The clean slab systems, on the other hand, exhibit strong differences in features between the Vanadium +3 in HS state and the Tantalum +3 in LS state (Figures ). The bond decomposed ICOHP pattern is simpler for Ta +3 which is nonmagnetic featuring some anti-bonding orbitals, with decrease the ICOHP relative to O* with Ta +5 , and the ICOHP value of -4.92 eV. A more complicated pattern is for HS V +3 where we find some anti-bonding states in spin down channel (dashed line, right side) as well as a small bonding state in up-channel (full line, right side), and the ICOHP value of -3.60 eV. The ICOHP analysis correctly predicts that HS has less bonding than LS case. However, HS and LS states of V and Ta feature different relative and adsorption energies, of 0.69 eV vs. -1.97 eV. In contrast, the predicted DICOHP is actually larger in value for V than for Ta. The only way to correctly account for this discrepancy is to attribute additional stabilizing exchange energy to 3 unpaired electrons of V +3 that are non-bonding, based on the arguments routed in crystal-field theory. In fact, the covalent energy based on off-diagonal ICOHP of Dronskowski and Blochl's study was developed to capture the effects of the bonding, nonbonding, and anti-bonding orbitals as projected on bonds, but not the 3d localized (non-bonding) orbitals of the metal (diagonal terms). Please note that these orbitals are orthogonal to bond by definition and thus have negligible overlap. The direct comparisons of adsorption energies to DICOHP in these two systems tells us that ICOHP of LS cases fails to capture the missing stabilizing energy of the localized (non-bonding) orbitals and DICOHP therefore is overestimated relative to DE. This energy difference disappears when we replace HS vs LS V +3 . We approximate the missing energy of the crystal field of V and Cr to be ~ -2eV. The challenge is there fully quantifying the size of these contributions directly from ab-initio results, which is now subject of our future work.