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

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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 C n - rotation by 2π/n angle * S n - improper rotation (rotation by 2π/n angle and reflection in the plane perpendicular to the axis) σ h - horizontal reflection plane (perpendicular to the principal axis) ** σ v - vertical reflection plane (contains the principal axis) σ d - diagonal reflection plane (contains the principal axis and bisect the angle between two C 2 axes perpendicular to the principal axis) * - n is an integer ** - principal axis is a C n 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

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Example Cyclopropane has TWO C 3 axes: C 3 and C 3 2

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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 (1) Acetone (2) Chloromethane (3) Sulfur chloro pentaflouride (4) Ethene (5) Cyclopropane (6) Platinum tetrachloride (7) Ethanediol (8) Propadiene (9) Hydrogenperoxide (10) Methanol

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Group work: Results (1) Acetone (C2v) (2) Chloromethane (C3v) (3) Sulfur chloro pentaflouride (C4v) (4) Ethene (D2h) (5) Cyclopropane (D3h) (6) Platinum tetrachloride (D4h) (7) Ethanediol (C2h) (8) Propadiene (D2d) (9) Hydrogenperoxide (C2) (10) 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. http://www.webqc.org/symmetry.php

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Use in Spectroscopy and Crystallography

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

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

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http://symmetry.jacobs-university.de

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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

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Examples

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Chirality http://www.scribd.com/doc/4802356/Symmetry-and-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 http://molwave.com “3DSymm” to see the symmetry operation in 3Dhttp://molwave.com

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