Chapter 5 Answers to Self-test Questions

5.1 What is the colour of the solution giving rise to the spectrum shown in Figure 5.2?

The absorption band in Figure 5.1ST stretches from 1000 to 500 nm, meaning that the red and significant portion of the green parts of the incident light are absorbed, so solutions of [VO(H₂O)₅]²⁺ have a characteristic blue colour.

 

Figure 5.1ST. UV-vis-NIR spectrum of 0.1 M [VO(H₂O)₅]²⁺.

 

5.2

(a) Calculate the absorbance of peaks that have 50%, 10% and 1% transmission.

(b) Calculate the %transmission for peaks with an absorbance of 2, 3 and 4.

 

• For 50% transmission, I_t /I₀ = 0.5, so the absorbance A = −log₁₀(0.5) = 0.30. For 10% transmission, A = −log₁₀(0.1)= 1.00, and for 1% transmission, A = −log₁₀(0.01) = 2.00. (These values show the non-linearity of the transmission scale.)
• An absorbance value of 2 corresponds to 1% transmission, an absorbance value of 3 corresponds to 0.1% transmission and 4 to 0.01% transmission. These values indicate why absorption spectra get very noisy when A is greater than 3, as there are very few photons arriving at the detector.

 

 

5.3 Convert the following wavelength values to their corresponding wavenumber (cm⁻¹) units. 1000 nm, 600 nm, 400 nm, 250 nm. (A useful conversion is the value in nm = 10⁷/cm⁻¹)

1000 nm = 10000 cm⁻¹ (1000 nm = 10⁷/10000cm⁻¹)

600 nm = 16667 cm⁻¹ (16700 cm⁻¹ to three significant figures)

400 nm = 25000 cm⁻¹

250 nm = 40000 cm⁻¹

5.4 Predict which one of the following complexes will have the more intense d-d transitions: cis-[Co(en)₂F₂]⁺ or trans-[Co(en)₂F₂]⁺ (en = H₂NCH₂CH₂NH₂)

d-d transitions are forbidden by the orbital selection rule (Δl = 1) and the bands associated with them are therefore weak. If there is a centre of symmetry (inversion centre) then the Laporte (parity) selection rule which also makes the d-d transitions forbidden is also operative. As trans-[Co(en)₂F₂]⁺ has a centre of symmetry whereas cis-[Co(en)₂F₂]⁺ does not, this indicates the latter will have the more intense d-d bands.

5.5 What sort of coordination environments would be best for a commercial pigment based on d-d transitions in a transition metal complex?

The molar absorptivity (ε_max) is greatest for compounds without an inversion centre. Therefore, amongst the common geometries for transition metal complexes a tetrahedral coordination environment would be the best as this would give the maximum colour per metal centre based on the d-d transitions. To achieve the highest colour density per metal centre, charge transfer bands would be preferable.

5.6 Calculate ε_max for the most intense bands in the other spectra in Figure 5.10.

The molar absorptivities, ε_max, in units of dm³ mol⁻¹ cm⁻¹ are given in red in the spectra in Figure 5.6ST.

 

 
Figure 5.6ST Electronic absorption spectra of aqueous solutions of the first row transition metals, showing the ε_max values in red.

The concentration of the saturated solution of MnCl₂ is assumed to be 3 M. The peak with negative absorbance in this spectrum at 10500 cm⁻¹ in this spectrum is due to an overtone or combination band of water, and because of the very high concentration of the MnCl₂ there is less H₂O in the sample beam than the reference beam. This is also the cause of the missing data below 9000 cm⁻¹.

 

5.7 The spectrum of [TiCl₆]³⁻ has an absorption at 769 nm, that of [TiF₆]³⁻ at 518 nm and [TiBr₆]³⁻ at 877 nm. Calculate Δ_oct (in cm⁻¹) for each of these, and comment on the values.

Each of these complexes is Ti³⁺, and so has a d¹ configuration. As there is only one spin-allowed transition for d¹ configurations, Δ_oct can be read straight from the spectral data. Δ_oct is usually presented in cm⁻¹units, and the values to three significant values are given below.

[TiBr₆]³⁻ at 877 nm, 11400 cm⁻¹

[TiCl₆]³⁻ 769 nm, 13000 cm⁻¹

[TiF₆]³⁻ 518 nm, 19300 cm⁻¹

This corresponds to the order of the ligands in the spectrochemical series (see Section 5.5.3.1)

5.8 Use the spectra of [Ni(H₂O)₆]²⁺ and [Ni(en)₃]²⁺ (en = ethylenediamine, or 1,2-diaminoethane) in Figure 5.20 to determine Δ_oct for these two complexes. Comment on the values obtained.

Both [Ni(H₂O)₆]²⁺ and [Ni(en)₃]²⁺ are octahedral Ni²⁺ complexes with a d⁸ configuration with three spin-allowed transitions. In the case of octahedral d⁸, Δ_oct corresponds to the lowest energy d-d transition. However, some care needs to be exercised as these are not always observable, but as three clear bands with appropriate molar absorptivity values are observed in both spectra, it is reasonable in this case to determine the value of Δ_oct.

Figure 5.8ST Electronic absorption spectra of [Ni(H₂O)₆]²⁺ and [Ni(en)₃]²⁺.

 

In Figure 5.8ST the first peak in the spectrum of [Ni(H₂O)₆]²⁺ is at ca. 8500 cm⁻¹ and that for [Ni(en)₃]²⁺ is at 11250 cm⁻¹. Therefore, Δ_oct for [Ni(H₂O)₆]²⁺ is 8500 cm⁻¹, and Δ_oct for [Ni(en)₃]²⁺ is 11250 cm⁻¹. This is the order of the ligands in the spectrochemical series.

This assignment could be checked with the use of a d⁸ Tanabe-Sugano diagram.

5.9 The spectrum of [Rh(NH₃)₆]³⁺ has two d-d transitions at 32800 and 39200 cm⁻¹, and in the spectrum of [Ir(NH₃)₆]³⁺ they are at 39800 and 46800 cm⁻¹. Estimate Δ_oct for these complexes, and compare the values to that of [Co(NH₃)₆]³⁺.

[Rh(NH₃)₆]³⁺ and [Ir(NH₃)₆]³⁺ are Rh³⁺ (4d⁶) and Ir³⁺ (5d⁶), respectively. As they are 4d and 5d transition elements they are expected to be low spin, and this is confirmed by the presence of two bands in each case. Δ_oct can be estimated for low-spin d⁶ complexes by adding a quarter of the difference between the first two spin-allowed transitions to the lower value.

For [Rh(NH₃)₆]³⁺ the observed d-d transitions are at 32800 and 39200 cm⁻¹, giving Δ_oct = 34400 cm⁻¹

For [Ir(NH₃)₆]³⁺ the observed d-d transitions are at 39800 and 46800 cm⁻¹, giving Δ_oct = 41550 cm⁻¹

Δ_oct for [Co(NH₃)₆]Cl₃ is 23000 cm⁻¹, and the values for [Rh(NH₃)₆]³⁺ and [Ir(NH₃)₆]³⁺ show that Δ_oct increases on going from 3d to 4d to 5d. The explanation is that as the principal quantum number n increases, the orbitals become larger so there is a greater difference between the extent of interaction of the t_2g and e_g metal d orbitals with the ligand orbitals. This increases the energy between the t_2g and e_g metal d orbitals, and hence increases Δ_oct.

5.10 When an excess of NCS⁻ is added to a solution of [Co(H₂O)₆]²⁺, the pale pink solution turns a very deep blue. What does this indicate about the structure of cobalt in the two complexes, and propose a structure for the NCS⁻ complex.

There are two changes reported to the d-d transitions when NCS⁻ is added to a solution of [Co(H₂O)₆]²⁺, the first is that the colour changes from pink to blue, and the second that the intensity changes from pale pink to very deep blue. The first is related to the energy of the transitions and the second to their allowedness, which is dependent on the selection rules. An increase in intensity is usually associated with a relaxation of the selection rules, and for transition metal complexes this is most usually related to the Laporte/parity selection rule, so that the loss of a centre of symmetry (inversion centre) results in greater intensity. As the reaction uses an excess of NCS⁻ it can be assumed that there is total ligand exchange to form tetrahedral [Co(NCS)₄]²⁻ (NCS⁻ can be regarded as a pseudo halide). As there is no inversion centre in tetrahedral complexes the Laporte/parity selection rule is no longer operative so the d-d transitions will be less forbidden and gain intensity. In addition the orbital selection rule (Δl = ±1) is also relaxed as the metal 4p orbitals have the same symmetry as the metal t₂ orbitals and can mix, so the transitions are no longer pure d-d. The change in colour from pink for the octahedral complex to blue for tetrahedral complex is in line with a reduction of Δ on going from octahedral to tetrahedral (Δ_tet = ⁴/₉Δ_oct). However it is not so simple as there are three spin-allowed transitions for each, but not all are in the visible part of the spectrum. (Spectra of [Co(H₂O)₆]²⁺ and [CoCl₄]²⁻ are given in Figure 5.56)

5.11 Calculate ε_max for the d-d peaks in Figure 5.23, assuming a pathlength of 1 cm.

The molar absorptivities, ε_max, can be calculated using the Beer Lambert Law (A= εcl) for the d-d peaks in Figure 5.11ST and are given to two sig. fig in the table below.

	λmax /cm−1	Abs	εmax /dm3 mol−1 cm−1
1.2 mM [Co(NH3)5ONO]Cl2	20500	0.075	63
	29000	0.33	280
1.2 mM [Co(NH3)5NO2]Cl2	22000	0.11	92
	30500	2.2	1800

The change in ε_max is due to differential effects of the nitrito and nitro ligands on the orbital and Laporte/parity selection rules.

5.11ST Electronic absorption spectra of isomerisation of 1.2 mM solution of [Co(NH₃)₅(ONO)]Cl₂ to [Co(NH₃)₅(NO₂)]Cl₂ in 0.1 M HClO₄ at 40° C for 90 min. Inserts show spectra of initial and final complexes

5.12 Some iron(II) complexes can be changed reversibly between high-spin and low-spin by changing the temperature because Δ and the electron pairing energy, P, are very delicately balanced. These are known as spin-crossover complexes and the iron(II) examples tend to contain a FeN₆ coordination environment. By consideration of the spectrochemical series suggest ligand donor atoms which might be used to produce spin-crossover complexes of Fe(III).

As the ligand field splitting parameter, Δ, is larger for iron(III) than iron(II), to obtain spin-crossover conditions for iron(III), weaker field ligands than those containing nitrogen will be required. This indicates halogen ligands or those containing sulfur. As a result of this some of the most common iron(III) spin-crossover complexes contain bidentate ligands with two sulfur donor atoms such as dithiocarbamate (S₂CNR₂ or S₂CNRR¢).

5.13 In general, transition metals in high oxidation states become weaker oxidising agents as the Group is descended, as we have seen with [ReO₄]⁻ and [MnO₄]⁻  . Predict a colour and position of the LMCT band in the UV-vis spectrum for the [MoO₄]²⁻ and the [MoS₄]²⁻ ions.

[CrO₄]²⁻ is yellow with a charge transfer transition at 27000 cm⁻¹ (370 nm), so for [MoO₄]²⁻ the analogous charge transfer transition will be at higher energy, so [MoO₄]²⁻ is predicted to be colourless/white. The lowest energy charge transfer transition is at 42700 cm⁻¹ and it is a white/colourless solid. As S²⁻ is easier to reduce than O²⁻ the charge transfer will be at a lower energy in [MoS₄]²⁻ than [MoO₄]²⁻, and is therefore expected to be coloured. The first charge transfer transition in [MoS₄]²⁻ is at 21300 cm⁻¹ and as a result it is a dark orange colour.

5.14 Predict the form of the UV-vis spectrum of CdTe.

What colour would you expect of rutile, TiO₂, that had been chemically modified so that its band gap absorption had a tail that was just in the visible region?

From the pattern in Figure 5.26 it is expected that the absorption edge of CdTe will be at longer wavelength/lower energy than that of CdSe. The band gap for CdTe is ca. 860 nm, which means that it absorbs all visible light and is therefore a black material. CdTe finds use in thin film photovoltaic solar cells, including in some very large photovoltaic power stations.

Pure TiO₂ is colourless as the band gap absorption edge is in the UV part of the spectrum, but when it is chemically modified or doped, the absorption edge can move to lower energy so that the tail is in the visible, and this will give rise to a yellow colouration (see Figure 5.1).

5.15 The first charge transfer absorption band observed in the UV-vis spectrum of the [CoF₆]²⁻ anion is at 28300 cm⁻¹ calculate an optical electronegativity for Co(IV). A new compound was isolated and proposed to contain either the [CoCl₆]²⁻ or [CoCl₆]³⁻ anion. Its first charge transfer band was at 36000 cm⁻¹. Determine which anion is present in this compound.

E_exp = 28300 cm⁻¹ and the optical electronegativity (c_opt) from Table 5.4 for F⁻ is 3.9, therefore using

E_exp = 30000[χ_opt(ligand) − χ_opt(metal)],

χ_opt(Co⁴⁺) = 3.9 − (28300/30000) = 3.0

[CoCl₆]²⁻ contains Co⁴⁺; χ_opt(Co⁴⁺) = 3.0, χ_opt(Cl⁻) = 3.0

[CoCl₆]³⁻ contains Co³⁺; χ_opt(Co³⁺) = 1.8, χ_opt(Cl⁻) = 3.0

E_exp(Co³⁺) = 30000[3.0 – 1.8] = 36000 cm⁻¹

E_exp(Co⁴⁺) = 30000[3.0 – 3.0] = 0 cm⁻¹

This analysis indicates that the calculated first LMCT band Co³⁺ (E_exp(Co³⁺)) at 36000 cm⁻¹ is in excellent agreement with the experimental observation. Therefore, the new compound contains [CoCl₆]³⁻. The optical electronegativities of Co⁴⁺ and Cl⁻ are so similar that the first ligand to metal charge transfer transition is at very low (effectively zero) energy. This means that in practice the Cl⁻ will reduce the Co⁴⁺ (or more intuitively the Co⁴⁺ will oxidise the Cl⁻) permanently, rather than transiently.

5.16 The iron(III)-ruthenium(II) analogue of Prussian blue, Fe(III)₄[Ru(II)(CN)₆]₃.18H₂O, is dark purple with an IVCT band at 495 nm. What does this tell us about the extent of delocalisation in the two materials?

The presence of an IVCT band indicates that there is delocalisation in the mixed iron(III) and ruthenium(II) Prussian blue analogue. The energy of the IVCT band is inversely proportional to the extent of electron delocalisation between the metal centres, i.e. more delocalisation is expected for lower energy IVCT transitions. Therefore, a shift in energy from 680 nm (14700 cm⁻¹) for Fe(III)[Fe(III)Fe(II)(CN)₆].xH₂O (Fe₄[Fe(CN)₆].xH₂O) to 495 nm (20200 cm⁻¹) for Fe(III)₄[Ru(II)(CN)₆].18H₂O indicates a greater extent of electronic localisation in the mixed iron ruthenium Prussian blue analogue, which is in fact dark purple. In the dark green all ruthenium analogue the IVCT band is at 1000 nm (10000 cm⁻¹) indicating greater delocalisation. (J. N. Behera, D. M. D’Alessandro, N. Soheilnia and J. R. Long, Chem. Mater. 21 1922 (2009).))

5.17 Why are the solutions of Tb³⁺ and Yb³⁺ essentially colourless?

In the spectrum of Tb³⁺ in Figure 5.17ST all of the transitions are very weak with very small ε_max values. Apart from a very very weak peak at 20500 cm⁻¹ there are no bands in the visible part of the spectrum (12500 – 26000 cm⁻¹), although there are peaks at 10250 cm⁻¹ in the NIR and a series of weak peaks starting at 26500 cm⁻¹ in the UV.

In the Yb³⁺ spectrum there are no peaks in the visible part of the spectrum, although the tail into the UV may contribute a very weak yellow hue to concentrated solutions.

Figure 5.11ST Electronic absorption spectra of f–f transitions in Pr³⁺, Tb³⁺, Er³⁺, and Yb³⁺ aqueous solutions.

5.18 Determine the spin multiplicity of the atomic fⁿ configurations.

 

fn	Σ	MS	2S+1	name
f0, f14	0	0	1	‘singlet’
f1, f13	½	+½, −½	2	‘doublet’
f2, f12	1	+1, 0, −1	3	‘triplet’
f3, f11	3/2	+3/2, +1/2, −1/2, −3/2	4	‘quartet’
f4, f10	2	+2, +1, 0, −1, −2	5	‘quintet’
f5, f9	5/2	+5/2, +3/2, +1/2, −1/2, −3/2, −5/2	6	‘sextet’
f6, f8	3	+3, +2, +1, 0, −1, −2, −3	7	‘septet’
f7	7/2	+7/2, +5/2, +3/2, +1/2, −1/2, −3/2, −5/2, −7/2	8	‘octet’

 

5.19 Determine the term for total orbital angular momentum L = 4 and total spin angular momentum S = 0.

If L = 4, the total orbital angular momentum is represented by G. If the total spin angular momentum S is 0, then the spin multiplicity, 2S + 1 is 1. Therefore, the term is ¹G.

5.20 The allowed terms for d⁷ are ²H, ²G, ⁴F, ²F, ²D, ²D, ⁴P, ²P, identify the ground term.

There is also a very quick and easy way to determine the ground term for any configuration using Hund’s 1^st and 2^nd rules. For d⁷, l = 2 so m_l = 2, 1, 0, -1, -2. The seven electrons occupy the d-orbitals with parallel spins (to satisfy Hund’s 1^st rule) starting on the left with the highest value of m_l (to satisfy Hund’s 2^nd rule) and working across as shown in Figure 5.20ST.

Figure 5.20ST

Σμ_Σ = ½ + ½ + ½ + ½ + ½ − ½ − ½ = ³/₂  S = ³/₂ \ 2S+1 = 4

Σμ_l = 2 + 1 + 0 – 1 – 2 + 2 + 1 = 3  \ L = 3 Þ F

Therefore, the ground term is ⁴F.

The arrangement of electrons in Figure 5.20ST is one of (2L + 1)(2S + 1), i.e. 28 microstates that all have the same energy. This is just the one with the highest value of M_L and M_S that we are well trained in drawing out as the ground state configuration.

5.21 Sketch the ordering and energy intervals of the levels in the ⁷F ground terms of Eu³⁺ and Tb³⁺.

The ⁷F term is split by spin-orbit coupling into levels with J = 0 to 6. The ordering is dependent on Hund’s third rule so that for Eu³⁺ with a 4f⁶ configuration the ⁷F₀ lies lowest in energy, but for Tb³⁺ with a 4f⁸ configuration the ⁷F₆ lies lowest in energy. Application of Eqn 5.4 gives the energy of the levels relative to the terms. It is also important to note that the separation between the levels is given by the Landé interval rule, which states that the energy between two levels is simply λ times the J value of the larger of the two adjacent levels.

A sketch is given in Figure 5.21ST

Figure 5.21^ST Ordering of the levels in the ⁷F ground terms of Eu³⁺ and Tb³⁺.

5.22 Calculate the single electron spin-orbit coupling constant,ζ, for Tb³⁺ using the data in Figure 5.36 and Figure 5.37.

The transition energies and their assignments are given in Figure 5.22ST. The derivedλ values, the Landé interval rule, and ζ = −2λΣ for Tb³⁺, yields the values in the table below.

Observed transition /cm−1	Difference /cm−1	Assignment		λ / cm−1	ζ / cm−1
20380 cm−1	−1990	5D4→ 7F6		−332	1990
18390 cm−1	−1230	5D4 → 7F5		−246	1476
17160 cm−1	−1020	5D4 → 7F4		−255	1530
16140 cm−1		5D4 → 7F3

 

Figure 5.22ST Emission spectrum of 12.5 μM Tb³⁺ dpa complex at 250 nm excitation.

As for Eu³⁺ there is a spread of values because of the breakdown in the Russell-Saunders approach for high values of J. The literature value of ζ for Tb³⁺ is 1709 cm⁻¹.

5.23 Determine the ground terms for the other high-spin dⁿ configurations using the spin multiplicity and orbital degeneracy method outlined above (ignore the trailing subscripts). Check these against those in Table 5.6 which have the trailing subscripts for completeness. Repeat the process for tetrahedral terms and check against Table 5.6.

The ground terms for high-spin octahedral and tetrahedral transition metal ions are shown in Figure 5.23ST(a) and Figure 5.23ST(b), respectively. You should note the pattern that dⁿ and dⁿ⁺⁵ have the same orbital label, and that the term for dⁿ octahedral is equivalent to the term for d^10-n tetrahedral.

Figure 5.23ST(a) Ground terns for high-spin octahedral transition metal ions.

 

 

Figure 5.23ST(b) Ground terms for high spin tetrahedral transition metal ions.

5.24 Calculate the terms for the ground and spin-allowed excited states for octahedral high-spin d⁷ complexes, and hence identify the number of spin-allowed transitions.

The ground term for d⁷ with a t_2g⁵e_g² configuration is ⁴T as there are three unpaired electrons giving a spin multiplicity of f4, and three orbital permutations to give T. There are two spin-allowed excited ⁴T terms derived from one electron transitions with t_2g⁴e_g³ configurations. The two members easiest to spot are shown in the ⁴T terms below. There is also a spin-allowed two electron transition resulting in a ⁴A term for the t_2g³e_g⁴ configuration. Therefore, there are three spin-allowed transitions for high-spin d⁷ complexes. The terms shown in Figure 5.24STinclude the trailing subscript for completeness, but identifying these is a long-winded exercise (see simple d² example in the text), and it is best to look them up in the Tanabe-Sugano diagrams.

Figure 5.24ST Ground and spin-allowed excited terms for octahedral d⁷ complexes.

5.25 The first two spin-allowed d-d transitions in trans-[CrCl₂(H₂O)₄]⁺ (Figure 5.44(a)) are at 16510 and 23450 cm⁻¹. Using the d³ Tanabe-Sugano diagram (Figure 5.45) and Lever plot (Figure 5.46) calculateΔ, B and predict the position of the third spin-allowed transition.

As trans-[CrCl₂(H₂O)₄]⁺ is d³, the first d-d transition at 16510 cm⁻¹ in Figure 5.25ST(a) is equivalent to Δ_oct.

Figure 5.25ST(a) Electronic absorption spectra of (i) 0.05 M trans-[CrCl₂(H₂O)₄]⁺ and (ii) 0.15 M [Cr(H₂O)₆]³⁺.

However, in order to determine B it is necessary to make use of the d³ Tanabe-Sugano diagram, and/or the Lever plot of ratios of the spin-allowed transition energies. The ratio of the first two spin-allowed transitions at 16510 cm⁻¹ (⁴T_2g ¬ ⁴A_2g) and 23450 cm⁻¹ (⁴T_1g ¬ ⁴A_2g) is 1.420. Using this value and the Lever ratio plot diagram a value for Δ/B of 23.4 can be obtained. This also shows that the only realistic assignment of these two features is to the first two spin-allowed transitions. This ratio can also be obtained by measuring ratio directly (i.e. with a ruler) from the Tanabe-Sugano diagram. These workings are shown in the figures below.

Figure 5.25ST (b) Tanabe-Sugano diagram for octahedral d³ and (c) Lever plot of ratios of transition energies for d³/d⁸, including workings for trans-[CrCl₂(H₂O)₄]⁺.

As the gradient of the ⁴T_2g ¬ ⁴A_2g transition is 1.00, this gives a value of E/B = 23.4 for the ⁴T_2g ¬ ⁴A_2g transition, and hence a value of 705 cm⁻¹ for B (The B values are reported to the nearest 5 or 10, given the accuracy of the process). To check this value against the second transition it is necessary to draw a vertical line at 23.4 on either the Tanabe-Sugano diagram (Figure 5.25ST(b), or the Lever diagram (Figure 5.25(c)) and determine where this intercepts the ⁴T_1g line. This gives an E/B value of 33.2 for the ⁴T_1g ¬ ⁴A_2g transition, and a B value of 705 cm⁻¹. The third spin-allowed transition is predicted to be at E/B = 52.0 from both of the diagrams, and this corresponds to 36700 cm⁻¹, which is masked by the charge transfer transition in the UV part of the spectrum.

The Δ_oct value for trans-[CrCl₂(H₂O)₄]⁺ 16510 cm⁻¹ is smaller than that for [Cr(H₂O)₆]³⁺ (17080 cm⁻¹) as expected given the position of Cl⁻ and H₂O in the spectrochemical series. The values of B of 706 cm⁻¹ for trans-[CrCl₂(H₂O)₄]⁺ is essentially the same as that for [Cr(H₂O)₆]³⁺ (705 cm⁻¹) using the same methodology, indicating a similar level of covalency in [Cr(H₂O)₆]³⁺ compared to trans-[CrCl₂(H₂O)₄]⁺.

5.26 Use the d⁸ Tanabe-Sugano diagram (Figure 5.49) and the three observed d-d transitions in [Ni(H₂O)₆]²⁺ at 8550, 14480 and 25370 cm⁻¹ and in [Ni(en)₃]²⁺ at 11280, 18350, 29040 cm⁻¹ (Figure 5.48) to calculate Δ_oct for [Ni(H₂O)₆]²⁺, and for [Ni(en)₃]²⁺. Using the ratio of the first and third transitions with either the d⁸ Tanabe-Sugano diagram (Figure 5.49) or the Lever plot of transition energy ratios (Figure 5.46) calculate B for [Ni(H₂O)₆]²⁺ and [Ni(en)₃]²⁺. The d-d spectrum of [Ni(NH₃)₆]²⁺ has peaks at 10750, 17500 and 28200 cm⁻¹, use these to calculate Δ_oct and B for this complex. Comment on the values of Δ_oct and how the values of B compare to the free ion value of 1042 cm⁻¹ in Table 5.9.

The spectra of [Ni(H₂O)₆]²⁺ and [Ni(en)₃]²⁺ are shown in Figure 5.26ST(a)

Figure 5.26ST(a) Electronic absorption spectra of [Ni(H₂O)₆]²⁺ and [Ni(en)₃]²⁺.

For d⁸ octahedral complexes the value of Δ_oct is given by the first spin-allowed d-d transition. So Δ_oct is 8550 cm⁻¹ for [Ni(H₂O)₆]²⁺, 10750 cm⁻¹ for [Ni(NH₃)₆]²⁺, and 11280 cm⁻¹ for [Ni(en)₃]²⁺. The ratio of the first and third transitions is 2.967 for [Ni(H₂O)₆]²⁺, 2.623 for [Ni(NH₃)₆]²⁺and 2.574 for [Ni(en)₃]²⁺. Using the T_1g(P)/T_2g(F) line on the Lever ratio plot (Figure 5.26ST(c)) gives Δ/B of 9.2 for [Ni(H₂O)₆]²⁺, 12.2 for [Ni(NH₃)₆]²⁺and 12.9 for [Ni(en)₃]²⁺. The workings for [Ni(H₂O)₆]²⁺ are shown in red, those for [Ni(NH₃)₆]²⁺ in blue and those for [Ni(en)₃]²⁺ in green. As Δ_oct is equivalent to the first d-d transition in d⁸ complexes this means the gradient of the ³T_2g line is 1.0 and that therefore E/B is 9.2 for [Ni(H₂O)₆]²⁺, 12.2 for [Ni(NH₃)₆]²⁺and 12.9 for [Ni(en)₃]²⁺. These values can then be used to obtain B, which is 930 cm⁻¹ for [Ni(H₂O)₆]²⁺, 880 cm⁻¹ for [Ni(NH₃)₆]²⁺, and 875 cm⁻¹ for [Ni(en)₃]²⁺. (The B values are reported to the nearest 5 or 10, given the accuracy of the process.) The Δ/B ratios can also be used to check the B values using the E/B values for the third transition. These are 27.3 for [Ni(H₂O)₆]²⁺, 32.0 for [Ni(NH₃)₆]²⁺and 33.1 for [Ni(en)₃]²⁺, which give B values of 930, 880 and 875, respectively. The B values and E/B data can also be used to predict the position of the second spin-allowed transitions. For [Ni(H₂O)₆]²⁺ B is 930 cm⁻¹ and E/B is 15.3 for the second transition indicating a transition energy of 14230 cm⁻¹. For [Ni(NH₃)₆]²⁺ B is 880 cm⁻¹ and E/B is 19.5, giving a transition energy of 17160 cm⁻¹. For [Ni(en)₃]²⁺ B is 875 cm⁻¹ and E/B is 20.5 implying a transition energy of 17940 cm⁻¹. These values are in reasonable agreement with the experimental ones, especially given possibility of the spin-forbidden transitions discussed in Example 5.26, and the accuracy of using the charts.

The values of Δ_oct are in line with the position of the ligands in the spectrochemical series. The values of B are all lower than the free ion value of 1042 cm⁻¹. This is an example of the nephelauxetic effect (see Section 5.15), and the greater reduction of B for the NiN₆ coordination environment indicates a greater extent of covalency in the bonding than in the Ni(OH₂)₆ coordination environment. The Δ_oct and B values for [Ni(NH₃)₆]²⁺ and [Ni(en)₃]²⁺ are similar, with the Δ_oct and B values of [Ni(en)₃]²⁺ being slightly larger and smaller, respectively, than those of [Ni(NH₃)₆]²⁺.

Figure 5.26ST (b) Octahedral d⁸ Tanabe-Sugano diagram, and (c) Lever (ratio of transition energies) plot for d³/d⁸. Analysis shown for [Ni(H₂O)₆]²⁺, [Ni(NH₃)₆]²⁺ and [Ni(en)₃]²⁺.

5.27 Use Figure 5.54 and/or Figure 5.55 and the data in Figure 5.21 ([Co(NH₃)₆]Cl₃, 21070, 29460 cm⁻¹; [CoCl(NH₃)₅]Cl₂, 18810, 27540 cm⁻¹) to calculate Δ_oct and B for [Co(NH₃)₆]Cl₃ and [CoCl(NH₃)₅]Cl₂. Compare these values with those in Example 5.9.

The electronic absorption spectra of [Co(NH₃)₆]Cl₃ and [CoCl(NH₃)₅]Cl₂ are shown in Figure 5.27ST(a)

Figure 5.27ST(a) Electronic absorption spectra of [Co(NH₃)₆]Cl₃ and [CoCl(NH₃)₅]Cl₂.

For [Co(NH₃)₆]Cl₃, the first two spin-allowed in these low-spin d⁶ complexes are at 21070 and 29460 cm⁻¹ giving a ratio of 1.398. In [CoCl(NH₃)₅]Cl₂ they are at 18810, 27540 cm⁻¹ giving a ratio of 1.464. These are shown in the plots below.

Figure 5.27ST (b) Octahedral d⁶ Tanabe-Sugano diagram, and (c) Lever (ratio of transition energies) plot for low-spin d⁶. Analysis shown for [Co(NH₃)₆]Cl₃ and [CoCl(NH₃)₅]Cl₂.

For [Co(NH₃)₆]Cl₃ (shown in red) a ratio of 1.398 indicates a Δ/B value of 36.85, and E/B values of 33.9 and 47.3. In conjunction with the transition energies of 21070 and 29460 cm⁻¹ this gives values of B of 620 and 623 cm⁻¹, which can be taken to be 620 cm⁻¹. Using this in conjunction with Δ/B of 36.85, implies a value of Δ_oct of 22850 cm⁻¹.

For [CoCl(NH₃)₅]Cl₂ (shown in green) the ratio of 1.464 indicates a Δ/B value of 30.7, with E/B values of 27.85 and 40.8 for the 18810 and 27540 cm⁻¹ transitions, yielding B values of 675 and 675 cm⁻¹. Using the Δ/B value of 30.7 and B of 675 cm⁻¹ gives a value of Δ_oct of 20720 cm⁻¹.

Using the more simple approach in Example 5.9 values of 23000 cm⁻¹ and 21000 cm⁻¹ were obtained for [Co(NH₃)₆]Cl₃ and [CoCl(NH₃)₅]Cl₂, respectively, compared to 22850 and 20720 cm⁻¹ using this more sophisticated approach. Therefore, the simple method gives acceptable values of Δ_oct.

5.28 Calculate ε_max for the peaks in Figure 5.56(b), and compare these with the values in Figure 5.56(a) and Table 5.1. The literature value of ε_max for [CoCl₄]²⁻ is 580 dm³ mol⁻¹ cm⁻¹, what does your value indicate about the extent of reaction between [Co(H₂O)₆]²⁺ and HCl to form [CoCl₄]²⁻? As dⁿ tetrahedral configurations can be covered by d^10-n octahedral Tanabe-Sugano diagrams, use the d³ Tanabe-Sugano diagram (Figure 5.45 and Appendix 4) and the reported values of Δ_tet (3120 cm⁻¹) and B (710 cm⁻¹) for [CoCl₄]²⁻ to assign the features in Figure 5.56(b). It should be noted that for both the octahedral and tetrahedral Co²⁺ complexes the lowest energy transitions were outside the range of conventional spectrometers, and a detailed analysis using the Tanabe-Sugano diagrams was necessary to confirm the assignments.

The electronic absorption spectra of the 0.2 M [Co(H₂O)₆]²⁺ solution, and that diluted tenfold by 8 M HCl to give a 0.02 M solution of [CoCl₄]²⁻ are shown in Figure 5.28ST(a).

 

Figure 5.28ST(a) Electronic absorption spectra of (i) 0.2 M [Co(H₂O)₆]²⁺ and (ii) 0.02M [CoCl₄]²⁻ (tenfold dilution of solution (i) with 8 M HCl).

Assuming 1 cm pathlengths, the values of ε_max are given below.

 

	λmax /cm−1	Abs	εmax /dm3 mol−1 cm−1
0.2 mM [Co(H2O)6]2+	8000	0.29	1.5
	19500	0.94	4.7
	21350	0.64	3.2
0.02 mM [CoCl4]2−	14500	1.36	68
	15100	1.29	65
	15950	0.89	45

 

The ε_max values for [Co(H₂O)₆]²⁺ are consistent with those for an octahedral complex in Table 5.1. The experimental values for [CoCl₄]²⁻ derived from Figure 5.28ST(a) are about an order of magnitude smaller than the literature values for [CoCl₄]²⁻. Despite the spectrum being dominated by the spectral features of [CoCl₄]²⁻ the low values indicate that the equilibrium between [Co(H₂O)₆]²⁺ and [CoCl₄]²⁻ still lies a long way over to the left-hand side (Figure 5.28ST(b). The weaker peak at ca 19000 cm⁻¹ is indicative of some remaining octahedral complexes, but as it is at lower energy than the initial peak it is most likely due to a mixed Cl/H₂O environment. In the analogous reaction using NCS⁻ discussed in Self Test 5.10, it is necessary to add acetone to the reaction mixture to drive the equilibrium to the right-hand side by removing water from the cobalt coordination sphere.

 

Figure 5.28ST(b) Equilibrium between [Co(H₂O)₆]²⁺ and [CoCl₄]²⁻ in the presence of excess HCl.

With Δ_tet = 3120 cm⁻¹ and B = 710 cm⁻¹, Δ/B = 4.39, and this vertical line is shown in the d³ Tanabe-Sugano diagram in Figure 5.28ST(c). Using this line, the transition energies can be predicted using the horizontal lines, and these, together with the assignments, are shown in the table below. There are no g subscripts on the terms as there is no inversion centre in tetrahedral complexes.#

 

Therefore, the complex peak at ca. 15000 cm⁻¹ in Figure 5.28ST(a) can be assigned to the ⁴T₁ (P) ¬ ⁴A₂ transition, as the other two transitions are predicted to be below the energy range of the experiment, and are essentially in the IR part of the spectrum. The lowest energy transition at 3100 cm⁻¹ is equivalent to Δ_tet, as expected for tetrahedral d⁷ (and also octahedral d³ and d⁸ and tetrahedral d²). As in the case of the spectrum of saturated MnCl₂ (Figure5.57), the negative absorbance features around 10000 cm⁻¹ are due to the overtones and combination bands of water not ratioing out because of the high concentration of HCl present which results in a slightly smaller amount of water in the sample compared to the reference beam.

 

Figure 5.28ST(c)Tanabe-Sugano diagram for d⁷ tetrahedral complexes adapted from the d³ octahedral Tanabe-Sugano diagram by removal of g subscripts, and expanding over area of interest.

Although it is tempting to assign the fine structure on the 15000 cm⁻¹ band in Figure 5.28ST(a) to vibrational fine structure (as in the spectrum of [MnO₄]⁻), it is thought to be due to spin-forbidden transitions to the ²E, ²T₁, (and to a lesser extent the ²T₂ and ²A₁) terms derived from the ²G atomic term which are in close proximity to the ⁴T_1g (P) term for the Δ/B ratio of 4.39, as shown in Figure 5.28ST(c).

The very substantial increase in molar absorptivity for the tetrahedral complex implies that some of the selection rules have been relaxed. There is no reason to think that the spin selection rule has been relaxed, therefore this must be down to the orbital and Laporte components of the dipole selection rule. The T_dpoint group does not contain an inversion centre, so the Laporte selection rule is no longer operative, and the d orbital labels are just e and t₂. The metal d_xy, d_xz and d_yz orbitals also have the same symmetry as the metal p orbitals (t₂) and this mixes some p character into these d orbitals which relaxes the orbital selection rule (Δl = ± 1) so that the d-d transitions are no longer pure d to d, but d to d/p.