Various orbital-dependent exchange-only potentials are studied which exhibit correct long-range asymptotic behavior. We present the application of these potentials for polymers and by one of these potentials for molecules. Kohn-Sham type periodic calculations have been carried out for polyethylene in order to make valuable comparison of these potentials with each other as well as with Hartree-Fock and exchange-only LDA $\left(X\alpha \right)$ methods. The difference between total energies and highest occupied orbital energies obtained with Hartree-Fock methods and with localized exchange potentials is larger for this polymer than for atoms or molecules. Various properties of the band structure are also calculated. The band gap strongly depends on the basis 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 experimental gap $(\sim 8.8$ eV). For the total energy and the exchange energy, the various orbital-dependent exchange-only and Hartree-Fock results differ only slightly, but for the highest occupied orbital energy the difference is more pronounced. The Kohn-Sham band gap obtained with the optimized effective potential method is corrected with the exchange contribution to the derivative discontinuity of the exchange-correlation potential. The corrected band gap obtained with the Slater’s exchange potential is $9.7$ eV.

• Received 12 October 1998

DOI:https://doi.org/10.1103/PhysRevB.60.5429