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

25. Reducible vs. Irreducible Representations of Groups:
Example: effect of operations on x, y, z axes alone
Examine the effect of the operation on the x, y, and z axes.
If unchanged, character = 1; if reversed, character = -1.

26. Gxyz Gx Gy Gz Representations of Groups:
Example: effect of operations on x, y, z axes together
Gxyz Gx Gy Gz

27. Character Tables
Mullikan symbols
Irreducibile represenations

28. Order = # symmetry operations = 6 (sum of numbers on top)
Definitions by Example:
Order = # symmetry operations = 6 (sum of numbers on top)
Classes = grouping of similar operations = 3 (number of groups on top)
Dimensions = # under E operation
Order of group = (characters under E)2

29. Symmetry Applications: Vibrations
1. Examine x, y, z changes for each atom.
2. An atom that moves gets zeros for each.
3. Those not moving get 1 or -1 for each axis.
4. Add them up to get reducible representation for atomic motions.
5. Break reducible representation up to get list of irreducible representation.
# irrrep= 1/order (#operations in class)(character of redrep)(character of irrerep)
6. All motions = degrees of freedom = 3n
Translations = 3 and go by x, y, z functions.
Rotations = 3 and go by Rx. Ry, and Rz functions.
7. Vibrations are what’s left over.
IR active translate as x, y, z functions.
Raman active translate as xy, xz, yz, z2, etc. functions.

30. G Vibrational Analysis for Water
Consider result of operation on each axis, accounting for change in sign, and then add that column. C2: z stays the same = x rotates by 180o and sign changes, so = -1 G
all
motions

31. Deconvoluting reducible representation to irreducible representations.

32. Deconvoluting reducible representation to irreducible representations.

33. Identify translational and rotational modes.
Identify Vibrational Modes as IR or Raman Active.
G = 3 A1 + 1 A2 + 3 B1 + 2 B2
all
motions

35. Vibrational Analysis for AmmoniaG
all
motions

36. Vibrational Analysis of Carbonyl Vibrations: count number of unmoved CO groups

37. Vibrational Analysis of Carbonyl VibrationsG
CO groups

38. Vibrational Analysis of Carbonyl VibrationsG
CO groups