Desymmetrization of the Tetrahedron: Stereogenic Centers

Abstract

In undergraduate teaching, stereochemical issues in the molecule Cabcd, formed by an sp3 hybridized carbon atom bonded to four substituents, a, b, c, and d, are usually analyzed using drawings or molecular models that represent the molecules as regular tetrahedra with the substituents at the vertices. Strictly speaking, however, Cabcd can only have the geometry of a regular tetrahedron if all substituents are identical, as in methane CH4 or tetrachloromethane CCl4. Other combinations of substituents, such as a – b – c – d (but also a – b – c = d, or a = b – c = d, or a = b = c – d) give rise to structures that cannot be modeled as regular tetrahedra, since the bond lengths and bond angles in such molecules are nonequivalent. Despite this, only structures belonging to five symmetry point groups, Td, C3v, C2v, Cs, and C1, are possible, irrespective of whether Cabcd is modeled as a regular tetrahedron or as irregular tetrahedra having different, substituent-dependent bond lengths and bond angles. While the regular tetrahedron is the more straightforward model and is preferable for rationalizing stereochemistry at the undergraduate level for molecules containing stereogenic centers , it is important that both the instructor and students be fully aware that the tetrahedral model represents a simplification and that the use of irregular tetrahedra would be physically more realistic.