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Top of Page Molecular Structures of Organic Compounds - Symmetry of Molecules

On this page numerous examples of molecules belonging to different point groups are provided. For a detailed descriptions on the symmetry and properties of point groups (including the corresponding stereographic projections, shapes of objects, list of essential symmetry elements, and a detailed description on how to determine the point group of a given molecule) see the 'Symmetry and Point Groups' section of this web site.

Symmetry and Point Groups
Symmetry Elements of a 3D-Object
Top of Page C1 Point Group - 3D Structures
The simplest point group C1 contains only one trivial symmetry operation, the identity operation E. This is the point group of all asymmetrical molecules and molecular conformations. These molecules must be chiral:

Point Group C1

(S)-2-Bromo-butane L-Phenylalanine Alpha-D-Glucose
C1 C1 C1
Top of Page Ci Point Group - 3D Structures
If a molecule possesses only an inversion center i and no other symmetry elements, it belongs to the point group Ci. Examples of this group are commonly found with meso-type structures such as meso-tartaric acid.

Point Group Ci

(2S,3R)-Tartaric acid Cyclo-(D-Ala-L-Ala)
Ci Ci
Top of Page Cs Point Group - 3D Structures
This point groups has a mirror plane σ as the only symmetry element. Many (flat) aromatic molecules belong to this group.

Point Group Cs

Propene 1-Chloro-ethene (Vinylchloride) Cis-1,2-Cyclopentene Chinolin
Cs Cs Cs Cs
Top of Page Cn Point Groups - 3D Structures
Molecules in this group have a single n-fold rotation axis Cn as their symmetry element. These compounds must be chiral, and many of the most important ligands used in stereoselective synthesis of organic chemistry belong to the C2 point group.

Point Group Cn

2,2'-bis(Methoxy)-1,1'-binaphthyl Penta-2,3-diene (2R,3R)-Tartaric acid D-Mannitol 9bH-Phenalene 3,7,11-Trimethyl-cyclododeca-1,5,9-triene 2,6,7-Trimethyl-1-aza-bicyclo[2.2.2]octan Calix[4]arene Derivative Alpha-cyclodextrin
C2 C2 C2 C2 C3 C3 C3 C4 C6
Top of Page Cnv Point Groups - 3D Structures
Molecules having a n-fold rotation axis Cn and n vertical mirror planes σv belong to the Cnv point group. Linear molecules which do not possess an inversion center or a horizontal mirror plane σh belong to the C∞v point group, because all rotations about their axis are symmetry operations (conical molecules).

Point Group Cnv

Formaldehyde (Z)-1,2-Dichloro-ethene 1,3-Dimethylbenzene (m-Xylol) Phenanthrene Chloroform tert-Butyl-bromide Calix[4]arene Chloro-acetylene
C2v C2v C2v C2v C3v C3v C4v C∞v
Top of Page Cnh Point Groups - 3D Structures
Molecules belonging to the Cnh point group feature a n-fold rotation axis Cn and a horizontal mirror plane σh.

Point Group Cnh

1,3-Butadiene 1,4-Dibromo-2,5-dichloro-benzene (E)-1,2-Dichloro-ethene 1,3,5-Trihydroxy-benzene
C2h C2h C2h C3h
Top of Page Dn Point Groups - 3D Structures
A molecule that has a n-fold principal axis and n twofold axes perpendicular to the principal axis belongs to the Dn point group. All molecules in this point group must be chiral.

Point Group Dn

Twistane Potassium sodium tris(oxalato)-iron(iii) trihydrate Perchloro-triphenylamine Threefold Knot (not a real molecule)
D2 D3 D3 D3
Top of Page Dnh Point Groups - 3D Structures
If, in addition to a n-fold principal axis and n twofold axes perpendicular to it, a horizontal mirror plane σh is present in a molecular structure, the point group is described as Dnh. The D∞h point group includes all linear molecules with an center of inversion, which also implies a horizontal mirror plane σh (cylindrical molecules).

Point Group Dnh

Ethene 1,4-Dibromo-benzene [2.2]Paracyclophane Cyclopropane AuCl4(-) Ferrocene (ecliptic) Benzene Coronene Acetylene
D2h D2h D2h D3h D4h D5h D6h D6h D∞h
Top of Page Dnd Point Groups - 3D Structures
The Dnd point groups include the symmetry elements of Dn and n dihedral mirror planes σd bisecting the angles formed by pairs of C2 axes.

Point Group Dnd

Prop-1,2-diene Biphenyl Cyclooctatetraene Cyclohexane Ethane (staggered conformation) Ferrocene (staggered)
D2d D2d D2d D3d D3d D5d
Top of Page Sn Point Groups - 3D Structures
Molecules which have not been classified by one of the above C or D point groups, but which possess one rotary-reflection axis Sn only (n must be even and ≥ 4), belong to the Sn point groups. Molecules of point groups Sn with n > 4 are rare.

Point Group Sn

Co4Cp4 Tetraphenylmethane 1,3,5,7-Tetrabromo-2,4,6,8-tetramethyl-cyclooctane 2,3,7,8-Tetramethyl-spiro[4.4]nonane [6.5]Coronane
S4 S4 S4 S4 S6
Top of Page Tetrahedral Point Groups - 3D Structures
The tetrahedral point groups are characterized by the presence of four C3 principal axes (and three C2 axes). The Td group is the point group of a regular tetrahedron. If, in addition, a center of inversion is present, the point group is Th (molecules of this group do not look like tetrahedrons, but retain the rotational symmetry of a tetrahedron). All objects possessing the rotational symmetry of a tetrahedron, but no plane of reflection or center of inversion are based on the simpler point group T. Molecules of this group must be chiral, and examples are very rare.

Point Group T, Th, and Td

Ga4 Cluster Fe[(C5H5N)6]2+ Methane Neo-pentane Tetra-tert-butyl-tetrahedrane Adamantane
T Th Td Td Td Td
Top of Page Octahedral Point Groups - 3D Structures
The octahedral point groups O and Oh feature three C4 principal axes (and four C3 axes as well as multiple C2 axes). A regular octahedron and a cube both belong to the Oh point group. In analogy to the tetrahedral point group T, the octahedral group O retains the rotational symmetry of an regular octahedron, but none of its planes of reflection or the center of inversion. Examples of molecules belonging to the O point group are extremely rare (these molecules must be chiral!).

Point Group O and Oh

Cr(CO)6 PtCl6(2-) PF6(-) Cubane
Oh Oh Oh Oh
Top of Page Icosahedral Point Groups - 3D Structures
The icosahedral point groups I and Ih posses six C5 principal axes (amongst 10 C3 and 15 C2 axes). In analogy to the octahedral point groups O and Oh the I group does contain all rotational symmetry elements, but no mirror planes or center of inversion. Molecules belonging to this chiral point groups are extremely rare. Shapes belonging to the more symmetrical Ih point groups are the dodecahedron and the icosahedron.

Point Group I and Ih

Dodecahedrane B12H12(2-) [60]Fullerene (C60)
Ih Ih Ih
Top of Page Spherical Point Group
The Kh point group resembles the symmetry of perfect spheres. Obviously, only atoms but no molecules belong to this point group.

Point Group Kh

For more information on other research topics, please refer to the complete list of publications and to the gallery of graphics and animations.

© Copyright PD Dr. S. Immel

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