Chiral molecules with polyhedral T, O, or I symmetry: Theoretical solution to a difficult problem in stereochemistry

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Ever since point groups of symmetry have been used to describe molecules after Van't Hoff and Le Bel proposed tetrahedral structures for carbon atoms in 1874, it remains difficult to design chiral molecules with polyhedral symmetry T, O, or I. Past theoretical and experimental studies have mainly accomplished molecular structures that have the conformations for satisfying the T symmetry. In this work, we present a general theoretical approach to construct rigid molecular structures that have permanently the symmetry of T, O, and I. This approach involves desymmetrization of the vertices or the edges of Platonic solid-shaped molecules with dissymmetric moieties. Using density functional theory (DFT) and assisted model building and energy refinement (AMBER) computational methods, the structure, the rigidity, and the symmetry of the molecule are confirmed by assessing the lowest energy conformation of the molecule, which is initially presented in a planar graph. This method successfully builds molecular structures that have the symmetry of T, O, and I. Interestingly, desymmetrization of the edges has a more stringent requirement of rigidity than desymmetrization of the vertices for affording the T, O, or I symmetry.