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1. Use a group theoretical approach to propose a molecular orbital scheme for the electron network of trimethylenemethane. Trimethylenemethane has a planar, D3 3h, structure. H₂C =CH₂ a. Using the three 2p, orbitals on the terminal C atoms as a basis, generate a reducible representation. Note that the z-axis is perpendicular to the plane of the page. Reduce this representation to its component irreducible representations. You should end up H₂C with one non-degenerate irreducible representation and one doubly degenerate irreducible representation. - b. Use projection operators to project out the appropriate linear combinations of the basis orbitals to make reasonable SALCs. To obtain the non-degenerate SALC, use the projection operator on Q₁. For the doubly degenerate pair, one SALC can be obtained by using the appropriate projection operator on ₁. The second can be obtained by using the appropriate projection operator on (9₂ 93). Sketch the resulting SALCs. c. Sketch the four molecular orbitals. You will get one bonding MO, one antibonding MO and two non-bonding MOS. d. Sketch a plausible MO diagram for the species. Place the proper number of electrons in the diagram. One resonance structure of trimethylenemethane is shown.

1. Use a group theoretical approach to propose a molecular orbital scheme for the electron network of trimethylenemethane. Trimethylenemethane has a planar, D3 3h, structure. H₂C =CH₂ a. Using the three 2p, orbitals on the terminal C atoms as a basis, generate a reducible representation. Note that the z-axis is perpendicular to the plane of the page. Reduce this representation to its component irreducible representations. You should end up H₂C with one non-degenerate irreducible representation and one doubly degenerate irreducible representation. - b. Use projection operators to project out the appropriate linear combinations of the basis orbitals to make reasonable SALCs. To obtain the non-degenerate SALC, use the projection operator on Q₁. For the doubly degenerate pair, one SALC can be obtained by using the appropriate projection operator on ₁. The second can be obtained by using the appropriate projection operator on (9₂ 93). Sketch the resulting SALCs. c. Sketch the four molecular orbitals. You will get one bonding MO, one antibonding MO and two non-bonding MOS. d. Sketch a plausible MO diagram for the species. Place the proper number of electrons in the diagram. One resonance structure of trimethylenemethane is shown.

Principles of Modern Chemistry
Principles of Modern Chemistry
8th Edition
ISBN:9781305079113
Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Chapter6: Quantum Mechanics And Molecular Structure
Section: Chapter Questions
Problem 39P: The photoelectron spectrum of HBr has two main groups of peaks. The first has ionization energy...
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1. Use a group theoretical approach to propose a molecular orbital scheme for the electron network of trimethylenemethane. Trimethylenemethane has a planar, D3 3h, structure. H₂C =CH₂ a. Using the three 2p, orbitals on the terminal C atoms as a basis, generate a reducible representation. Note that the z-axis is perpendicular to the plane of the page. Reduce this representation to its component irreducible representations. You should end up H₂C with one non-degenerate irreducible representation and one doubly degenerate irreducible representation. - b. Use projection operators to project out the appropriate linear combinations of the basis orbitals to make reasonable SALCs. To obtain the non-degenerate SALC, use the projection operator on Q₁. For the doubly degenerate pair, one SALC can be obtained by using the appropriate projection operator on ₁. The second can be obtained by using the appropriate projection operator on (9₂ 93). Sketch the resulting SALCs. c. Sketch the four molecular orbitals. You will get one bonding MO, one antibonding MO and two non-bonding MOS. d. Sketch a plausible MO diagram for the species. Place the proper number of electrons in the diagram. One resonance structure of trimethylenemethane is shown.
Transcribed Image Text:1. Use a group theoretical approach to propose a molecular orbital scheme for the electron network of trimethylenemethane. Trimethylenemethane has a planar, D3 3h, structure. H₂C =CH₂ a. Using the three 2p, orbitals on the terminal C atoms as a basis, generate a reducible representation. Note that the z-axis is perpendicular to the plane of the page. Reduce this representation to its component irreducible representations. You should end up H₂C with one non-degenerate irreducible representation and one doubly degenerate irreducible representation. - b. Use projection operators to project out the appropriate linear combinations of the basis orbitals to make reasonable SALCs. To obtain the non-degenerate SALC, use the projection operator on Q₁. For the doubly degenerate pair, one SALC can be obtained by using the appropriate projection operator on ₁. The second can be obtained by using the appropriate projection operator on (9₂ 93). Sketch the resulting SALCs. c. Sketch the four molecular orbitals. You will get one bonding MO, one antibonding MO and two non-bonding MOS. d. Sketch a plausible MO diagram for the species. Place the proper number of electrons in the diagram. One resonance structure of trimethylenemethane is shown.
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