Designing Quantum Spaces of Higher Dimensionality from a Tetranuclear Erbium-Based Single-Molecule Magnet.

The spin relaxation of an Er 3+ tetranuclear single-molecule magnet, [Er(hdcCOT)I] 4 , (hdcCOT = hexahydrodicyclopentacyclooctatetraenide dianion), is modeled as a near-tetrahedral arrangement of Ising-type spins. Combining evidence from single-crystal X-ray diffraction, magnetometry, and computational techniques, the slow spin relaxation is interpreted as a consequence of symmetry restrictions imposed on quantum tunneling within the cluster core. The union of spin and spatial symmetries describe a ground state spin-spin coupled manifold wherein 16 eigenvectors generate the 3D quantum spin-space described by the vertices of a rhombic dodecahedron. Analysis of the experimental findings in this context reveals a correlation between the magnetic transitions and edges connecting cubic and octahedral subsets of the eigenspace convex hull. Additionally, the model is shown to map to a theoretically proposed quantum Cayley network, indicating an underexplored synergy between mathematical descriptions of molecular spin interactions and quantum computing configuration spaces.