Density Functional Calculations of Electronic Structure, Charge Distribution, and Spin Coupling in Manganese−Oxo Dimer Complexes

We have calculated the electronic structures of five different manganese−oxo dimer complexes using density functional methods combined with the broken symmetry and spin projection concepts. The number of carboxylate, oxo, and peroxo bridging ligands was varied, and the terminal ligands were triazacyclononane (TACN). The formal Mn oxidation states varied from Mn^III₂ and Mn^IIIMn^IV to Mn^IV₂. These complexes have been synthesized and their X-ray structures and magnetic properties measured previously. We have calculated the Heisenberg spin coupling parameters J and resonance delocalization parameters B for all of these systems. Despite the very small energy differences involved, there is a good correspondence between calculated and experimental Heisenberg J parameters. We have analyzed potential changes in the calculated effective Heisenberg coupling J_eff for the mixed-valence Mn^IIIMn^IV complexes when partial or complete delocalization due to the B parameter is taken into account. These changes depend also on the energy of the relevant intervalence band. Surprisingly, in the two mixed-valence systems studied, the high spin S = ⁵/₂ state lies below S = ⁷/₂. This is consistent with spin coupling between Mn with site spins S₁ = 1, S₂ = ³/₂, corresponding to intermediate spin Mn(I) and Mn(II) respectively, instead of the coupling expected from the formal oxidation states, S₁ = 2, S₂ = ³/₂ from high spin Mn(III) and Mn(IV). The spin and charge distributions in the broken symmetry ground states are also consistent with intermediate spin S₁ = 1, S₂ = ³/₂. The calculated charge distributions show strong metal−ligand covalency. In fact, as the formal oxidation states of the Mn sites increase, the net Mn charges generally show a slow decrease, consistent with a very strong ligand → metal charge transfer, particularly from μ-oxo or μ-peroxo ligands. TACN is a better donor ligand than carboxylate, even when calculated on a per donor atom basis. The ligand atom charge transfer order is peroxo ≥ oxo ≫ TACN > acetate. The TACN > acetate ordering is expected from the spectrochemical series, but the strong charge transfer and strong metal−ligand covalency of peroxo and oxo ligands with the Mn sites cannot be simply related to their positions in the spectrochemical series. In the Mn^IV₂(μ-O)₂(μ-O₂)(TACN)₂, each peroxo oxygen has a small charge (−0.3), much less than found for each μ-O atom (−0.7). The high-spin S = 3 state lies quite low in energy, 8 kcal/mol from our calculations and about 4 kcal/mol based on the experimental Heisenberg spin coupling parameters. Potential molecular oxygen dissociation pathways involving a spin S = 1 state are discussed. Effective ligand field diagrams are constructed from the calculated energy levels which display the competition between spin polarization splitting and the ligand field t_2g−e_g splitting and allow comparisons of electronic structure among different complexes. The electronic structure and spin coupling of these complexes was also compared to the corresponding “core-only” complexes where both TACN ligands were removed, yielding a far weaker ligand field. There is a strong ferromagnetic shift in the “core-only” complexes compared with the complete TACN complexes, also showing the effects of a weaker ligand field.