Symmetry & Group Theory In Chemistry May 2026

A Character Table is the "cheat sheet" for a point group. It lists how different properties (like orbitals or vibrations) change under the group’s operations. Labels like A1gcap A sub 1 g end-sub B2cap B sub 2 that describe the symmetry of a function. Characters ( ): Integers (usually

A is an action (like a rotation) that leaves the molecule looking exactly as it did before. Each operation is associated with a symmetry element (the point, line, or plane where the action happens). Identity ( ): Doing nothing. Every molecule has this. Rotation ( Cncap C sub n ): Rotating by around an axis. (e.g., C2cap C sub 2 180∘180 raised to the composed with power Reflection ( ): Reflecting through a plane. σvsigma sub v (vertical): Contains the main rotation axis. σhsigma sub h (horizontal): Perpendicular to the main axis. Inversion ( Symmetry & Group Theory in Chemistry

Symmetry determines "selection rules" (whether a transition is allowed or forbidden). A Character Table is the "cheat sheet" for a point group

Only orbitals of the same symmetry can overlap to form bonds. This is the basis of SALCs (Symmetry Adapted Linear Combinations). Vibrational Spectroscopy: Characters ( ): Integers (usually A is an