A Keplerian Ag90 nest of Platonic and Archimedean polyhedra in different symmetry groups

Abstract

Polyhedra are ubiquitous in chemistry, biology, mathematics and other disciplines. Coordination-driven self-assembly has created molecules mimicking Platonic, Archimedean and even Goldberg polyhedra, however, nesting multiple polyhedra in one cluster is challenging, not only for synthesis but also for determining the alignment of the polyhedra. Here, we synthesize a nested Ag 90 nanocluster under solvothermal condition. This pseudo-T h symmetric Ag 90 ball contains three concentric Ag polyhedra with apparently incompatible symmetry. Specifically, the inner (Ag 6) and middle (Ag 24) shells are octahedral (O h), an octahedron (a Platonic solid with six 3.3.3.3 vertices) and a truncated octahedron (an Archimedean solid with twenty-four 4.6.6 vertices), whereas the outer (Ag 60) shell is icosahedral (I h), a rhombicosidodecahedron (an Archimedean solid with sixty 3.4.5.4 vertices). The Ag 90 nanocluster solves the apparent incompatibility with the most symmetric arrangement of 2-and 3-fold rotational axes, similar to the arrangement in the model called Kepler's Kosmos, devised by the mathematician John Conway.

Multiscale Assembly of [AgS4] Tetrahedrons into Hierarchical Ag–S Networks for Robust Photonic Water

“…[ 1–7 ] Given the molecular structure at the atomic level, they provide an ideal platform for understanding the evolution of functional materials (and their functions) from atomic, molecular, sub‐nanometer to nanometer scale. [ 8–12 ] In addition to the latest developments in atomically precise ultrasmall particles (mainly limited to below 3 nm), there is also a need to realize their programmable structure (or self‐assembly) into functional materials with a high level of hierarchy, complexity, and accuracy, up to the micro‐ or even macroscale. [ 13–20 ] This multiscale assembly of atomically precise ultrasmall particles provides a reliable platform for the bottom‐up construction of artificial functional materials across all scales, which is an intrinsic requirement for manifesting universal functionality in nature and life.…”

Protection of Ag Clusters by Metal‐Oxo Modules

“…[1][2][3][4][5][6][7][8][9][10] Generally, a silver cluster should consist of a silver metallic kernel and an organic peripheral ligand shell. [11][12][13][14][15] Such combination facilitates the crystallization and stabilization of the target monodisperse nanoclusters. According to classic hard and soft acids and bases theory (HSAB), softbase organic ligands would be more preferable for stabilization of soft-acid Ag atoms in forming the Ag clusters.…”

Cu Doping‐Induced Transformation from [Ag62S12(SBut)32]2+ to [Ag62−xCuxS12(SBut)32]4+ Nanocluster

“…[4][5][6][7][8][9][10][11][12][13] For example, the stability and catalytic activity of Au nanoclusters can be immensely enhanced after doping with Pd, Pt, Ag or other foreign metal atoms. [14][15][16][17][18][19][20][21][22] In addition, the AuÀ Ag bimetallic nanoclusters often exhibit a higher photoluminescence intensity compared with that of mono-silver nanoclusters. [23,24] Although some properties of nanoclusters could be improved with the additional of dopant.…”