Lattice effects on bonding, covalency, and transferred hyperfine interaction in K2NaCrF6 and CrF3

Abstract

The effects of the crystal lattice potential on bonding and covalency parameters of K2NaCrF6 and CrF3 have been investigated in terms of a partially relaxed lattice model described earlier. The theoretical values of different quantities in these two crystals are compared with the Hartree–Fock predictions on the CrF3−6 cluster in vacuo. In K2NaCrF6, the lattice potential reduces the orbital energies of the metal and ligand valence MO’s by 16.8 and 15.7 eV, respectively. In CrF3 these figures are 0.5 eV smaller. The 3d states, which have positive orbital energies in the cluster-in vacuo calculation, become bound states by the action of the lattice potential. The overlap populations suffer different changes in MO’s of different symmetries. The bonding MO’s turn out to be less bonding and the antibonding MO’s still less antibonding, the net effect being an increase in the total overlap population. The covalency parameters λπ and γπ are proportional to the square root of the ligand–metal π overlap and change with the internuclear distance RML as R−3ML and R−2ML , respectively. This calculation suggests that some 15% of the value of these parameters can be attached to the 3d radial expansion. CrF3 appears to be slightly less covalent than K2NaCrF6 according to the values of both γπ and the theoretical nephelauxetic ratio. The observed spin-transfer parameter fπ cannot be reproduced by simple models such as the metal–ligand orthogonalization or the first-order perturbation mixing of the 3dπ and 2pπ states. Our spin-restricted cluster calculation gives fπ values in reasonable agreement with neutron diffraction and resonance spectroscopy data and predicts that fπ varies as R−6ML . The cluster–lattice interaction gives a small contribution to fπ but it seems to be appropriate for explaining the differences in fπ which a given cluster shows in different lattices.