 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 1.16 eV for Si, 3.32 eV for GaN, and 3.48 eV for ZnO. The OEP energies of semicore $d$ states are also greatly improved compared to LDA.

• Received 29 March 2012

DOI:https://doi.org/10.1103/PhysRevB.85.235126