Theoretical equations of Zeeman energy levels for distorted metal complexes with ${}^5T_{2g}$ ground terms

Abstract

The theoretical equations of Zeeman energy levels, including the zero-field energy levels and the first- and second-order Zeeman coefficients, have been derived for fifteen states of the $^5T_{2g}$ ground term, considering the axial ligand-field splitting and the spin–orbit coupling. The equations are expressed as the functions of three independent parameters, $\Delta$, $\lambda$, and $\kappa$, where $\Delta$ is the axial ligand-field splitting parameter, $\lambda$ is the spin–orbit coupling parameter, and $\kappa$ is the orbital reduction factor. The equations are useful in simulating magnetic properties (magnetic susceptibility and magnetization) of the complexes with $^5T_{2g}$ ground terms, e.g. octahedral high-spin iron(II) complexes.