Group Theory in Chemistry

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Presentation transcript:

Group Theory in Chemistry Point Groups Dr. Christoph, Phayao University 8.11.11

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

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. http://www.webqc.org/symmetry.php

Example Cyclopropane has TWO C3 axes: C3 and C32

Coordination System Use the “right hand rule”!

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

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)

Point Groups Every molecule has a set of symmetry elements. This set is called the Point Group of the molecule. http://www.webqc.org/symmetry.php

Use in Spectroscopy and Crystallography

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

Point Groups and Crystal Structures http://en.wikipedia.org/wiki/Space_group

http://symmetry.jacobs-university.de

Tetrahedral Td Octahedral Oh Linear: C∞h for X-X / D ∞h for X-Y http://en.wikibooks.org/wiki/Introduction_to_Mathematical_Physics/N_body_problem_in_quantum_mechanics/Molecules

Examples

Chirality http://www.scribd.com/doc/4802356/Symmetry-and-Chirality

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 ?

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 http://molwave.com “3DSymm” to see the symmetry operation in 3D