Abstract
In nature, protein subunits on the capsids of many icosahedral viruses form rotational patterns, and mathematicians also incorporate asymmetric patterns into faces of polyhedra. Chemists have constructed molecular polyhedra with vacant or highly symmetric faces, but very little is known about constructing polyhedra with asymmetric faces. Here we report a strategy to embellish a C3h truxene unit with rotational patterns into the faces of an octahedron, forming chiral octahedra that exhibit the largest molar ellipticity ever reported, to the best of our knowledge. The directionalities of the facial rotations can be controlled by vertices to achieve identical rotational directionality on each face, resembling the homo-directionality of virus capsids. Investigations of the kinetics and mechanism reveal that non-covalent interaction among the faces is essential to the facial homo-directionality.
Highlights
In nature, protein subunits on the capsids of many icosahedral viruses form rotational patterns, and mathematicians incorporate asymmetric patterns into faces of polyhedra
Fuller conceived of face-rotating polyhedra (FRP)[10], wherein each face of a polyhedron rotates around its central axis, transferring the two-dimensional (2D) chirality of the faces into the 3D chirality of the polyhedron (Fig. 1a)
The truxene fragment loses its mirror symmetry in a polyhedron and becomes a rotational face, resulting in five possible stereoisomers for 1; these configurations are named after the directionalities of the exterior faces as CCCC and AAAA, CCCA and CAAA and CCAA
Summary
Protein subunits on the capsids of many icosahedral viruses form rotational patterns, and mathematicians incorporate asymmetric patterns into faces of polyhedra. The construction of chiral molecular polyhedra follows two strategies: to use predetermined 3D chiral building blocks as the edges[30,32], vertices[33,34] or faces[35,36] of polyhedra to transfer 3D chirality of the components to the 3D chirality of the chiral structures, or to use achiral components to generate chiral metal-organic polyhedra[37,38,39,40,41,42] during a self-assembly process. The truxene fragment loses its mirror symmetry in a polyhedron and becomes a rotational face, resulting in five possible stereoisomers for 1; these configurations are named after the directionalities of the exterior faces as CCCC and AAAA (homo-directional with T symmetry), CCCA and CAAA (hetero-directional with C3 symmetry) and CCAA (hetero-directional with S4 symmetry)
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