): A rotation followed by a reflection through a perpendicular plane. 2. Point Groups
A vibration must change polarizability (matches quadratic terms like
) that show if a property stays the same or flips sign during an operation. 4. Chemical Applications Symmetry & Group Theory in Chemistry
A vibration must change the molecule's dipole moment (matches in the character table).
Only orbitals of the same symmetry can overlap to form bonds. This is the basis of SALCs (Symmetry Adapted Linear Combinations). Vibrational Spectroscopy: ): A rotation followed by a reflection through
): Passing every atom through a center point to the opposite side. Improper Rotation ( Sncap S sub n
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 This is the basis of SALCs (Symmetry Adapted
Molecules are classified into based on their collection of symmetry elements. Low Symmetry: C1cap C sub 1 (no symmetry), Cscap C sub s (only a plane), Cicap C sub i (only inversion). High Symmetry: Tdcap T sub d (tetrahedral like CH4cap C cap H sub 4 Ohcap O sub h (octahedral like SF6cap S cap F sub 6 D∞hcap D sub infinity h end-sub (linear with inversion like CO2cap C cap O sub 2 Standard Groups: Cnvcap C sub n v end-sub Dnhcap D sub n h end-sub , etc., defined by the arrangement of axes and planes. 3. Character Tables