Ligand-Driven Exchange Coupling in ${\rm Mn}_{4}$ Single-Molecule Magnets

Distorted cubane [Mn⁴⁺Mn₃³⁺(μ₃-L^2-)₃(μ₃-X^-)(Z)^3-(dbm)₃^-] ( L=O; X=various; Z=(OAc)₃; dbmH=dibenzoyl-methane) single-molecule magnets (SMMs) have been studied by first-principles calculations. Our earlier studies showed that the basic mechanism of antiferromagnetic Mn⁴⁺-Mn³⁺ coupling (J_AB) is determined by the π type hybridization among the d_z² orbitals at the Mn³⁺ sites and the t_2g orbitals at the Mn⁴⁺ site through the p orbitals at the μ₃-L^2- ions. This result allows us to predict that ferrimagnetic structure of Mn⁴⁺Mn₃³⁺ molecules will be the most stable with the Mn⁴⁺-(μ₃-L^2-)-Mn³⁺ angle α ≈ 90^° , while synthesized Mn⁴⁺Mn₃³⁺ molecules have α ≈ 95^°. One approach is suggested to design new Mn⁴⁺Mn₃³⁺ SMMs having a much more stable ferrimagnetic state. This approach is controlling the Mn⁴⁺-(μ₃-L^2-)-Mn³⁺ exchange pathways by rational variations in ligands to strengthen the hybridization between Mn ions. In this paper, by combining variations in the L and Z ligands, ten new high-spin [Mn⁴⁺Mn₃³⁺(μ₃-L^2-)₃(μ₃-F^-)₃(Z)^3-(CH(CHO)₂)₃^-] ( L=NCGeH₅, NGeCH₅, NGe₂H₅, NSiGeH₅, or NGeSiH₅; Z=(OAc)₃ or MeC(CH₂NCOMe)₃ ) molecules have been designed. Our calculated res- - ults show that these ten modelling Mn₄ molecules have α ≈ 90^° and J_AB/k_B in the range of (-231.6, -147.4) K, in which the molecule with [L,Z]=[NCGeH₅,MeC(CH₂NCOMe)₃] has the highest J_AB/k_B of - 231.6 K corresponding to α = 89.23^°. This value is over 3 times larger than that of synthesized Mn₄ SMMs. Our calculated results demonstrate combining variations in the L and Z ligands as an effective way to tailor intramolecular exchange coupling of the Mn₄ molecules. The results would give some hints for synthesizing new SMMs.