Superexchange and Spin−Orbit Coupling in Chlorine-Bridged Binuclear Cobalt(II) Complexes

Quantum chemical ab initio calculations are performed for the magnetic exchange coupling in binuclear chlorine-bridged Co(II) complexes of the form L 3 CoCl 3 CoL 3 . In order to simplify the calculations, the terminal ligands are replaced with He-type model ligands L. The calculations are carried out at the restricted open-shell Hartree−Fock (ROHF), complete active space SCF (CASSCF), and valence configuration interaction (VCI) levels, with inclusion of spin−orbit coupling and external magnetic fields. The 12-fold degenerate 4 T 1g ground state of the Co 2+ cation in a perfect octahedral ligand field is split by the trigonal distortion in the complex and by spin−orbit coupling. Both effects have the same order of magnitude, 200−500 cm - 1 . The ground state of either cation is a Kramers doublet, E 1/2, separated by about 300 cm - 1 from the lowest excited states. The coupling of the two E 1/2 ground states through the chlorine bridges is antiferromagnetic; the binuclear complex has a nondegenerate A 2 ‘ ‘ ground state, followed by a nondegenerate first excited A 1 ‘ state 15 cm - 1 above the ground state and a 2-fold degenerate second excited E‘ ‘ state at 57 cm - 1 . The next states are about 300 cm - 1 higher in energy. From these energy levels the magnetic susceptibility χ is calculated by means of a Boltzmann average. χ shows a substantial anisotropy: χ ∥ is rather large because of a first-order Zeeman splitting of the E‘ ‘ state in a magnetic field parallel to the molecular axis, while χ ⊥ is small since it is only caused by second-order Zeeman effects. The calculated temperature dependence of χ agrees fairly well with experimental data; however, a phenomenological Heisenberg−Dirac−van Vleck Hamiltonian cannot be used to describe the measured susceptibility data.