Evolution on the Size of Protected Metal Clusters by Assembly of Au₄ and Au₆ Units

Perfect tetrahedra and octahedra are the fundamental building blocks of FCC lattices; however, even distorted versions of these polyhedra can assemble into periodic HCP and BCC metal structures. In the case of protected metal clusters (PMCs), protecting ligands such as thiols, alkynyls, carbenes, and phosphines are responsible for the observed distortion of their metal frameworks due to the strong covalency of M-S, M-C, and M-P bonds (M stands for metal atoms). This work examines the assembly of tetrahedral and octahedral units and their relationship to the inner cores of PMCs. For instance, a perfect or distorted tetrahedron can share 1, 2, or 3 vertices with another tetrahedron, forming M₇(<i>D</i> _3<i>d</i> or <i>D</i> _3<i>h</i> ), M₆(<i>D</i> _2<i>h</i> or <i>C</i> _2<i>h</i> ), and M₅(<i>D</i> _3<i>h</i> ) units, respectively. Accordingly, M₇ units containing differently oriented tetrahedra can serve as building blocks for the FCC and HCP structures. Similarly, one octahedron sharing 1, 2, and 3 vertices yields M₁₁(<i>D</i> _4<i>h</i> or <i>D</i> _2<i>h</i> ), M₁₀(<i>D</i> _2<i>h</i> ), and M₉(<i>D</i> _3<i>h</i> ) units, respectively. The assembly of one octahedron and two tetrahedra along one <i>C</i> ₃ axis yields an M₈ unit displaying <i>D</i> _3<i>d</i> , <i>D</i> _2<i>h</i> , or <i>C</i> _2<i>h</i> symmetry. In contrast, the icosahedral M₁₃ cluster is composed of 20 distorted tetrahedra, while an M₁₂ shell can be identified in structures formed by 20 octahedra. Regarding decahedral structures, they contain pentagonal bipyramids (M₇ units with a <i>D</i> _5<i>h</i> symmetry) assembled with five distorted tetrahedra. It is noteworthy that unlike in FCC or HCP atomic arrangements, M₅, M₇, and M₉ units are not present in BCC lattices. This study implements an algorithm that successfully generates atomic positions by capping an inner core with tetrahedra or octahedra, revealing the pivotal role of the type and distribution of polyhedral units in defining the anatomy and bonding of PMCs, and offering new insights into their structural understanding.