The bias is due to the difference in the Hubbard term between the bare MOF and the bound case and its origin is here explained. We recall that, for a given value of U , the Hubbard term is larger when the occupation numbers n are more fractional (closer to 1/2) (see second term of equation 1). As expected from a molecular orbital picture (see Figure ), when the d z 2 is empty (Fe and Mn in LS) the occupation number associated with the atomic projector d z 2 increases upon binding. This is due to the fact that in the bare MOF without any bound molecule this is an atomic-like orbital which is empty and therefore its occupa-tion number is close to zero. In the bound case, due to the orbital mixing between the metal and the gas molecule, the occupation number increases due to the contribution from the low lying ligand-like states to the projection onto the d z 2 . In Table we also report the changes in the eigenvalues of the occupation matrix for the bare MOF and for the bound cases. Because the hybridization is stronger for more strongly bound molecules, the occupation number associated with d z 2 increases from almost 0.050 in the case of CO2 where the molecule's orbitals are expected to mix negligibly with the metal, to 0.300 in the case of strongly bound CO. This leads to values of the Hubbard energy term that increase as a function of the orbital mixing between the metal and the molecules. As a consequence, the binding energies computed using the full energy expression of PBE+D3+U are always lower (weaker binding) than the density-corrected PBE+D3[U] case and the difference between the values computed using the two approaches also increases from weak to strongly bound molecules. As an example, the CO binding energy is predicted to be 0.754 eV using PBE+D3+U while the density corrected scheme gives and 2.344 eV. The difference in the Hubbard energy between the bare and the bound cases, ∆(EU), is also reported in Table . Because the occupation numbers of the octahedrally coordinated Fe barely change in the different cases, this difference corresponds to the twice the difference (bias) in binding energy between the two sets of calculations (two bound molecules per unit cell). The full list of values of binding energies computed using PBE+D3+U and PBE+D3[U] is reported in the SI. For Ni, the opposite behavior is found with stronger binding energies than the density-corrected scheme. The bias is substantially lower for Fe and Mn in HS, and for Ni in LS (see SI), as expected from a half occupied d z 2 orbital and substantially weaker binding between the metal and the molecules.