(a) Assume H₂O is linear, please construct a molecular orbital energy level diagram for "linear" H₂O, and you can use the D₂h point group for convenience. (6%)

21. Fe(η⁵-Cp)(η¹-Cp)(CO)₂ is a classic organometallic complex with two Cp ligands (Cp = C₅H₅⁻ = cyclopentadienyl) having different coordination modes. Note: η¹-Cp is written as κ¹-Cp in the IUPAC convention. (10%)(a) Draw the molecular structure of the complex. Remember to include H atoms and indicate double, triple, and aromatic bonds when necessary. (4%)(b) ¹H NMR spectroscopy of the complex at room temperature only shows two signals, with one from η⁵-Cp and the other from η¹-Cp. Is this result consistent with the molecular structure you draw in (a)? Explain why this is the case and what experiment you would do to verify your explanation. (6%)

(b) Similarly, construct the molecular orbital diagram for bent H₂O. Note: for (a) and (b), please indicate how the H group orbitals interact with the appropriate orbitals of O and label the symmetry of the highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO). (6%)

(c) From these two MO diagrams, would you expect H₂O to be linear or bent? Explain. (3%)

(a) Sketch the structure of the anion as accurately as possible (Hint: is the conformation eclipsed or staggered?) (3%)

(b) Give the oxidation state and d-electron count for Re. (2%)

(c) Estimate the bond order of the Re-Re metal-metal bond. Briefly explain why. (5%)

24. The following table gives the octahedral crystal field splitting energy (Δo) values for Co(III) complexes. Explain the order in terms of the σ- and π-donor and σ- and π-acceptor properties of the ligands. (10%)

25. In a face-centered cubic unit cell, please show that identical atoms occupy 74.0% of the total unit cell volume. (5%)

25. (10 points) The salt LiBr has a Li−Br distance of 275 pm (1 pm = 10⁻¹² m) and has the NaCl structure.(A) (3 points) Draw the unit cell of the molecule.(B) (2 points) How many atoms of Li and Br are there in a unit cell?(C) (2 points) Calculate the mass of a unit cell.(D) (3 points) What is the density of LiBr?

24. (6 points) The following molecule is a monoatomic B(0) molecule reported in 2024 by Pranckevicius and coworkers. The authors draw the following Lewis structure that has a partial double bond between boron and carbon and a radical on boron. List at least three experimental techniques that could be used to support their proposed structure and briefly explain your reasoning.

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