Revisiting the quasi-aromaticity in polynuclear metal chalcogenide clusters and their derivative "cluster-assembly" crystalline structures

The concept of aromaticity is primarily invented to account for the high stability of conjugated organic compounds that possess a specific structural and chemical stability with (4n + 2) π electrons. In 1988, quasi-aromaticity was theoretically proposed for the Mo₃S₄⁴⁺ core in the Mo₃(μ₃-S)(μ-S)₃(χ-dtp)₃(μ-dtp) L compound (χ: chelating ligand; dtp: (EtO)₂PS₂^-) illustrated by canonical molecular orbitals. However, the origin of the quasi-aromaticity and chemical bonding remains ambiguous, lacking a thorough analysis in terms of stability and quantitative measurement of the aromatic character. Thus, in this work, we systematically reported the electronic structure and aromaticity of a series of polynuclear metal chalcogenide clusters [M₃X₄(H₂O)₉]⁴⁺ (M = Cr, Mo, W, and Sg; X = O, S, Se, and Te) to explore an efficient tool of NICS index values at specific points to measure the quasi-aromaticity and to figure out the (d-p-d) π three-center bonding as the predominant origin from the arrangement of three Mo atoms and three bridged X atoms. Interestingly, derived from the Mo₃⋯S₃ quasi-plane, the extended sandwich cluster model of a S₃⋯Mo₃⋯S₃ (Mo₃S₆) structure can be seen as the seed unit of the popular MoS₂ nanomaterials, with the resemblance between both molecular and periodic systems regarding geometries, electronic structures, and chemical bonding. Additionally, the highly symmetric Mo₃S₄ core in [Mo₃X₄(H₂O)₉]⁴⁺ can be arranged in a staggered and stacked manner to create the Mo₆S₈^2- building block, corresponding to the crystalline structures in BaMo₆S₈ Chevrel phases, albeit with slight deformations. But the neutral Mo₆S₈ cluster can be seen as the seed structure for the Mo₃S₄ periodic materials for the high resemblance in terms of geometry, electronic structures and chemical bonding. Drawing upon the observed similarities between cluster models and materials, we propose a new concept termed "cluster-assembly" materials. This concept involves the expansion from a high-symmetry and/or aromatic stable cluster seed unit to form the corresponding derivative materials, presenting an alternative paradigm for investigating crystals and enriching our comprehension of the stabilities exhibited by both gas-phase clusters and solid-state materials. The concept of "cluster-assembly" materials not only contributes to the formulation of design strategies for novel materials or stable clusters but also provides valuable insights into the extension of periodic aromaticity.