Orbital dependent exchange-only methods for periodic systems

Various orbital-dependent exchange-only potentials are studied which exhibi t correct long-range asymptotic behavior. We present the application of the se potentials for polymers and by one of these potentials for molecules. Ko hn-Sham type periodic calculations have been carried out for polyethylene i n order to make valuable comparison of these potentials with each other as well as with Hartree-Fock and exchange-only LDA (X alpha) methods. The diff erence between total energies and highest occupied orbital energies obtaine d with Hartree-Fock methods and with localized exchange potentials is large r for this polymer than for atoms or molecules. Various properties of the b and structure are also calculated. The band gap strongly depends on the bas is set. The larger basis set makes the Kohn-Sham eigenvalue gap too low at about 4.4 eV while the minimal basis set results in value close to the expe rimental gap (similar to 8.8 eV). For the total energy and the exchange ene rgy, the various orbital-dependent exchange-only and Hartree-Fock results d iffer only slightly, but for the highest occupied orbital energy the differ ence is mon pronounced. The Kohn-Sham band gap obtained with the optimized effective potential method is corrected with the exchange contribution to t he derivative discontinuity of the exchange-correlation potential. The corr ected band gap obtained with the Slater's exchange potential is 9.7 eV. [S0 163-1829(99)07731-0].