symmetry operations and elements

further chem
symmetry operation → 3D transformation leaving molecule
“apparently unchanged”

symmetry element → axis/point/plane with respect to which the operation is carried out

types:

element: whole of the molecule
operation: identity

element: n-fold axis of rotation
operation: rotation by 360˚/n

a molecule can have multiple rotation axes
the principle axis is that with the highest value of n

element: mirror plane
operation: reflection

vertical → contains principal axis
horizontal → to principal axis

element: centre of inversion
operation: inversion (passing each point through the center of inversion and out to the same distance on the other side of the molecule)

element: improper rotation axis
operation: rotation by 360˚/n and reflection in plane perpendicular to rotation axis