Inelastic Neutron Scattering on an Mn10 Supertetrahedron: Assessment of Exchange Coupling Constants, Ferromagnetic Spin Waves and an Analogy to the Hückel Method

Platonic and Archimedean solids in discrete metal-containing clusters

Metal-containing clusters have attracted increasing attention over the past 2-3 decades. This intense interest can be attributed to the fact that these discrete metal aggregates, whose atomically precise structures are resolved by single-crystal X-ray diffraction (SCXRD), often possess intriguing geometrical features (high symmetry, aesthetically pleasing shapes and architectures) and fascinating physical properties, providing invaluable opportunities for the intersection of different disciplines including chemistry, physics, mathematical geometry and materials science. In this review, we attempt to reinterpret and connect these fascinating clusters from the perspective of Platonic and Archimedean solid characteristics, focusing on highly symmetrical and complex metal-containing (metal = Al, Ti, V, Mo, W, U, Mn, Fe, Co, Ni, Pd, Pt, Cu, Ag, Au, lanthanoids (Ln), and actinoids) high-nuclearity clusters, including metal-oxo/hydroxide/chalcogenide clusters and metal clusters (with metal-metal binding) protected by surface organic ligands, such as thiolate, phosphine, alkynyl, carbonyl and nitrogen/oxygen donor ligands. Furthermore, we present the symmetrical beauty of metal cluster structures and the geometrical similarity of different types of clusters and provide a large number of examples to show how to accurately describe the metal clusters from the perspective of highly symmetrical polyhedra. Finally, knowledge and further insights into the design and synthesis of unknown metal clusters are put forward by summarizing these "star" molecules.

Multimodeling Approach to Ferromagnetic Spin-Wave Excitations in the High-Spin Cluster Mn18Sr Observed by Inelastic Neutron Scattering

The magnetism of the mixed-valence high-spin cluster [Mn₁₈SrO₈(N₃)₇Cl(MedhmpH)₁₂(MeCN)₆]Cl₂ (1) exhibiting intramolecular ferromagnetic interactions was studied using inelastic neutron scattering (INS), and reliable values for the exchange coupling constants were determined based on the quality of simultaneous fits to the INS and magnetic data. The challenge of the huge size of the Hilbert space (3 375 000) and many exchange coupling constants (7 assuming a C₃ symmetry) generally encountered in large spin clusters was resolved as follows: (a) The results of the restricted Hilbert space ferromagnetic cluster spin wave theory were compared to the experimental spectroscopic data. The observed INS transitions were thus assigned to spin wave excitations in a bounded ferromagnetic spin cluster and moreover could be visualized in a straightforward way based on this theory. (b) Simultaneously, Quantum Monte Carlo (QMC) calculations of the temperature-dependent magnetic susceptibility with the same parameter set were compared to the experimental data. Application of state-of-the-art QMC algorithms, as available in the open source ALPS package, in ferromagnetic clusters avoids the full Hamiltonian diagonalization without sacrificing calculation accuracy of the magnetic susceptibility down to the lowest temperatures, which was crucial for the successful analysis. The combined fits revealed two exchange-coupling models with equally good overall agreement to the data. Our preferred model was inspired by magnetostructural correlations and is consistent with them. The model involves three different exchange interactions, one describing the interaction between the core Mn^III spins J_a = 14.3(1.0) K and two interactions linking the core and the peripheral Mn^II spins: J_b = 8.3(4) K and J₆ = 3.6(4) K. The use of open-source QMC software and our systematic approach to fitting multiple sets of data obtained by different experimental techniques are described in detail and are generally applicable for understanding large ferromagnetically coupled clusters.