The Marriage of Sierpiński Triangles and Platonic Polyhedra

Abstract

Fractal structures with self-similarity are of fundamental importance in the fields of aesthetic, chemistry and mathematics. Here, by taking advantage of constructs the rational geometry-directed precursor design, we report the construction of two fascinating Platonic solids, the Sierpiński tetrahedron ST-T and the Sierpiński octahedron ST-O, in which each possesses a fractal Sierpiński triangle on their independent faces. These two discrete complexes are formed in nearquantitative yield from the multi-component self-assembly of truncated Sierpiński triangular kernel L 1 with tribenzotriquinacene-based hexatopic and anthracenebased tetratopic terpyridine ligands (L 3 and L 4 ) in the presence of metal ions, respectively. The enhanced stabilities of the 3D discrete structures were investigated by gradient tandem mass spectrometry (gMS 2 ). This work provides new constructs for the imitation of complex virus assemblies and for the molecular encapsulation of giant guest molecules.

The oxygen reduction reaction on M-MO x (M=Fe/Co) carbon-based catalyst through DFT calculations

“…This work's calculational model is based on a single layer of nitrogen-doped graphene substrate with a supercell 5×5×1, a 15Å vacuum layer. According to the theoretical study of the full electronic structure of the cube Fe 3 O 4 and Co 3 O 4 , the spin-polarization is set [21] (Chen et al 2020), and the DFT+U method [22][23] [24] (Dudarev et al 1998) (Xu et al 2015) (Ding et al 2020) is used to correct the intra-atomic Coulomb interactions (U eff =U-J) between the strongly correlated Fe 3d(U eff =3.8eV) and Co 3d (U eff =3.0eV) orbital electrons [25][26] [27] The doping model M-MO x (M=Fe/Co)/GC is shown in Figure 1 The adsorption energy can be used to estimate the surface stability of adsorption, e.g., in the O 2 adsorption of M-MO x (M=Fe/Co)/GC, the adsorption energy is calculated according to the following formula:…”

Triamine and Tetramine Edge-Length Matching Drives Heteroleptic Triangular and Tetragonal Prism Assembly

“…Stang, Schmittel, Fujita, and others have developed elegant approaches to drive the selective self-sorting of mixtures of subunits into single heteroleptic metal–organic assemblies. Approaches pioneered by Clever, Wang, and others have leveraged a good geometric match between different ligand types. Zhang and co-workers have utilized both geometric matching between ligands and principles of charge separation to generate heteroleptic architectures from paneling ligands …”