Merging the Symmetry Interaction and Directional Bonding Approaches for the Design and Analysis of Supramolecular Architectures

The design of many supramolecular materials requires an understanding of the geometric complementarity of molecular subunits. In recent decades, the directional bonding and symmetry interaction approaches have given rise to a vast array of supramolecular architectures resembling various Platonic, Archimedean and other geometries. However, even in terms of these design principles it is challenging to accurately predict the supramolecular structure which will occur when complementary subunits are combined in synthesis. In this work, we use key principles of the symmetry interaction and directional bonding approaches, and adapt them to obtain analytical solutions describing symmetry-allowed geometric relationships between bonding vectors in the cubic, icosahedral, and dihedral point groups. This analysis puts forward two angular parameters; the ”mutual bonding angle” μ which describes the angle between two bonding directions on the same molecular subunit, and the “secondary bonding angle” ψ which describes the angle between a bonding direction of a molecular subunit and its associated rotational symmetry axis. We show that these angular parameters are not fixed quantities, and that the formation of a solid which bears a given point symmetry relies on the combination of molecular subunits with appropriate μ and ψ parameters. This updated methodology will be useful in the design of supramolecular solids, as well as their structural analysis.