In order to study the Kohn-Sham frontier molecular orbital energies in the complete basis limit, a comparative study between localized functions and plane waves, obtained with the local density approximation exchange-correlation functional is made. The analyzed systems are ethylene and butadiene, since they are theoretical and experimentally well characterized. The localized basis sets used are those developed by Dunning. For the plane-waves method, the pseudopotential approximation is employed. The results obtained by the localized basis sets suggest that it is possible to get an estimation of the orbital energies in the limit of the complete basis set, when the basis set size is large. It is shown that the frontier molecular orbital energies and the energy gaps obtained with plane waves are similar to those obtained with a large localized basis set, when the size of the supercell and the plane-wave expansion have been appropriately calibrated. (C) 2004 American Institute of Physics.