Chapter 4 Symmetry and its Applications

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Presentation transcript:

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

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.

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

Character Tables Mullikan symbols Irreducibile represenations

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

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.

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 = 1 x rotates by 180o and sign changes, so = -1 G all motions

Deconvoluting reducible representation to irreducible representations.

Deconvoluting reducible representation to irreducible representations.

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

Vibrational Analysis for Ammonia G all motions

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

Vibrational Analysis of Carbonyl Vibrations G CO groups

Vibrational Analysis of Carbonyl Vibrations G CO groups