Summary for Determining Point Group for a Molecule
C
n (proper rotation): a rotation axis of symmetry, where
n
is the order of the
rotation axis or “foldedness”.
The number of degrees of the rotation is related to
n
by 360/
n
.
The “major axis” in a molecule is the rotation axis with the highest order (highest
value of n).
Types of Point Groups:
1.
C
n
,
C
n
h
,
C
n
v
-these three do not have a
C
2 axis perpendicular to the major axis.
-in
C
n
h
, the '
h
' indicates a horizontal mirror plane of symmetry present.
-in
C
n
v
, the '
v
' indicates a vertical mirror plane of symmetry present.
-vertical mirror planes include the major axis.
-horizontal mirror planes are perpendicular to the major axis.
-if both types are present, horizontal takes precedent.
2.
D
n,
D
n
h
,
D
n
d
-these three do have a
C
2 axis perpendicular to the major axis.
-in
D
n
h
, the '
h
' indicates a horizontal mirror plane of symmetry present.
-in
D
n
d
, there are vertical mirror planes present, but no horizontal planes.
3. Linear Groups:
a)
C∞v
(unsymmetric) (i.e. H–Cl)
b)
D∞h
(symmetric) (i.e. O=C=O)
4. Platonic Solids:
a) tetrahedral-
Td
(i.e. CH4)
b) octahedral-
Oh
(i.e. SF6)
c) icosahedral-
Ih
(i.e. C60, B12H122-)
