1

Chem 104A, UC, Berkeley

Groups generated by an Sn axis: Snn odd Cnhn even: Sn

iCS 2

H

HCl

Cl

F

FhC3

Chem 104A, UC, Berkeley

2

Chem 104A, UC, Berkeley

4

342

244 },,,{

S

SCSSE

1,3,5,7-tetrafluorocyclooctatetraene

F

F

F

F

Chem 104A, UC, Berkeley

3

Chem 104A, UC, Berkeley

Chem 104A, UC, Berkeley

Dihedral groups:Groups with a Cn axis plus n perpendicular C2 axes: Dn

C2H6 partly rotated (not staggered, not eclipsed).

},,,,,{ ''2

'22

2333 CCCCCED

4

Chem 104A, UC, Berkeley

Chem 104A, UC, Berkeley

Other example:

32422 )( NHHCNHCo

22422 )( NHHCNHPt

5

Chem 104A, UC, Berkeley

Chem 104A, UC, BerkeleyGroups with a Cn axis, n C2 axes and a h plane: Dnh

Example: Eclipsed Conformation of Hydrazine, N2H4

},,,),(),(),(,{ 2222 xzyzxyh ixCyCzCED

6

Chem 104A, UC, Berkeley

D3h: BF3

}'',',,,,,'',',,,,{ 533222

2333 vvvhh SSCCCCCED

Chem 104A, UC, Berkeley

D4h: PtCl4

7

Chem 104A, UC, Berkeley

,....},,,.........,.....,,{

,

2

22:

SiCCE

BeFHD

hv

h

n-gonal prism

Chem 104A, UC, Berkeley

n-gonal prism

8

Chem 104A, UC, Berkeley

Groups with a Cn axis, n C2 axes, and n d planes: Dnd

Symmetry Elements for D3d Point Group (A2X6)

C2H6 staggered.

}'',',,,,,'',',,,,{ 566222

2333 dddd SSiCCCCCED

d: dihedral reflection planes (bisects v or C2)

Chem 104A, UC, Berkeley

9

Chem 104A, UC, Berkeley

}',,'',',,,,{ 2234422 ddd CCSSCED

Allene

C

C

C

staggered regular polygons (n-gonal antiprism)

Chem 104A, UC, Berkeley

B2Cl4

10

Chem 104A, UC, Berkeley

Chem 104A, UC, Berkeley

Groups with very high symmetry: multiple high-fold rotation axes

The platonic solids: polyhedra constructed from regular polygons with all vertices and edges equivalent: 5 possibilities only.

icosahedron