1. Group Theory in Chemistry
Point Groups Dr. Christoph, Phayao University

3. Content Board exercise: How to draw 3D models (molecules / crystals)
Group work: each group gets a molecules name -> draw the structure, build a model, find symmetry elements
Point Groups for molecules and crystals
Flow Chart to find a Point Group Practise with the molecules before
myphayao.com: online quiz and tutorials

4. Symmetry Elements E - the identity operation
Cn - rotation by 2π/n angle *
Sn - improper rotation (rotation by 2π/n angle and reflection in the plane perpendicular to the axis)
σh - horizontal reflection plane (perpendicular to the principal axis) **
σv - vertical reflection plane (contains the principal axis)
σd - diagonal reflection plane (contains the principal axis and bisect the angle between two C2 axes perpendicular to the principal axis)
* - n is an integer ** - principal axis is a Cn axis with the biggest n. Molecule belongs to a symmetry point group if it is unchanged under all the symmetry operations of this group.

5. Example
Cyclopropane has
TWO C3 axes:
C3 and C32

6. Coordination System
Use the “right hand rule”!

7. Group work:
Draw and build these molecules Find symmetry elements and point groups
Acetone
Chloromethane
Sulfur chloro pentaflouride
Ethene
Cyclopropane
Platinum tetrachloride
Ethanediol
Propadiene
Hydrogenperoxide
Methanol

8. Group work: Results
Acetone (C2v)
Chloromethane (C3v)
Sulfur chloro pentaflouride (C4v)
Ethene (D2h)
Cyclopropane (D3h)
Platinum tetrachloride (D4h)
Ethanediol (C2h)
Propadiene (D2d)
Hydrogenperoxide (C2)
Methanol (Cs)

9. Point Groups Every molecule has a set of symmetry elements.
This set is called the Point Group of the molecule.

10. Use in Spectroscopy and Crystallography

11. Example from crystallography:
The unit cell of NaCl has Oh symmetry !
In crystallography Herman-Maugin definition: F m3m
(F = face centered, m3m = Oh)

12. Point Groups and Crystal Structures

15. Tetrahedral Td Octahedral Oh Linear: C∞h for X-X / D ∞h for X-Y

16. Examples

21. Chirality

22. Order of Symmetry
= the number h of symmetry elements for one point group !
For example:
Ammonia = C3v has order 6 (E + 2 C3 + 3 sv)
The higher the order, the higher the symmetry !
Which one has higher symmetry:
C4v or D2h ?

23. End of Part 1 about Symmetry Point Groups
For a molecule (or any structure) we can find symmetry operations which leave the molecule unchanged.
These operations are:
Identity E (for each molecule)
Rotations Cn
Mirrors σ
Inversion i
... And the combination Sn (combine Cn + σ )
The sum of all possible operations for a molecule define its point group.
The name of the point group indicates the main symmetry elements: for example: D4h indicates a C4 axis and σh)
Try the program at “3DSymm” to see the symmetry operation in 3D