Chirality

A chiral molecule is that cannot be transformed to itself with any mirror transformation. An achiral molecule can be transformed to itself with a mirror transformation. Chiral molecules are important because they are optically active in the sense that they can rotate the plane of polarized light passing through the molecular sample. A molecule may be chiral only if it does not have an axis of improper rotation $S_n$. Note, that the molecule with a center of inversion $i$ belongs to $S_2$ group and thus cannot be chiral. Similarly, because $S_1 = \sigma$, any molecule with a mirror plane is achiral.

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