Class Summary 10/27/04

Exam #1

10/27 MORE SYMMETRY

We looked at the MO’s in the allyl and cyclobutadiene systems as examples

Determine how AO’s relate to one another

This way, one can determine the contributions of the AO’s in a given MO

This is all projection operators, over and over again

Symmetry-Adapted MO’s

1) Identify the AO for your basis set (e.g. allyl, 3 2p orbitals, f₁, f₂, f₃)

2) Identify point group (e.g. allyl, C_2v)

3) Evaluate how basis set components transform upon symmetry operations

4) Get reducible representation, G

5) Solve G to find irreducible representations by Projection Operators

PROJECTION OPERATORS

h: order of group (i.e. # of symmetry operations, e.g. C_2v, h = 4)

c_m,n: character for symmetry type m and operation n (e.g. in C_2v, c_A1,E = 1)

G_n: character of the n operation in G, the reducible representation

The number of orbitals with symmetry type m in G is given by

Allyl system recall G = A₂ + 2 B₂

2B₂ = f₂ - (f₁ + f₃) Highest MO

A₂ = f₁ - f₃

1B₂ = f₂ + (f₁ + f₃) Lowest MO

Cyclobutadiene (rectangular, D_2h) G = B_1g + B_2g + A_u + B_3u

Highest MO	Au		f1 - f2 + f3 - f4
	B1g		f1 + f2 - f3 - f4
	B2g		f1 - f2 - f3 + f4
Lowest MO	B3u		f1 + f2 + f3 + f4

USEFUL LINKS

http://bilbo.chm.uri.edu/CHM501/fall2001homework12answers.html

This is an example for PYRIDINE. Not bad.

http://www.reciprocalnet.org/edumodules/symmetry/mainpage.html

A useful set of pages illustrating symmetry elements and point groups (a little slow…)

http://www.science.siu.edu/chemistry/tyrrell/group_theory/sym1.html

A straight-forward (text) description of symmetry elements and point groups

http://newton.ex.ac.uk/research/semiconductors/theory/people/goss/symmetry/index.html

A site that is EXTREMELY complete. Way beyond the scope of CHM 668. This site also has point group tables online.

http://www.mpip-mainz.mpg.de/~gelessus/group.html

Point group tables site

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