Exchange interactions, charge delocalization, and spin relaxation in a mixed-valence di-iron complex studied by Mössbauer spectroscopy

Exchange interactions and charge transfer in the Fe²⁺Fe ³⁺ pair of the mixed valence [Fe₂S ₂(dimethylmethanebisbenzimidazolate)₂]^3- trianion have been studied by analysis of Mössbauer spectra in the temperature range of 1.5-180 K and in applied fields of 10 mT, 0.35 T, and 6.2 T. The low-temperature spectra reveal a ground state with total spin S _t=1/2 and hyperfine parameters intermediate between values for a Fe²⁺Fe³⁺ localized mixed-valence pair and a fully delocalized system where the two iron atoms are equivalent. A consistent set of hyperfine parameters has been derived by fitting the spectra with a stochastic relaxation model taking into account spin relaxation in the S_t=1/2 state and electron hopping between the iron ions. An interpretation of the values of the hyperfine parameters has been given by solving a spin Hamiltonian, which includes antiferromagnetic and double exchange in an asymmetric Fe ²⁺Fe³⁺ pair and which allows partial electron delocalization. Using the value a²=0.8 for the delocalization coefficient and an estimate of Δ=105 cm^-1 for the difference between the S_t=1/2 and the first excited S_t=3/2 state we have derived limits for the exchange-coupling constant J, the double-exchange parameter B, and the energy difference E_A-E_B arising from the two possible configurations Fe_A²⁺Fe_B ³⁺ and Fe_A³⁺Fe_B²⁺, i.e., 70 cm^-1≲J≲300 cm^-1, 0< |B| ≲395 cm ^-1, and 0< |E_A-E_B| ≲590 cm ^-1.