Energy Levels in Pentacoordinate d⁵ to d⁹ Complexes

Energy levels of pentacoordinate d5 to d9 complexes were evaluated according to the generalized crystal field theory at three levels of sophistication for two limiting cases of pentacoordination: trigonal bipyramid and tetragonal pyramid. The electronic crystal field terms involve the interelectron repulsion and the crystal field potential; crystal field multiplets account for the spin–orbit interaction; and magnetic energy levels involve the orbital– and spin–Zeeman interactions with the magnetic field. The crystal field terms are labelled according to the irreducible representations of point groups D3h and C4v using Mulliken notation. The crystal field multiplets are labelled with the Bethe notations for the respective double groups D’3 and C’4. The magnetic functions, such as the temperature dependence of the effective magnetic moment and the field dependence of the magnetization, are evaluated by employing the apparatus of statistical thermodynamics as derivatives of the field-dependent partition function. When appropriate, the formalism of the spin Hamiltonian is applied, giving rise to a set of magnetic parameters, such as the zero-field splitting D and E, magnetogyric ratio tensor, and temperature-independent paramagnetism. The data calculated using GCFT were compared with the ab initio calculations at the CASSCF+NEVPT2 level and those involving the spin–orbit interaction