Analysis of the Puzzling Exchange-Coupling Constants in a Series of Heterobimetallic Complexes

The exchange-coupling constants (J) in a series of bimetallic complexes with an M²⁺(μ-OH)Fe³⁺ core (M = Mn, Fe, Ni, and Cu; series 1), which were reported in a recent study ( Sano et al. Inorg. Chem. 2017 , 56 , 14118 - 14128 ), have been analyzed with the help of density functional theory (DFT) calculations. The experimental J values of series 1 showed the remarkable property that they were virtually independent of metal M. This behavior contrasts with that observed for a related series of complexes with M²⁺Fe³⁺ cores reported by Chaudhuri and co-workers ( Biswas et al. Inorg. Chem. 2010 , 49 , 626 - 641 ) (series 2) in which J increases toward the upper end of the series. Broken symmetry DFT calculations for J, which yielded values in good agreement for the MnFe and NiFe complexes of series 1, gave for the CuFe complex a J value that was persistently much larger than that obtained from the experiment. Attempts to bridge the discrepancy by invoking various basis sets and corrections for hydrogen-bonding effects on J were not successful. The J values for series 1 were subsequently analyzed in the context of an exchange pathway model. From this analysis, it emerged that, in addition to the regular 2e-pathways, which contribute antiferromagnetic terms to J, there are also 3e-pathways that contribute ferromagnetic terms and have the propensity to keep J constant along series 1. It is shown that, while DFT evaluates the 2e-pathway terms reliably, this method seriously underestimates the 3e-pathway contributions, resulting in a too high J value for the CuFe complex of series 1. The pathway analysis of series 2 reveals that the 3e-pathway contributions to J are considerably smaller than those in series 1, resulting in J values that increase toward the upper end of the series, in accordance with the experiment.