We next investigated the quality of calculated J-coupling parameters by employing optimized AP structures. As described earlier, we considered three different approaches for calculating J-couplings -NP (Eq.( )), SP (Eq.( )), and AP (Eq.( )). Table gives Jcouplings calculated by Eqs. ( )-( ) on AP geometries using the B3LYP and LC-ωPBE approximate density functionals. In all cases, calculated J-coupling values had the correct sign, indicating that hybrid functionals (with or without range separation included) predict the correct ground state. In addition, NP J-couplings are always smaller in magnitudes than those obtained by AP. This result is in line with the suggestion that NP counteracts the overestimation of J-couplings by DFT. Comparing NP and AP results with experimental data, it is clear that the non-projection approach yields better agreement with experiment. Importantly, it should be kept in mind that the magnitudes of the J-couplings in these systems are much smaller than the typical error limits associated with DFT calculations. Assuming a normal distribution for the error in DFT energy calculations, the calculated HS and LS energies can be related to the true energies according to,