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**Group Theory in Chemistry**

Point Groups Dr. Christoph, Phayao University

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**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

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**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.

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Example Cyclopropane has TWO C3 axes: C3 and C32

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Coordination System Use the “right hand rule”!

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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

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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)

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**Point Groups Every molecule has a set of symmetry elements.**

This set is called the Point Group of the molecule.

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**Use in Spectroscopy and Crystallography**

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**Example from crystallography:**

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

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**Point Groups and Crystal Structures**

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

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Examples

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Chirality

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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 ?

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**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

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