Molecular Symmetry: The Point Group - Introduction to Coordination Chemistry - page 279

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YES

YES

Is the molecule
linear?

Is there a centre
of inversion?

D ∞ h

NO

NO

C ∞ v

YES YES YES

Are n C 2 axes present
perpendicular to the C n axis?

Is there a principal
C n axis?

Does a σ h plane lie
perpendicular to the C n axis?

D nh

NO

NO NO

YES

Is the C n axis contained
in n

D nd

σ v planes ?

YES

YES NO

σ h plane lie
perpendicular to the C n axis?

Does a

Is there a mirror
plane ?

C s C nh

D n

NO

NO

YES YES

Is there a centre of
inversion ?

Is the C n axis contained
in n

C i C nv

σ v planes ?

NO

NO

C n

C 1

Figure B.2
Simplified flow chart for assignment of a symmetry group. Special high symmetry groups (T d ,O h ,
I h ) are not included in this chart, and need to be identified separately; it applies to other and generally
lower symmetry molecules, which are more often met in reality.

It is possible with the flow chart and careful examination of drawings and or three-
dimensional models of a complex to assign the point group with reasonable rapidity and
success after some practice. To assist further, a list of the point groups of basic higher
symmetry structures are collected in Table B.3 below. Those shown assume identical
ligands in all sites. You should assume that these shapes with a mixture of different ligands
will be of lower symmetry and have a lower symmetry point group. This aspect is illustrated

Ta b l e B . 2 Point groups.

Point group Symmetry elements involved

C s One plane of symmetry.

C i A centre of symmetry.

C n One n -fold rotation axis.

D n One n -fold rotation axis (about the principal axis) and n horizontal twofold axes.

C nv One n -fold rotation axis (about the principal axis) and n vertical planes.

C nh One n -fold rotation axis (about the principal axis) and one horizontal plane.

D nh One n -fold rotation axis (about the principal axis, as for D n ), one horizontal

plane, and n vertical planes containing the horizontal axes.

D nd One n -fold rotation axis (about the principal axis, as for D n ), and vertical planes

bisecting angles between the horizontal axes.

S n Systems with alternating axes ( n = 4, 6, 8).

C ∞ v ,D ∞ h Linear systems with an infinite rotation axis.

T d ,O h ,O,I h ,I Special groups: tetrahedral, octahedral, cubic and icosahedral