Symmetry & Group Theory In Chemistry -

A vibration must change polarizability (matches quadratic terms like

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

) that show if a property stays the same or flips sign during an operation. 4. Chemical Applications Symmetry & Group Theory in Chemistry

): A rotation followed by a reflection through a perpendicular plane. 2. Point Groups

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 Point Groups Molecules are classified into based on

Symmetry determines "selection rules" (whether a transition is allowed or forbidden).

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 By categorizing a molecule’s symmetry

are the mathematical tools chemists use to describe and predict the behavior of molecules based on their shape . By categorizing a molecule’s symmetry, we can simplify complex quantum mechanical problems, predict spectroscopy results, and understand bonding. 1. Symmetry Elements and Operations