A new DF-LCAO (density functional with local combination of atomic orbitals) method is used to calculate the electronic properties of 3,4,9,10 perylenetetracarboxylic dianhydride (PTCDA), C6H6, CH4, and CO. The method, called the OO (orbital occupancy) method, is a DF-based theory, which uses the OOs instead of to calculate the exchange and correlation energies. In our calculations, we compare the OO method with the conventional local density approximation approach. Our results show that, using a minimal basis set, we obtain equilibrium bond lengths and binding energies for PTCDA, C6H6, and CH4 which are respectively within 6, and 10–15% of the experimental values. We have also calculated the affinity and ionization levels, as well as the optical gap, for benzene and PTCDA and have found that a variant of Koopmans' theorem works well for these molecules. Using this theorem we calculate the Koopmans relaxation energies of the σ- and π-orbitals for PTCDA and have obtained this molecule's density of states which compares well with experimental evidence.