Molecular symmetry

Molecular symmetry describes the spatial operations that leave a molecule indistinguishable from its original arrangement. It is classified using symmetry elements and the mathematical groups they form.

Symmetry element: A geometric feature, such as an axis or plane, about which a symmetry operation is performed. Axes, planes, and centers identify the spatial features underlying molecular symmetry.
Character table: A tabulation of the irreducible representations and symmetry-operation characters of a point group. It summarizes each molecular point group’s representations and supports selection-rule analysis.
Infrared spectroscopy: A technique that measures absorption of infrared radiation by molecular vibrations. Only vibrations that change dipole moment absorb infrared radiation, a condition shaped by symmetry.
Chirality: The property of an object that makes it non-superimposable on its mirror image. A molecule with an improper rotation axis is achiral, linking symmetry directly to mirror-image behavior.
Symmetry operation: A transformation that maps an object onto an indistinguishable arrangement. Rotations and reflections are operations used to test whether a molecule is symmetric.
Irreducible representation: A representation of a group that cannot be decomposed into smaller representations. Irreducible representations classify how molecular motions and orbitals transform under symmetry.
Raman spectroscopy: A spectroscopic technique that measures inelastic scattering of light by molecular vibrations. Symmetry determines which vibrational modes change polarizability and appear in Raman spectra.
Conformational isomerism: The existence of distinct molecular arrangements interconverted by rotation about single bonds. A molecule’s symmetry can change as it adopts different conformations.
Point group: A group of symmetry operations that leave at least one point fixed. A molecule’s symmetry operations are organized into a point group.
Selection rule: A condition determining whether a transition between physical states is allowed. Symmetry determines whether molecular transitions can interact with light.

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