The Relationship between Chirality and Symmetry

Molecules that possess certain elements of symmetry are not chiral, because the element of symmetry ensures that the mirror image forms are superimposable. The most common example is a plane of symmetry, which divides a molecule into two halves that have identical placement of substituents on both sides of the plane. A trivial example can be found at any tetrahedral atom with two identical substituents, as, for example, in 2-propanol. The plane subdivides the 2-H and 2-OH groups and the two methyl groups are identical. 

More elaborate molecules can also have a plane of symmetry. For example, there are only three stereoisomers of tartaric acid (2,3-dihydroxybutanedioic acid). Two of these are chiral but the third is achiral. In the achiral stereoisomer, the substituents are located with respect to each other in such a way as to generate a plane of symmetry. Compounds that contain two or more stereogenic centers but have a plane of symmetry are called meso forms. Because they are achiral, they do not rotate plane polarized light. Note that the Fischer projection structure of meio-tartaric acid reveals the plane of symmetry. 

Plane of symmetry in the eclipsed conformation of meso-tartaric acid 

A less common element of symmetry is a center of symmetry, which is a point in a molecule through which a line oriented in any direction encounters the same environment (structure) when projected in the opposite direction. For example, trans, trans, cA-2,4-dichloro-l,3-dimethylcyclobutane has a center of symmetry, but no plane of symmetry. It is achiral. 

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