# symmetry - Chemistry 3140: Advanced Inorganic Chemistry...

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Click to edit Master subtitle style Chemistry 3140: Advanced Inorganic Chemistry Chapter 6: Symmetry and Group Theory

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What is Symmetry? Though not obvious now, the mathematical realm of symmetry has proven enormously useful when applied to chemistry. What we have is essentialy abstract math applied to real molecules with real structures.

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Technical Definition In technical language, an object (a molecule or a Lego block) possesses symmetry if some operation can be done on it, and the result is indistinguishable from the starting position. A symmetry element is an action that leaves the molecule apparently unchanged.
Naturally, we start off with Lego blocks …

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Beyond rotational symmetry is mirror symmetry …
Mirror and Rotational Symmetry Two instances of mirror symmetry: And 1800 rotational symmetry . ..

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Mirror and Rotational Symmetry This has only mirror symmetry in screen . .. This has only 180o rotational symmetry . .. If you tried to do a 1800 rotation on the first one …
A Square has both 90o and 180o rotational symmetry. It also has several mirrors . ..

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There are more types of symmetry than mirror and rotational. There are five symmetry elements that we will look at:
The C2 rotation and the two mirror planes of water. Note these mirrors are called σv planes . .. mirror planes that contain the highest rotation axis

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The mirror and rotation axes in a square planar molecule like XeF4.
C 6 Benzene shows all three types of mirror planes. σh is the plane of the molecule. There are plenty of other elements of symmetry here like C3 and C2 rotations. C6 is the highest order rotation axis here, and is the most important.

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Inversion vs. Reflection Though the appearance after the operation is the same, note how inversion and reflection of ethylene are a bit different.
Improper Rotation The improper S4 rotation of a tetrahedron. Ethane in the staggered configuration has an S6.

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This is a nice example of something much easier to see with molecular models.
The three symmetry elements of water (C2 and two σv) The four symmetry elements of ammonia (C3 and three σv)

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+Z -Z +Y -Y +X -X Imagine the xz plane is a mirror plane. What parts of any object on this set of axes is affected by the reflection? One way to think of it is this: a mirror plane changes the coordinates of an object in one dimension. Imagine an object, like a molecule, on this set of axes . ..
+Z -Z +Y -Y +X -X Now perform a rotation around the z axis. Do you see how a C2 rotation would reverse the coordinates of an object on both the x and y axes? A rotation axis affects two dimensions simultaneously.

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+Z -Z +Y -Y +X -X Imagine an inversion center operation. An inversion center reverses the coordinates of all three axes simultaneously.
+Z -Z +Y -Y +X -X So, what does an identity operation do? What does an S4

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## This note was uploaded on 05/31/2011 for the course CHEM 3341 taught by Professor Staff during the Spring '08 term at Georgia Southern University .

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symmetry - Chemistry 3140: Advanced Inorganic Chemistry...

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