Conventional ESR spectral analyses and quantum chemical calculations of high-spin cobalt(II) complexes with large ZFS tensors revisited: Exact g- and hyperfine tensors’ relationships between fictitious spin-1/2 and true spin Hamiltonian approaches

High-spin metallocomplexes having sizable zero-field splitting (ZFS) tensors feature in both exotic magnetic materials and many biological systems. The magnetic properties of such compounds have frequently been determined by conventional X-band ESR spectroscopy with the help of fictitious spin-1/2 Hamiltonian approaches. The determined g ^eff -values, however, never agree, in a straightforward manner, with those ( g ^true -values) of the true g -tensors, which are obtained from reliable quantum chemical calculations. In this work, we have revisited the X-band ESR spectra of four important penta-coordinated cobalt(II) complexes (complex 1 and 2 , A. A. Fischer, et al., Dalton Trans. 46 , 13229 (2017); complex 3 and 4 , P. Kumar, et al., J. Am. Chem. Soc. 141 , 10984 (2019), P. Kumar, et al., Inorg. Chem. 59 , 16178 (2020)) in their quartet states, deriving the exact relationships between the fictitious spin-1/2 and true magnetic tensors including hyperfine ones. Double perturbation treatments combined with the Zeeman and hyperfine interaction perturbations have been invoked to derive the relationships, giving physical insights into the complex exact relationships. Accuracy of the simplified relationships relevant to hyperfine tensors has been examined compared with the exact ones. The full sets of the principal values of the g -, hyperfine, and rank-2 ZFS tensors of the complexes have been evaluated from the canonical peaks of the assigned | M _S  = ± 3/2>-dominant transitions as well as the weak signals attributed to the | M _S  = ± 1/2>-dominant transitions. The absolute D -values amount to ~ 10 cm ^–1 ( D  < 0) for complexes 1 – 3 . Quantum chemical calculations for the true magnetic tensors provide their salient electronic structures, which have not been disclosed in the previous works.