The analysis of the C(1s) and O(1s) core-level binding energies (CLBEs) of selected molecules computed by means of total energy Hartree-Fock (ΔSCF-HF) differences shows that in some cases, the calculated values for the C(1s) are larger than the experiment, which is unexpected. The origin of these unexpected errors of the Hartree-Fock ΔSCF BEs is shown to arise from static, nondynamical, electron correlation effects which are larger for the ion than for the neutral system. Once these static correlation effects are included by using complete active space self-consistent field (CASSCF) wave functions that include internal correlation terms, the resulting ΔSCF BEs are, as expected, smaller than measured values.