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Unformatted text preview: 1s with F 2pz). For more complex systems, determining which orbitals can interact is greatly facilitated by assigning symmetry labels to them. Why is this? We have already employed the idea that: Orbitals (whether AOs, GOs, or MOs) must have the SAME SYMMETRY in order to combine. Therefore, if symmetry labels are assigned to all orbitals and group orbitals, ones are capable of combining can be determined. How do we go about assigning symmetry labels to orbitals in a given molecule? We will use the ideas of group theory and character tables. Group Theory Method for Determining Molecular Orbitals Steps for assigning symmetry labels to orbitals: 1.
2.
3. Determine the point group of the molecule Place the molecule in the Cartesian coordinate system. ↳ The z
axis should be the highest order rota0on axis. Find the character table for that point group If the molecule is in the C∞v or D∞h point group, use the C2v or D2h character table instead of the C∞v or D∞h character table. 4. By visual analysis of the eﬀect of each symmetry opera0on in the point group on each orbital or GO, determine which irreducible representa0on and symmetry label corresponds to each orbital. 5. IF the orbital or GO you are analyzing does NOT correspond to any of the irreducible representa0ons in the character table corresponding to the molecule’s point group, then the orbital is not a valid orbital for that molecule! Assigning Symmetry Labels to the Orbitals in CO2 1. Determine the point group for CO2: Point group = D∞h (this is a linear triatomic molecule like FHF
!) 2. Place the molecule in the Cartesian coordinate system Highest order axis is z
axis = OCO axis 3. Find the appropriate character table: use the D2h character table rather than the D∞h character table. 4. Determine irreducible representa0ons and symmetry labels for each orbital. The D2h point group contains the following symmetry elements: E, C2(z), C2(y), C2(x), i, σ(xy), σ(xz), σ(yz). Determine the character of each of the GOs for the oxygen atoms in CO2 with respect to each of these symmetry elements. That will give their labels. x O
y C O z x O C Group Orbitals for CO2 O z y In
Phase Combina0ons Out
of
Phase Combina0ons ϕA  ϕB ϕA + ϕB py + py py
py 2p px + px 2p pz + pz px
2x pp
pz
pz s + s 2s
F H F 2s
F HFF H F s
s 2s F H F Assigning Symmetry Labels to the Orbitals in CO2 A comment about the Labels in the D2h Character Table D2h E C2(z) C2(y) C2(x) i σ(xy) σ(xz) σ(yz) Ag 1 1 1 1 1 1 1 1 x2, y2, z2 B1g 1 1...
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This note was uploaded on 03/28/2014 for the course CHM 2311 taught by Professor Richardson during the Winter '09 term at University of Ottawa.
 Winter '09
 richardson
 Atom, Mole

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