Group Theory Flashcards
E
description: identity
operation: no change
Cn
description: n-fold axis of symmetry
operation: rotation about the axis by 360°/n
σ
description: plane of symmetry
operation: reflection through the plane
i
description: center of symmetry
operation: reflection through the center
Sn
description: n-fold rotation-reflection axis of symmetry (improper rotation)
operation: rotation about the axis by 360°/n followed by reflection through a plane perpendicular to the axis
Principal axis
if a molecule contains several symmetry axes, then the one with the largest value of n is called the principal axis
σv, σh
if a plane of symmetry is parallel to a unique axis or to a principal axis, it is designated by σv (vertical), σh (perpendicular)
σd
if a plane of symmetry bisects the angle between two-fold axes that are perpendicular to a principal axis, designated by σd (dihedral)
Dn
point groups that have an n-fold axis and an two-fold axes perpendicular to it
Td
tetrahedral
C2v
Symmetry elements: E, C2, 2σv
Molecular examples: H2O, CH2Cl2, C6H5Cl
C3v
Symmetry elements: E, C3, 3σv
Molecular examples: NH3, CH3Cl
C2h
Symmetry elements: E, C2, i, σh
Molecular examples: trans-HClC=CClH
D2h
Symmetry elements: E, 3C2 (mutually perpendicular)
i, 3σv (mutually perpendicular)
Molecular examples: C2H4 (ethene)
D3h
Symmetry elements: E, C3, 3C2 (perpendicular to the C3 axis), σh, S3, 3σv
Molecular examples: SO3, BF3
