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.

Draw an MO diagram to explain the existence of the trihydrogen cation (H3+). Hint: it forms a cyclic structure. Use individual 1s orbitals from H atoms to form your molecular orbitals (don’t worry about forming LGOs; determine the symmetries of the MOs using the projection operator method and sketch approximate wavefunctions for each). How many electrons are present in this molecule? What is the bond order? What type of bonding is this?

3. Calculate the coefficients c+ and c. and energies E+ and E. for the bonding and anti- bonding H₂ Molecular orbitals. HAA = HBB = -13.6 eV and HAB = -14.3 eV. Assume that SAB = 0.3

1. Give the point group for each of the following molecules: H H H CI F F H H. CI BrH BrH Br Br Br Br CI H. Сyclohexane (chaй) Cyclohexane (boat) Ferrocene (staggard) Ferrocene (eclisped) 2. Give the point group for each of the following atomic and molecular orbitals: 88 dy d22 o bond n bond z antibond sp3

On one-electron oxidation of a five valence electron AH₂ compound (C₂, point group) to a closed shell (no unpaired electrons) four valence electron C₂, cationic species, what is the symmetry of the highest energy occupied molecular orbital, and what happens to the energy of this orbital when the four valence electron AH2 C2y cation changes to a Doch geometry? O 2a₁ and stabilised (decreases in energy) O 2a₁ and destabilised (increases in energy) O 1b2 and stabilised (decreases in energy) O b₁ and no change in energy

3. Assign each molecule or ion to its proper point group. a. cyclopropylene b. aziridine (hint: be very mindful of lone pairs) c. NbF,2-