Mechanisms of EPR hyperfine coupling in transition metal complexes

A detailed quantum chemical analysis of the underlying principles of hyperfine coupling in 3d transition metal complexes has been carried out. The explicit evaluation of one- and two-electron integrals for some atomic systems has been used to understand the spin polarization of the core shells. While spin polarization enhances the exchange interaction of the 2s and 2p shells with the singly occupied orbitals, the opposite spin polarization of the 3s and 3p shells arises from the required orthogonality to the 2s and 2p shells, respectively. Gore-shell spin polarization in molecules is found to be proportional to the spin population in the valence 3d orbitals hut to depend little on other details of bonding. In contrast, the spin polarization of the valence shelf depends crucially on the overlap between the singly occupied and certain doubly occupied valence orbitals. Large overlap leads to pronounced spin polarization of these orbitals and, among other things, likely to spin contamination when using UHF wave functions or hybrid density functionals. The role of core- and valence-shell spin polarization for dipolar hyperfine couplings in transition metal complexes is discussed. It is demonstrated that great care should be exercised in deriving spin populations or even orbital compositions from dipolar couplings alone.