Origin of Dissimilar Single-Molecule Magnet Behavior of Three Mn^II₂Mo^III Complexes Based on [Mo^III(CN)₇]^4– Heptacyanomolybdate: Interplay of Mo^III–CN–Mn^II Anisotropic Exchange Interactions

The origin of contrasting single-molecule magnet (SMM) behavior of three Mn^II₂Mo^III complexes based on [Mo^III(CN)₇]^4– heptacyanomolybdate is analyzed; only the apical Mn₂Mo isomer exhibits SMM properties with <i>U</i>_eff = 40.5 cm^–1 and <i>T</i>_B = 3.2 K, while the two equatorial isomers are simple paramagnets [Qian, K.; J. Am. Chem. Soc. 2013, 135, 13302]. A microscopic theory of anisotropic spin coupling between orbitally degenerate [Mo^III(CN)₇]^4– complexes (pentagonal bipyramid) and bound Mn^II ions is developed. It is shown that the [Mo^III(CN)₇]^4– complex has a unique property of uniaxial anisotropic spin coupling in the apical and equatorial Mo^III–CN–Mn^II pairs, <i>H̑</i>_eff = −<i>J</i>_<i>xy</i>(<i>S</i>_Mo^<i>x</i><i>S</i>_Mn^<i>x</i> + <i>S</i>_Mo^<i>y</i><i>S</i>_Mn^<i>y</i>) – <i>J</i>_<i>z</i><i>S</i>_Mo^<i>z</i><i>S</i>_Mn^<i>z</i>, regardless of their actual low symmetry. The difference in the SMM behavior originates from a different ratio between the anisotropic exchange parameters <i>J</i>_<i>z</i> and <i>J</i>_<i>xy</i> for the apical and equatorial Mo–CN–Mn groups. In the apical Mn₂Mo isomer, an Ising-type anisotropic spin coupling (<i>J</i>_<i>z</i> = −34, <i>J</i>_<i>xy</i> = −11 cm^–1) produces a double-well potential of spin states resulting in SMM behavior. Exchange anisotropy of an <i>xy</i>-type (|<i>J</i>_<i>z</i>| < |<i>J</i>_<i>xy</i>|) in the equatorial Mn₂Mo isomers results in a single-well potential with no SMM properties. The prospects of anisotropic uniaxial spin coupling in engineering of high <i>U</i>_eff and <i>T</i>_B values are discussed