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.

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, C_s, C_i or linear C_∞v, D_∞h) or high symmetry (T_d, O_h, I_h..).
For all other molecules find the rotation axis with the highest n, the highest order Cn axis of the molecule.
Does the molecule have any C₂ axes perpendicular to the C_n 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.
Does it have any mirror plane (σ_h) perpendicular to the C_n axis? If so, it is C_nh or D_nh.
Does it have any mirror plane (σ_d,σ_v)? If so, it is C_nv or D_nd

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
C₁	E	CHFClBr	low order only E or E+ 1 other symmetry
Cs	E, σ_h	H₂CClBr
CI	E, i	HClBrC-CHClBr
Single axis groups
C_n	E, C_n	H₂O₂	only one rotational
Cnv	E, C_n , nσ_v	H₂0, 9-BBN
Cnh	E, C_n , σ_h, S_n	Boric acid [B(OH)₃]
S2n	E, S_2n	1,3,5,7 -tetrafluoracyclooctatetrane
C_∞v	E, C_∞, ∞ σ_v	HCl
Dihedral groups
D_n	E, C_n, nC₂	CoN₆	has nC₂ axes perp. to principal axis
D_nd	E, C_n, nC₂,S_2n	S₈(crown sulfur)
D_nh	E, C_n, nC₂,σ_h,nσ_v	BF₃, naphthalene(C₁₀H₁₀)
D_∞h	E,i,C_∞v, ∞ σ_v,	CO₂
Cubic groups
T_d	E, C₃, C₂,S₄,σ_d	CCl₄	7 groups but 3 common high order (T_d=24, O_h=48, I=120)
O_h	E, C₃, C₂,C₄,i,S₄, S₆,σ_d,σ_h	SF₆
I_h	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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