Chapter 4 Symmetry and its Applications Symmetry do

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Chapter 4 Symmetry and its Applications Symmetry = do something to a molecule and

Chapter 4 Symmetry and its Applications Symmetry = do something to a molecule and have it look the same

Representations of Groups: Example: effect of operations on x, y, z axes together

Representations of Groups: Example: effect of operations on x, y, z axes together

Reducible vs. Irreducible Representations of Groups: Example: effect of operations on x, y, z

Reducible vs. Irreducible Representations of Groups: Example: effect of operations on x, y, z axes alone

Character Tables

Character Tables

Definitions by Example: Order = # symmetry operations = 6 Classes = grouping of

Definitions by Example: Order = # symmetry operations = 6 Classes = grouping of similar operations = 3 Dimensions = # under E operation Order of group = (characters under E)2

Symmetry Applications: Vibrations Examine x, y, z changes for each atom. An atom that

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 = 3 n Translations = 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, z 2, etc. functions.

Vibrational Analysis for Water

Vibrational Analysis for Water

Vibrational Analysis of NH 3

Vibrational Analysis of NH 3

Vibrational Analysis of Xe. F 4

Vibrational Analysis of Xe. F 4

Vibrational Analysis of Xe. F 4

Vibrational Analysis of Xe. F 4

Vibrational Analysis of Selected Vibrational Modes: CO stretches: Can an IR spectrum distinguish between

Vibrational Analysis of Selected Vibrational Modes: CO stretches: Can an IR spectrum distinguish between these two isomers? Consider only the C-O axis. If it moves, = 0 ; if it stays, =1

cis-ML 2(CO)2

cis-ML 2(CO)2

trans-ML 2(CO)2

trans-ML 2(CO)2

trans-ML 2(CO)2

trans-ML 2(CO)2

Chapter 4 Homework 1, 2, 3, 5, 13, 16 a-e, 21, 23 (using items

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

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