Symmetry & Group Theory In: Chemistry

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

A vibration must change polarizability (matches quadratic terms like Symmetry & Group Theory in Chemistry

) that show if a property stays the same or flips sign during an operation. 4. Chemical Applications Molecules are classified into based on their collection

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

): Passing every atom through a center point to the opposite side. Improper Rotation ( Sncap S sub n

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 (