Chem 673, Problem Sets 4 & 5 Due Tuesday, December 3, Problems from Carter: Chapter 6: 6.1, 6.3, 6.7, 6.9 Chapter 7: 7.2a,b,e,g,i,j, 7.

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1 Chem 673, Problem Sets 4 & 5 Due Tuesday, December 3, 2013 Problems from Carter: Chapter 6: 6.1, 6.3, 6.7, 6.9 Chapter 7: 7.2a,b,e,g,i,j, 7.6, (1) Use the angular overlap table given on the back page of this homework set to show that... (a) The two e SALCs constructed from 3 σ-donors that form an equilateral triangle in the xy-plane have equal overlaps with px and py orbitals placed at the center of the triangle. (b) The two e SALCs constructed from 3 σ-donors that form an equilateral triangle in the xy-plane have equal overlaps with a dx2-y2 and dxy orbitals placed at the center of the triangle. (c) The two eg SALCs constructed from 6 σ-donors that form an octahedron (with ligands placed on the ±x, ±y, ±z axes have equal overlaps with a dx2-y2 and dz2 orbitals placed at the center of the octahedron. Now, (d) evaluate the overlaps of all 5 SALCs you find for 5 σ-donors that form a trigonal bipyramid (with 3 σ-donors forming an equilateral triangle in the xy-plane and two σ-donors on the ±z axis) with each of the 5 d orbitals. (2) The molecule shown below is an example of a metallacyclobutadiene. Unlike butadiene itself (see the Perturbation Theory handout), there is little difference in the C C or Re C bond distances within the ring. Starting with a d-orbital splitting diagram for an octahedral complex, show the expected energy level shift of the d levels for this complex. Count the bisdehydropropenyl ligand as anionic (as illustrated), so that the Re has a d-count of 6. Take into account the effect on σ and π bonding when replacing two cis-co ligands on a d6 M(CO)6 complex with the illustrated fragment (think about the bond lengths and angles too). Why is there no significant bond alternation? (3) For each of the following pairs of molecules and ions, sketch a d-orbital splitting diagram for the parent species and the substituted derivative. Draw the diagrams for each pair side-by-side and show how the orbital energies are expected to change on going from parent to derivative. Use the spectrochemical series to

2 guide you; recall that CO is a π acceptor and the oxo ligand is a strong π donor. (Explain your answers.) (a) [Co(NH3)6] 3+ trans-[co(nh3)4cl2] + (b) [PtCl4] 2 trans-ptcl2(nh3)2 (c) Mo(CO)6 trans-[moo2(co)4] (the d-count changes, oxide is a good π- donor) (d) [Mo(CN)6] 3 cis-[moo2(cn)4] 2 (the d-count changes) (4) Hydride (H ) ions can be doped into other salts as substitutional impurities. The figure at right shows the local vibrational transitions associated with (a) the substitution of H for F in fluorite (CaF2) and (b) the substitution of H for I in KI. In each diagram the solid line vertical arrows indicate the allowed IR transitions and the dashed line vertical arrows indicate transitions observed in the Raman spectra. For (a) and (b), derive the expected fundamental(s), 1 st overtone (2 quanta), and 2 nd overtone (3 quanta only for (a)) symmetries expected for this defect, assuming the surrounding CaF2 matrix participates to a negligible extent in the vibrations of the trapped hydride. Assign the symmetries of as many of the vibrational modes shown as possible from the information given. (5) The IR and Raman spectra of matrixisolated CrF 2, TiF 2 and CrF 3 are summarized below. What can you deduce about the geometries these three molecules? Compound IR/cm 1 Raman/cm 1 CrF 2 654, pol CrF 3 749, 177, pol TiF 2 740, 643, 171 no data

3 (6) The free-ion terms are split in an octahedral field in the manner given in the table below. (a) Using formulas given in class and in the handouts and notes, verify the results given for the D and H states. (b) For all the states, add two more columns to the table for D4h and D3h point groups. (You can sometimes save work by choosing an appropriate subgroup.) Splitting of the Free-Ion terms of d n configurations in an Octahedral G Field Free-Ion Term S P D F G H I A1g T1g Eg + T2g Terms in Oh A2g + T1g + T2g A1g + Eg + T1g + T2g E1g + 2T1g + T2g A1g + A2g + Eg + T1g + 2T2g (7) Read the Perturbation Theory and Subgroups handout before attempting this problem. In part (a) below, do the group-subgroup orbital correlations before applying perturbation theory it saves a lot of time (a) Construct an orbital correlation diagram that connects the d orbital levels of an octahedral ML 6 complex with those for a trigonal prismatic ML 6 complex (assume the ligands, L, are σ- donors). The diagram depicted below describes the motion that interrelates these two geometries. Note that the coordinate system used is not the conventional coordinate system for the octahedron, and though this does change the labeling of the Cartesian d orbitals for the octahedron, it doesn t change their symmetry, their form with respect to the ligands, or the d-orbital diagram. Assume that the motion is a pure rotation of the lower three ligands (the angles between the M-L bonds and the z-axis does not change). Be sure to label the irreducible representations for the orbitals in the initial, final, and intermediate geometries for rotation of the face shown.

4 $ $ (7) The wavefunctions for the four states arising from the (a 2u ) 2 (e g ) 2 configuration of cyclobutadiene (CB) are given at the bottom of p. 7 of the Antisymmetry handout. (a) Following the methods described on pp. 8-10, write expressions for the energies of all four states. To give the full answers for the 1 A 1g and 1 B 2g states, you will need to consider an integral not considered in the text (the + signs apply to the 1 A 1g state and the signs apply to the 1 B 2g state): ± ( ϕ a (1)ϕ a (2))H ( ϕ b (1)ϕ b (2))dτ 1 dτ 2 = ±e 2 ϕ a ϕ b (1) ϕ a ϕ b (2) dτ r 1 dτ 2 = ±K ab 12 (Explain why no one-electron terms survive.) (b) Find the Hückel π-orbital energies and orbitals for trimethylenemethane (TMM) which, like CB, is also a diradical: (c) Derive the symmetry of the all the states (singlets and triplets) that arise from the ground state configuration of TMM. (d) Following the methods described in this document, write expressions for the π orbital wavefunctions and energies of all the states. (e) Derive expressions for the energy gap between the triplet and the lowest-energy singlet for CB and TMM. (f) Only one of these two systems is thought to be a robust triplet. (A robust triplet is one for which the singlet-triplet gap is fairly large, perhaps 40 kj/mol or more.) From your results in part e, which do you think is the robust triplet and why? (You ll want to think about the nature of the parameters that go into the expressions you found for the energy gaps and to take into account the differences in the orbitals involved)

5 (8) The absorption spectra shown here are for trans-[crf2(en)2]clo4. Your task is to apply the same kind of the detailed treatment of the [trans- CoCl2(en)2] + ion given in class (including corrections) and in Cotton s text (Chemical Applications of Group Theory) to this case. Download and read the paper in which this data was reported (Inorg. Chem., 9, 188 (1970).) Green: T = 295 K; black: 4K. (a) What are the symmetries of the expected spin-allowed d-d transitions for this D4h ion? (Derive them all.) Show how these electronic transitions descend from transitions in an Oh ion. (b) What vibrational modes of the CrN4F2 core can possibly be involved in vibronic coupling? (c) Which transitions are vibronically allowed for z- or xy-polarized light? (d) When this paper was reported, there had been no report of the structure of trans- [CrF2(en)2]ClO4. Nevertheless, the authors confidently suggest that the bands at 21.7 and 29.3 kk are due to the 4 B1g 4 B2g and 4 B1g 4 A2g transitions ( kk is an old notation, 1 kk = 1 kilokayser = 1000 cm 1 ). Fully explain the basis of their confidence. (e) To the extent possible, assuming the authors confidence is justified, fully explain their assignment for the four transitions below 35,000 cm 1 in this figure. Be clear about how these transitions are related to analogous transitions for an octahedral complex (i.e., show how they descend from the transitions you can deduce from the Tanabe-Sugano diagram.) (f) For the ground state and each of the 4 A2g and 4 B2g excited states, it is possible to write a single-configuration wavefunction expression (for the MS = 3 /2 spin component) which can be written in graphical form for each state with spin-up arrows in particular orbitals. Since the descent of each of these states can be traced back to different Oh symmetry states, it is easy to get an expression for the energy difference between these states in an Oh ion. Using the methods illustrated in class and the formulas in the appendices of the Antisymmetry handout, find expressions for the transition energies from the ground state to the first two spin-allowed excited states for an Oh Cr(III) ion. Your answers should involve Racah parameter(s) and o (= 10 Dq). What is the energy difference between the two excited states? (g) One of the transition energy expressions you found in part (f) is an overestimate which one is it? [Hint: Look at all the quartet states in the Tanabe-Sugano diagram.] (h) For the D4h complex, derive expressions for the transition energies from the ground state to the 4 A2g and 4 B2g excited states. Your answers should involve Racah parameter(s) and d- orbital energy differences (supply a molecular orbital diagram for the D4h complex with those

6 energy differences clearly labeled). What is the energy difference between the two excited states? (i) Hitchman is a coauthor of this paper, but in the more recent book Ligand Field Theory and its Applications, he gives rather different values for the parameters B for [Cr(en)3] 3+ and [CrF6] 3 : they are respectively 639 cm 1 and 896 cm 1. These values suggest that the B value these authors used for trans-[crf2(en)2] +, 625 cm 1, may be far too small. If the weighted mean of the two prior values, 725 cm 1, had been used, how might the conclusions the authors reached concerning the relative σ- and π-donor strengths of F and en be changed?

7 Some Useful Overlap Integrals Between Central-Atom s, p, and d Orbitals and Ligand σ and π Orbitals a,b S(s,σ ) = S σ S(s,π S(z,σ ) = HS σ S(z,π ) = IS π S(z,π S(z 2,σ ) = 1 (3H 2 1)S 2 σ S(x 2 y 2,σ ) = 3 (F 2 G 2 )S 2 σ S(xy,σ ) = 3FGS σ S(xz,σ ) = 3FHS σ S( yz,σ ) = 3GHS σ S(z 2,π ) = 3HIS π S(z 2,π $ S(x 2 y 2,π ) = HIS π S(x 2 y 2,π S(xy,π S(xy,π ) = IS π S(xz,π ) = (I 2 H 2 )S π S(xz,π S( yz,π S( yz,π ) = HS π F = sinθ cosϕ G = sinθ sinϕ H = cosθ I = sinθ a π is a ligand π orbital with an axis lying in a plane containing the z-axis and the ligand; π is a ligand π orbital with an axis perpendicular to this plane. b For p z, d z 2, f xyz, etc. we use z, z 2, xyz, etc. c Ligand lies in the xz plane. For more general cases, a more complete table is needed. Reproduced from Burdett, Molecular Shapes, Table 1.1.