Net spin and polarization components of the spin density for the single determinant in the basis of paired orbitals

A decomposition of the spin density into the net spin density and polarization density for the unrestricted Kohn–Sham (KS) determinant in the basis of Löwdin–Amos–Hall paired orbitals (PO) is derived. In PO basis set, the net spin part of spin density is only determined by the manifold of occupied α‐spin orbitals which do not overlap with occupied β‐spin orbitals. In its turn, the polarization part is associated with the pairs of overlapping α and β orbitals. The decreased overlap in these pairs corresponds to the increased degree of spin polarization. As an example of the developed spin density decomposition, the complex of FeO with nitrobenzene (taken in the state with spin projection of Sz = 2) is considered for the B3LYP solution revealing substantial spin contamination for the KS determinant. The spin density decomposition predicts for this complex appreciable polarization density over the whole complex while the net spin density remains counter intuitive almost intact at FeO center. This result changes presumed mechanism of metal‐to‐ligand transfer of unpaired electrons from paramagnetic center to diamagnetic ligand having a high electron affinity. © 2012 Wiley Periodicals, Inc. The spin density given by the unrestricted determinant is decomposed into the contribution of the “truly” unpaired electrons and the contribution of the spin polarization by means of the paired orbitals. For the test complex of FeO with nitrobenzene at the B3LYP level, the developed analysis reveals unexpected transfer of the spin‐down electron from the closed shell of FeO to the nitro group while the unpaired d‐electrons counter intuitively remain almost intact.