1

Chem 324 Fall 2016 Problem Set 4 ANSWERS October 11, 2017

This problem set focuses on content from lecture note set 6 and 7.

From the textbook (H&S, 4th ed.) Self-Study exercises: p684, Q2; d1 configuration:

ms ml

1/2 2

1/2 1

½ 0

½ -1

½ -2

-1/2 2

-1/2 1

-1/2 0

-1/2 -1

-1/2 -2

The first five microstates arise from an S= ½, L=2 term. The second set also comes from an S= ½, L=2 term. Both terms are 2D. The are differentiated by the J value. The two terms are 2D5/2 and =2D3/2

p687,left column, Q3;

X=3, l= 1 so # microstates = 6! = 20 3! 3! p691, Q1,2,3;

1. Spin selection rule is ΔS = 0

p694 Q1,2,3; see references to answers on p694 and lecture notes p701 Q1,2,3

1. μeff of 1.77 is consistent with one unpaired electron. The complex has V(IV) which is d1 so all is good.

2. The complex has Cr in the +2 oxidation state so d4. If it were LS, S = 1 and μS would be 2.83 and an orbital contribution would probably lead to μeff just over 3. If HS, S= 2 μS would be 4.9 so the complex must be high spin because μeff = 4.85 BM

2

3. This complex is V(II) so d3, S = 3/2 and expect (and see) μS of about 3.9. End-of-chapter problems:

3

4

5

20.24

6

7

20.36b

20.37b

8

9

10

Additional problems 1. K4[Ni(CN)4] is a bright yellow salt that contains an unusual example of a low oxidation state nickel complex. (a) Name the type of electronic transition that is responsible for the yellow colour of this complex, and (b) explain why the colour is so intense. (Illustrate your answer with relevant, clearly labeled energy diagram(s) showing the orbitals that participate in the transition(s).) Must be MLCT because this is Ni(0), d10 – no dd or LMCT transitions possible. The intenseness of the colour is because it’s a CT transition (spin and Laporte allowed)

2. Consider the complex [Cr(en)3]3+. (a) (i) Draw a clear, fully labeled, partial Orgel diagram (just draw the half that is relevant) to indicate the number of absorption peaks you would expect to see due to d-d transitions in the electronic spectrum of this chromium complex. (ii) Write the expression describing each electronic transition using the appropriate term symbols.

Cr(III), d3, octahedral ν1

4T2g 4A2g ν2

4T1g(F) 4A2g ν2

4T1g(P) 4A2g note the use of (F) and (P) to disintguish the two T1g excited states.

11

(b) The experimentally observed electronic absorption spectrum for this chromium complex shows two broad peaks, with νmax at 20,000 cm–1 and 27,000 cm–1, respectively. Explain why this is different from your prediction in part (a). The peaks most likely correspond to ν1 and ν2 respectively – ν3 may be too high in energy to be observed. (c) Do you have sufficient information to find the value of ΔO for [Cr(en)3]3+? Explain. Yes. For this Orgel diagram ΔO = ν1 = 20,000 cm-1) 3. Match the following complexes with the most likely value of the magnetic moment. Explain your answers. Complexes Magnetic Moments [Ni(terpy)2]Br2 0.0 Fe(acac)3 2.8 Na[Cr(CH2SiMe3)4] 5.9 CoCl(PPh3)3 4.2 [Ni(terpy)2]Br2 octahedral d8, so two unpaired electrons, S=1, so moment = 2.8 Fe(acac)3 octahedral d5 high spin , S=5/2, moment = 5.9 (none of the others can have S=5/2 so

that’s why this one must be HS not LS Na[Cr(CH2SiMe3)4] tetrahedral Cr(III), d3 high spin (tetrahedral), S=2 μS = 3.87 but predict some sort of

orbital contribution so the most likely moment is 4.2 CoCl(PPh3)3 tetrahedral or square planar Co(I), d8. Given that the only moment choice left here is 0,

must be square planar.

4. In the electronic absorption spectrum of an octahedral complex, what is the relationship between λmax and the

preference for high spin or low spin configuration? What is the relationship between εmax and high spin/low spin

preference?

The larger λmax is, the smaller ΔO is, and the stronger the preference for high spin.

There is NO RELATIONSHIP between εmax and HS/LS preference.

5. Place the following five compounds in a list ordered according to the intensity of their visible spectra (i.e. the first complex in the list should be the least intensely absorbing and the last complex in the list should be the most intensely absorbing). Provide explanations for your answers. You may assume that the six-coordinate complexes are octahedral and the four-coordinate complexes are tetrahedral.

12

Comments rank [CoF4]2- d7 tetrahedral; dd spin and Laporte allowed; ε~100 4 [Cr(en)2(NH3)2]3+ d3 octahedral; dd spin allowed, Laporte forbidden: ε~10 3 [WO4]2- d0 tetrahedral; LMCT possible (think MnO4

-) ε ~10,000 5 Ni(PPh3)4 d10 tetrahedral; no dd or LMCT; no dd or CT; ε ~ 0 1 [Fe(trien)(H2O)2]3+ d5 high spin octahedral; dd spin and Laporte forbidden; ε ~0.01 2 6. The following complexes have the following d-d transitions:

[Ni(acac)3]- 8,500; 13,500; 25,300 cm-1 [Co(en)(trien)Cl]+ 8,000; 16,000; 19,400 cm-1

Discuss the spin-allowed ground and excited states, and assign all transitions in both complexes. Give the value of Δo for each complex. [Ni(acac)3]- octahedral Ni(II), d8. Ground state is 3A2g ν1 8,500 cm-1 3T2g 3A2g ν2 13,500 cm-1 3T1g(F) 3A2g ν3 25,300 cm-1 3T1g(P) 3A2g

ΔO = ν1 = 8,500 cm-1 [Co(en)(trien)Cl]+ octahedral Co(II), d7 HS. Ground state is 4T1g ν1 8,000 cm-1 4T2g 4T1g ν2; 16,000 cm-1 4T1g 4T1g ν3 19,400 cm-1 4A2g 4T1g

ΔO = ν3 -ν1 = 11,400 cm-1 7. Give the most likely ground state terms for the following compounds. Assume that six coordinate complexes are octahedral and four coordinate are tetrahedral. (a) [Ni(H2O)6]2+ octahedral Ni(II), d8; 3A2g (b) [Fe(CN)6]3- octahedral Fe(III), d5 LOW SPIN: 2T1g

(c) [FeCl6]3- octahedral Fe(III) d5 high spin : 6A1g

(d) [VCl4]3- tetrahedral V(I), d4 high spin: 5T2

(e) [CoCl4]2- tetrahedral Co(II), d7 high spin: 4A2 (g) [Ni(en)F4]- octahedral Ni(III), d7 high spin: 4T1g (h) [Ru(H2O)6]3+ octahedral Ru (III), d5 LOW SPIN: 2T1g (i) Co(acac)Cl2 (HS) tetrahedral Co(III), d6 high spin: 5E (j) Cu(acac)(NH3)(dien) octahedral Cu(I), d10: 1A1g

8. The electronic spectrum an aqueous solution of [Ni(en)3]2+ exhibits three broad absorption with λmax = 325, 550, and 900 nm. (a) suggest assignments for the electronic transitions. (b) which bands are in the visible region of the spectrum? What region of the spectrum are the bands falling outside the visible? (c) what is ΔO for this complex?

13

[Ni(en)3]2+ octahedral Ni(II), d8. Ground state is 3A2g λ1 900 nm 3T2g 3A2g outside visible (in near infrared) λ 2 550 nm 3T1g(F) 3A2g in visible regions λ 3 325 nm 3T1g(P) 3A2g outside visible (ultraviolet) ΔO corresponds to lowest energy electronic transition, or longest wavelength. λ1 =900 nm. We normally report ΔO in energy units. So 900 nm = 11,111 cm-1.

9. Explain all of the information/observations below for complexes A, B, and C and give the identity of M. Compound “A”: M(H2O)6

3+ one peak in UV-visible spectrum; μeff = 5.5BM Reduction of “A” by one electron gives Compound “B” M(H2O)6

2+ three UV-vis peaks, μeff = 4.5 BM Reaction of “B” with concentrated HCl gives Compound “C” MCl42- three UV-vis peaks, all lower in energy than peaks in “B”. μeff = 3.9 BM Compound A has only one electronic transition, so it must be one of d1, d4, d6, or d9. The large magnetic moment (most likely S = 2 + orbital contribution) rules out d1 or d9. Both d4, d6 could be consistent with data for A. Addition of one electron to “A” gives a species with three UV-vis peaks. This must correspond to d2, d3, d7, or d8 and must correspond to dn+1

for one of our two choices for “A”. This alone means that “A” must be d6 (and therefore “B” is a d7 ion). This is consistent with the UV-vis and the magnetic moment of 4.5 also makes sense because if d7 (HS) we’d predict S=3/2, so μS = 3.9 plus an orbital contribution. The metal is therefore cobalt. Compound C is tetrahedral d7, still expect 3 uv-vis peaks at lower energy (because ΔT < ΔO) and the magnetic moment is now close to the spin only value with an “A” ground state. 10. Complexes of acetylide ligands (RCC-) are isoelectronic to cyanide (NC-). Electronic spectral data for the two complexes shown below are as follows: Complex A has electronic transitions at 244nm, 312 nm, and 375 nm. Complex B has electronic transitions at 275nm, 345 nm, and 496 nm. Determine ΔO for both complexes and comment on where the acetylide ligand should be relative to cyanide in the spectrochemical series.

14

Both complexes are Cr(II), d3, ground state 4A2g. For these complexes, the lowest energy transition (= longest wavelength) will be equal to ΔO. A: longest wavelength = 375 nm = 26,700 cm-1 = Δo B: longest wavelength = 496 nm = 20,200 cm-1 = Δo Since the acetyide complex has a lower Δo than the corresponding cyanide complex, the acetylide ligand should be ranked LOWER in the spectrochemical series than cyanide. 11. The following two compounds – in which both anion and cation have d-block elements – have the following colours: Compound 1: [Mn(H2O)6]5+ [Cu(CN)6]5- violet Compound 2: [Mn(CN)6]- [Cu(H2O)6]+ yellow (a) what is the structural relationship between Compounds 1 and 2? (2) (b) Give a full explanation for the difference in colour of the two compounds. Assume that charge-transfer electronic transitions are not present in either compound. (6)

(a) they are coordination isomers. (b) in both isomers, Mn(V) has 2 d electrons, while Cu(I) has ten. So the colour cannot be coming from the Cu(I) part of the complexes since no d-d transitions can happen at all. The two Mn ions are Mn(H2O)6

5+ and Mn(CN)6-. Both are octahedral with two d electrons, so both have d-d transitions possible. The difference between the two must therefore arise from differences in Δo (Δoct). Cyanide is a strong field ligand so we predict Mn(CN)6- to have a larger Δo,

i.e. absorb higher energy (shorter wavelength) light compared to Mn(H2O)65+ with the weaker field

water ligands. The observed colours of the complexes are consistent with this –the water complex looks violet because it’s absorbing yellow, while the cyanide complex looks yellow because its absorbing violet.

15

12. In certain tetrahedral complexes, e.g. [NiCl4]2- or MnCl4 there can be some ambiguity in assignment of the two highest energy electronic transitions of their uv-vis spectra. Explain. The relevant Orgel diagram is shown below. Both ions listed above are tetrahedral and are d8 and d3 respectively. As such the spectroscopy makes use of the right hand side of this diagram. The value of ΔT may place it to the LEFT of the T1g/A2g crossing point (circled in blue) or to the right of it. The positioning of ΔT with respect to this point determines which of ν2 and ν3

correspond to transitions from the T1 ground state to the T1 or A2 excited state. For example, if ΔT is to the left of the crossing point in the diagram, then ν3 corresponds to a T1 T1

transition, whereas if ΔT is to the right of the crossing point then ν3 corresponds to a A2 T1 transition.

13. Describe three different ways in which the magnetic moment of a transition metal complex may change with temperature (i.e. what are different origins of deviations from Curie behavior?).

1. Orbital contribution 2. Spin-orbit coupling 3. Spin spin exchange (e.g. in dinuclear complex)