Magnetic exchange and valence delocalization in a mixed valence [Fe2+Fe3+Te2]+ complex: insights from theory and interpretations of magnetic and spectroscopic data

Abstract

A mixed valence binuclear Fe^2.5+–Fe^2.5+ (Robin–Day Class III) transition metal complex, [Fe^2.5+μTe₂Fe^2.5+]¹⁻, composed of two FeN₂Te₂ pseudo-tetrahedral units with μ-bridging Te²⁻ ligands was reported to exist in an unprecedented S = 3/2 ground state (Nature Chemistry, https://doi.org/10.1038/s41557-021-00853-5). For this and the homologous complexes containing Se²⁻ and S²⁻, the Anderson-Hasegawa double exchange spin-Hamiltonian was broadly used to interpret the corresponding structural, spectroscopic and magnetic data. First principles multireference ab initio calculations are used here to simulate magnetic and spectroscopic EPR data; analysis of the results affords a rationale for the stabilization of the S = 3/2 ground state of the Fe₂ pair. Complete Active Space Self-Consistent Field (CASSCF) calculations and dynamical correlation accounted for by means of N-Electron Valence Perturbation Theory to Second Order (NEVPT2) reproduce well the g-factors determined from simulations of X-band EPR spectra. A crucial technical tool to achieve these results is: (i) use of a localized orbital formulation of the many-particle problem at the scalar-relativistic CASSCF step; (ii) choice of state averaging over states of a given spin (at the CASCI/NEVPT2 step); and (iii) accounting for spin–orbit coupling within the non-relativistic Born–Oppenheimer (BO) many-particle basis using Quasi-Degenerate Perturbation Theory (QDPT). The inclusion of the S = 5/2 spin manifold reproduced the observed increase in the magnetic susceptibility (χT) in the high temperature range (T > 100 K), which is explained by thermal population of the S = 5/2 excited state at energy 160 cm⁻¹ above the S = 3/2 ground state. Theoretical values of χT from experimentally reported data points in the temperature range from 3 to 30 K were further computed and analyzed using a model which takes spin–phonon coupling into account. The model considerations and the computational protocols of this study are generally applicable to any Class I/II mixed valence dimer. The work can potentially stimulate further experimental and theoretical work on bi- and oligonuclear transition metal complexes of importance to bioinorganic chemistry and life sciences.