chapter 4 symmetry and its applications symmetry = do something to a molecule and have it look the...
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Chapter 4
Symmetry and its Applications
Symmetry = do something to a molecule and have it look the same
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Representations of Groups:Example: effect of operations on x, y, z axes together
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Reducible vs. Irreducible Representations of Groups:Example: effect of operations on x, y, z axes alone
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Character Tables
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Order = # symmetry operations = 6Classes = grouping of similar operations = 3Dimensions = # under E operationOrder of group = (characters under E)2
Definitions by Example:
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Symmetry Applications: Vibrations
Examine x, y, z changes for each atom.An atom that moves gets zeros for each.Those not moving get 1 or -1 for each.Add them up to get reducible representation for atomic motions.Break reducible representation up to get list of irreducible representation.
# irrrep= 1/order (#operations in class)(character of redrep)(character of irrerep)
All motions = degrees of freedom = 3nTranslations = 3 and go by x, y, z functions.Rotations = 3 and go by Rx. Ry, and Rz functions.
Vibrations are what’s left over.IR active translate as x, y, z functions.Raman active translate as xy, xz, yz, z2, etc. functions.
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Vibrational Analysis for Water
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Vibrational Analysis of NH3
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Vibrational Analysis of XeF4
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Vibrational Analysis of XeF4
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Vibrational Analysis of Selected Vibrational Modes: CO stretches:
Consider only the C-O axis. If it moves, = 0 ; if it stays, =1
Can an IR spectrum distinguish between these two isomers?
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cis-ML2(CO)2
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trans-ML2(CO)2
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trans-ML2(CO)2
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Chapter 4 Homework
1, 2, 3, 5, 13, 16 a-e, 21, 23 (using items from problems 4 and 5 only), 24, 25, 26, 27, 28