Problem 1 (1 point) Three center four electron (3c/4e) bonds were introduced in class. John F. Berry (Dalton Trans. 2012, 41, 700-713) discusses the effect of the larger density of states for the 3c/4e interaction than for the 2c/2e case. The 3c/4e system is expected to be not only more reactive than the 2c/2e system, but also more diverse in reactivity. To illustrate this concept, consider H 2 and [H 3 ]. 1. Sketch the MO diagram of H 2 and assign Mulliken symbols for all molecular orbitals. Write down all possible electronic configurations of H 2. Obtain all electronic states clearly indicating the configuration they correspond to and predict their relative energy. 2. Sketch the MO diagram of [H 3 ] and assign Mulliken symbols for all molecular orbitals. Write down all possible electronic configurations of [H 3 ]. Obtain all electronic states clearly indicating the configuration they correspond to and predict their relative energy. Problem 2 (2 points) The structure of [Mo 2 Cl 8 ] 4 is shown below. 1. Determine the point group of the molecule, the oxidation state, and the d-electron count of each Mo center. 2. Starting from the molecular orbital diagram of the [MoCl 4 ] fragment, sketch the molecular orbital diagram of [Mo 2 Cl 8 ] 4. Populate with electrons. Label each MO with the symmetry of the Mo Mo interaction. Sketch the HOMO and the LUMO of the molecule. 3. Assign Mulliken symbols to the HOMO and the LUMO of the molecule. 4. Consider the lowest energy and spin allowed electronic transition of this molecule. Write down the electronic configuration of the ground state and the excited state. From this, obtain the symmetry and the multiplicity of the ground state and the excited state. 5. Determine whether this transition is electric-dipole allowed with z polarization and with xy polarization. 6. The vibrations of [Mo 2 Cl 8 ] 4 transform as 3A 1g + 2B 1g + B 2g + 3E g + A 1u + 2A 2u + B 1u + 2B 2u + 3E u. Which of these vibrational modes may couple to give rise to vibronicly allowed transitions with z and xy polarized light? 1
Problem 3 (3 Points) Consider the following electronic spectrum of [PtCl 6 ] 2-. For this question, consider only the spectrum collected at 77 K (dashed line). Vertical scales are different for the left and right sides (in M -1 cm -1 ). [PtCl 6 ] 2- Solid line: 300 K Dashed line: 77 K a. Based on intensity, assign the three features as spin forbidden, spin allowed orbitally forbidden, or fully allowed. What is the origin of these transitions? (d-d, MLCT, LMCT) b. Determine the Pt oxidation state and d-electron count of this ion. List the first four (if applicable) spin-allowed d-d transitions that you expect for this ion in the correct field strength limit (using the appropriate Tanabe-Sugano diagram). c. What is the lowest-energy d-d transition (represented in state symbols) that you might see if the spin-selection rule is ignored? d. To explain the high intensity band do the following. Consider that the highest occupied ligandbased orbitals are of T 1u and T 2g symmetry. Determine the electron configuration for the lowest energy transition that is orbitally allowed. Identify the ground and excited states for this transition. e. The spectrum of [PtBr 6 ] 2- is shown below. Propose an explanation for the energy difference compared to [PtCl 6 ] 2- of the highest intensity bands based on the properties of the ligands. 2
[PtBr 6 ] 2- Solid line: 300 K Dashed line: 77 K f. Using the appropriate Tanabe-Sugano diagram, list the first four (if applicable) spin allowed d- d transitions for the following two ions: i. [Mn(CN) 6 ] 3- ii. [MnF 6 ] 3- g. Consider octahedral [Cu(H 2 O) 6 ] 2+. Draw the d-orbital splitting diagram, label with Mulliken symbols, and populate with electrons. How many spin-allowed d-d transitions do you expect for this ion? h. Three features attributable to d-d transitions can be resolved in the electronic spectrum for [Cu(H 2 O) 6 ] 2+. Propose a structural distortion that lowers the symmetry of this ion, and assign the new point group. i. Draw the new d-orbital splitting diagram corresponding to this new structure (consider aquo ligands as σ-donors and very weak π-donors). j. List the ground state for this distorted ion. Provide electron configurations and corresponding state symbols for the possible excited states. Provide an explanation for why three transitions are observed for this distorted ion. If coupling with a vibration is required to make any transitions vibronically allowed, indicate the symmetry of the vibrational mode required. 3
Problem 4 (2 points) a. Consider the following V III complexes: V(H 2 O) 3+ 6, VF 3-3- 6, and VCl 6. The table below contains the energies corresponding to the two lowest spin-allowed d-d transitions (υ 1 and υ 2 ). Assign the state symbols corresponding to these two transitions and fill in the table heading with the transition. b. Use the included Tanabe-Sugano Diagram to determine B and Δ o and complete the table below. (Estimate Δ o /B to the nearest 0.5) υ 1 (cm -1 ) υ 2 (cm -1 ) V(H 2 O) 3+ 17,800 25,700 [VF 6 ] 3+ 15,100 23,600 [VCl 6 ] 3+ 11,000 18,020 Ratio of υ 2 /υ 1 B (Racah Parameter) (cm -1 ) Δ o (cm -1 ) c. Rationalize the observed trends in B and Δ o values in terms of ligand properties. 4
Problem 5 (2 points) a. Sketch the four MOs corresponding the π-system of butadiene from the basis set of the four p- orbitals perpendicular to the plane of the molecule. Rank them in order of increasing energy, and indicate which orbitals are filled. b. Consider the electrocyclic ring opening of a substituted cyclobutene, shown below. Depending on the symmetry properties of the transition state of the molecule, different products can be envisioned, two which arise from a disrotatory process, and one which arises from a conrotatory process. What is the characteristic symmetry element of each process? What is the point group corresponding to the reaction coordinate for each process? (consider R=H and the movement of atoms as the reaction proceeds) c. This electrocyclic ring-opening reaction produces two π-bonds from a π-bond and a σ-bond. For the orbital reaction scheme transforming the σ-bond, determine if a conrotatory or disrotatory process is shown below. Next, draw the product corresponding to the opposite process. In the point group corresponding to each process, assign the Mulliken symbol of these two products. 5
d. Below are sketched the two σ and π orbitals of cyclobutene (corresponding to the π-system of butadiene) that are participating in the cyclization. Label them (σ, σ*, π, π*) and order them based on their energy. e. Draw the orbital correlation diagram for the conrotatory and disrotatory ring opening of cyclobutene. Start with the four orbitals of cyclobutene in the center of the diagram (energy order determined in part d). Correlate these orbitals to those of butadiene (determined in part a) in a disrotatory process to the left and a conroratory process to the right, making sure to order the orbitals correctly based on their energy in the starting material and product. Include Mulliken symbols in the point group of each process. Explain whether, based on this diagram, a conrotatory or disrotatory process is thermally allowed. f. Draw the state correlation diagram for the conrotatory and disrotatory ring opening of cyclobutene. Use only three states of cyclobutene: ground state, singlet first excited state, and a higher singlet excited state that corresponds to the electron configuration of one of the low-lying states in the butadiene products (ground state or first excited state). Include electron configurations and state symbols. Explain whether, based on this diagram, a conrotatory or disrotatory process is thermally allowed. What about from the first excited state of cyclobutene? 6
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