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Point Groups

Each molecule has a set of symmetry operations that describes the molecule's overall symmetry. This set of operations define the point group of the molecule.

The process used to assign a molecule to a point group is straightforward with a few exceptions. It is a procedure. Here are set of steps to quickly guide you.

  1. Look at the molecule and see if it seems to be very symmetric or very unsymmetric. If so, it probably belongs to one of the special groups (low symmetry: C1, Cs, Ci or linear C∞v, D∞h) or high symmetry (Td, Oh, Ih..).
  2. For all other molecules find the rotation axis with the highest n, the highest order Cn axis of the molecule.
  3. Does the molecule have any C2 axes perpendicular to the Cn axis? If it does, there will be n of such C2 axes, and the molecule is in one of D point groups. If not, it will be in one of C or S point groups.
  4. Does it have any mirror plane (σh) perpendicular to the Cn axis? If so, it is Cnh or Dnh.
  5. Does it have any mirror plane (σd,σv)? If so, it is Cnv or Dnd

For a complete version as a graphic of this procedure download either the PowerPoint version or Pdf version. If you print this procedure, it will help you during examples and exercises.

Non-rotational Groups

  • low order
  • only E or E+ 1 other symmetry
Cs E, σh H2CClBr

Single axis groups

Cn E, Cn H2O2
  • only one rotational
Cnv E, Cn , nσv H20, 9-BBN
Cnh E, Cn , σh, Sn Boric acid [B(OH)3]
S2n E, S2n 1,3,5,7 -tetrafluoracyclooctatetrane
C∞v E, C, ∞ σv HCl

Dihedral groups

Dn E, Cn, nC2


  • has nC2 axes perp. to principal axis
Dnd E, Cn, nC2,S2n S8 (crown sulfur)
Dnh E, Cn, nC2,σh,nσv BF3, naphthalene(C10H10)
D∞h E,i,C∞v, ∞ σv, CO2

Cubic groups

Td E, C3, C2,S4,σd CCl4
  • 7 groups but 3 common
  • high order (Td=24, Oh=48, I=120)
Oh E, C3, C2,C4,i,S4, S6,σd,σh SF6
Ih E, C3, C2,C5,i,S10, S6,σ [B12H12]-2

Now we will go through some examples. You can have your chart with you.

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