  Various orbital-dependent exchange-only potentials are studied which exhibit
correct long-range asymptotic behaviour. We present the first application of
these potentials for polymers and by one of these potentials for molecules.
Kohn-Sham type 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 methods. The Kohn-Sham band gap obtained
with the optimized effective potetial 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 close to the experiment.
