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Molecular orbitals and symmetry

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Outline. Book 2, chapter 7Test on Monday will cover chapter 7 from book 2Symmetry of atomic orbitals (central atom)Symmetry adapted linear combinations (SALC, pendant atoms). 2. Symmetry of atomic orbitals (central atom). s orbitals are symmetric with respect to all symmetry operationstrans
Molecular orbitals and symmetry

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1. Molecular orbitals and symmetry

2. Outline Book 2, chapter 7 Test on Monday will cover chapter 7 from book 2 Symmetry of atomic orbitals (central atom) Symmetry adapted linear combinations (SALC, pendant atoms) 2

3. Symmetry of atomic orbitals (central atom) s orbitals are symmetric with respect to all symmetry operations transform as the totally symmetric representation (listed first in the character table) p orbitals transform as the x, y, z coordinates d orbitals transform according to the species of their corresponding direct product note the simplification for 2z2-x2-y2 (z2) 3

4. The s framework in AB4 (Td) 4

5. Hybrid orbitals 5

6. Localized molecular orbital approach 6

7. Delocalized MO approach

8. Symmetry adapted linear combinations (SALCs) 8

9. 9

10. 10

11. Generalized approach to construct SALCs (1) 1. Use the directional properties of potentially bonding orbitals on the outer atoms (shown as vectors on a model) as a basis for a representation of the SALCs in the point group of the molecule. 2. Generate a reducible representation for all possible SALCs by noting whether vectors are shifted or non-shifted by each class of operations of the group. Each vector shifted through space contributes 0 to the character for the class. Each non-shifted vector contributes 1 to the character of the class. A vector shifted into the negative of itself (base non-shifted but tip pointing in the opposite direction) contributes -1 to the character for the class. 11

12. Generalized approach to construct SALCs (2) 3. Decompose the representation into its component irreducible representations to determine the symmetry species of the SALCs. The number of SALCs, including members of degenerate sets, must equal the number of atomic orbitals (AOs) taken as the basis for the representation. 4. Determine the symmetries of potentially bonding central-atom AOs by inspecting unit vector and direct product transformations listed in the character table of the group. Remember that an s orbital on a central atom always transforms as the totally symmetric representation of the group. 5. Central-atom AOs and pendant-atom SALCs with the same symmetry species will form both bonding and antibonding LCAO-MOs (LCAO = Linear Combination of Atomic Orbitals). 6. Central-atom AOs or pendant ?atom SALCs with unique symmetry (no species match between AOs and SALCs) form non-bonding MOs. 12

13. Constructing MO diagrams 1. Bonding MOs always lie lower in energy than the antibonding MOs formed from the same AOs. 2. Non-bonding MOs tend to have energies between those of bonding and antibonding MOs formed from similar AOs. 3. p interactions tend to have less effective overlap than sigma interactions. Therefore, p-bonding MOs tend to have higher energies than s-bonding MOs formed from similar AOs. 4. MO energies tend to rise as the number of nodes increases. Therefore, MOs with no nodes tend to lie lowest and those with the greatest number of nodes tend to lie the highest in energy. 5. Among s-bonding MOs, those belonging to the totally symmetric representation tend to lie lowest. 13

14. Photoelectron spectrum of methane 14

15. Notes about the PE spectrum of CH4 PE spectrum does not show the band arising from the two 1s C electrons. The delocalized MO approach predicts that there are 2 different energies with a population ratio of 3 : 1. The absence of 4 equal energy pairs can be seen as a necessary consequence of methane?s Td symmetry. Since the highest dimension irreducible representations in Td are triply degenerate (T1 and T2), there can be no higher than 3-fold degeneracy among the MOs. 15


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