Chapter 10 Answers to Self-test Questions

10.1 Predictisomer shift(s) for the main iron resonance(s) in the ⁵⁷Fe Mössbauer spectrum of Fe₃O₄.

Fe₃O₄ contains both Fe²⁺ and Fe³⁺ ions in an inverse spinel (AB₂O₄) structure with half the Fe³⁺ in tetrahedral (A sites) and half in octahedral (B) sites and with the Fe²⁺ also in the octahedral (B) sites. As these are in oxygen coordination environments they will all be high spin. Therefore, using Figure 10.6 we expect isomer shifts (δ) of 1.0 – 1.5 mm s⁻¹ for Fe²⁺ and 0.2 – 0.6 for Fe³⁺. The experimental spectrum gives δ of 0.28 mm s⁻¹ for the A sites and 0.67 mm s⁻¹ for the B sites. The former is characteristic of tetrahedral Fe³⁺, and although the octahedral B sites contain both Fe²⁺ and Fe³⁺ they are not distinct due to electron delocalisation (see Figure 10.14 for a room temperature spectrum).

10.2 Figure 10.10 shows the ⁵⁷Fe Mössbauer spectrum of Na₂[Fe(CN)₅NO].2H₂O. Interpret this spectrum in terms of the geometric and electronic contributions to the EFG and hence ΔE_Q.

NO is a non-innocent ligand, and as a two electron donor can behave as either NO⁺ or NO⁻. The Fe-N-O bond angle is linear in [Fe(CN)₅NO]²⁺, and this implies similar behaviour to CO and CN⁻ (rather than O₂), and hence it is formulated as NO⁺, which is isoelectronic with both CO and CN⁻. Therefore, the iron is present as Fe²⁺, with a d⁶ electronic configuration. With five cyanide ligands, and nitric oxide acting as a isolelectronic with CO and CN⁻ it is expected to be low-spin. The isomer shift value of −0.26 mm s⁻¹ is consistent with the range expected for low-spin Fe(II) in Figure 10.6. The large observed quadrupole splitting of 1.73 mm s⁻¹ could be associated with either an electronic or structural EFG. Although the t_2g⁶ configuration in low-spin octahedral iron(II) is split into b₂²e⁴ in [Fe(CN)₅NO]²⁺ the resultant electronic EFG is expected to be small (tending to zero). Therefore, the large observed quadrupole splitting is due to the geometric effects of the nitrosyl ligand. The effect of this structurally induced EFG is shown in the ⁵⁷Fe Mössbauer spectrum of Na₂[Fe(CN)₅NO] in Fig. 10.2ST.

 

Figure 10.2ST ⁵⁷Fe Mössbauer spectrum of Na₂[Fe(CN)₅(NO)].2H₂O at 80 K.

10.3 Figure 10.14 shows the room temperature ⁵⁷Fe Mössbauer spectra of γ-Fe₂O₃ (maghemite) and Fe₃O₄ (magnetite). Assign the spectra to the correct iron oxide.

γ-Fe₂O₃ only contains Fe³⁺, whereas Fe₃O₄ contains both Fe²⁺ and Fe³⁺ ions. Therefore, it might be expected that the ⁵⁷Fe Mössbauer spectrum Figure 10.3ST(a) is from γ-Fe₂O₃ as there is only one set of six lines, and that in Figure 10.3ST(b) is from Fe₃O₄, as there are two distinct sextets. Whilst this assignment is correct, the explanation is more complex as both γ-Fe₂O₃ and Fe₃O₄ adopt the inverse spinel structure with both tetrahedral and octahedral coordination of the iron.

 

 Figure 10.3ST Room temperature ⁵⁷Fe Mössbauer spectra of (a) γ-Fe₂O₃ and (b) Fe₃O₄. (Data from R. J. Armstrong, A. H. Morrish and G. A. Sawatzky, Phys. Lett., 23, 414 (1966) and I. S. Lyubutin, C. R. Lin, Y. V. Korzhetskiy, T. V. Dmitrieva and R. K. Chiang, J. Appl. Phys., 106, 034311 (2009))

 γ-Fe₂O₃

In contrast to α-Fe₂O₃, which has an hcp array of oxide ions (considered in Example 10.3), the structure of γ-Fe₂O₃ is based on an fcc array of oxide anions within an inverse spinel (AB₂O₄) structure. The A sites are tetrahedral, whereas the B sites are octahedral (with a trigonal distortion). As there are insufficient Fe³⁺ cations for all of the A and B sites, ¹/₉^th of the cation sites are vacant. The A and B sites align anti-parallel, but as these are not equal this means that maghemite is ferromagnetic (see Section 8.3), and as a result maghemite was commonly used in magnetic recording devices such as cassette tapes. As there are two distinct iron sites in maghemite, it might be expected that there will be two six line patterns in the ⁵⁷Fe Mössbauer spectrum. However, in the spectrum in Fig. 10.3ST(a) (data from R. J. Armstrong, A. H. Morrish and G. A. Sawatzky, Phys. Lett. 23 414 (1966)), there appears to be just one six line pattern. However, on closer inspection the features at 5 and 8.5 mm s⁻¹ are asymmetric, and this arises because the two expected patterns overlap. By application of an external magnetic field, analysis of the resultant spectra indicates that for the A sites δ = 0.27 mm s⁻¹ and B_hf = 48.8 T, whilst for the B sites δ = 0.41 mm s⁻¹ and B_hf = 49.9 T. Detailed analysis of the relative intensities of the two six line patterns indicated that the vacancies are largely in the octahedral B sub-lattice, and that the extent of covalency in the bonding is greater in the tetrahedral A sites than in the octahedral B sites. Crystallography indicates the cubic unit cell can be approximated to (Fe³⁺)₈[Fe³⁺_5/6ð_1/6]₁₆O₃₂, where (   ) indicates the A tetrahedral sites, [   ] the B octahedral sites and ð vacancies.

Fe₃O₄

Fe₃O₄ contains both Fe²⁺ and Fe³⁺ in an inverse spinel structure (AB₂O₄) with half the Fe³⁺ in the tetrahedral (A) sites and half in the octahedral (B) sites and with the Fe²⁺ also in the octahedral (B) sites. The room temperature spectrm of Fe₃O₄ shown in Figure 10.3ST(b) shows two overlapping sextets (data from I. S. Lyubutin, C. R. Lin, Y. V. Korzhetskiy, T. V. Dmitrieva and R. K. Chiang, J. Appl. Phys. 106 034311 (2009)). The lower intensity sextet (δ = 0.281 mm s⁻¹, ΔE_Q = -0.002 mm s⁻¹, B_hf = 48.96 T, Γ = 0.279 mm s⁻¹) is from the tetrahedral A site which contains Fe³⁺, the more intense sextet (δ = 0.667 mm s⁻¹, ΔE_Q = 0.002 mm s⁻¹, B_hf = 45.84 T, Γ = 0.408 mm s⁻¹) is from the B site. Although there are both Fe²⁺ and Fe³⁺ cations in the B site at room temperature (above the Verwey transition, T_V, of ca. 120 K), these are not distinct due to electron delocalisation. Below 120 K the structure is no longer cubic and the spectrum becomes very complex. For example the spectrum at 4 K requires five sextets to fit the data.

Therefore, the spectrum in Figure 10.3ST(a) is for γ-Fe₂O₃ and that for Fe₃O₄ is in Figure 10.3ST(b). These spectra together with those of α-Fe₂O₃ show how sensitive the ⁵⁷Fe Mössbauer spectra are at identifying different iron minerals.

10.4. The ³⁵Cl NQR frequencies of [TiCl₃Cp] and [TiCl₂Cp₂] are 8.1and 11.8 MHz, respectively. (Cp = [C₅H₅]⁻,) Use these NQR data to comment on the effect of the cyclopentadienyl ligands (which are better π donor ligands than Cl⁻) on the Ti-Cl bonding with respect to that in TiCl₄.

The increase in the ³⁵Cl NQR frequency from 6.05 MHz in TiCl₄, to 8.1 MHz in [TiCl₃Cp] and 11.8 MHz in [TiCl₂Cp₂] indicates an increase in the EFG at the chlorine nucleus. Using the Townes and Dailey approach the increase in NQR frequency indicates a reduction in the ionic character of the Ti-Cl bonding in the cyclopentadienyl complexes from 0.89 in TiCl₄, to 0.85 in [TiCl₃Cp] and 0.78 in [TiCl₂Cp₂]. This is also reflected in the T-Cl bond lengths which increase from 2.18 Å for TiCl₄, through 2.22 Å for [TiCl₃Cp] to 2.37 Å for [TiCl₂Cp₂].

The early work based on the Townes and Dailey relationship was explained as a decrease in the Ti-Cl p bonding on going from TiCl₄ to [TiCl₃Cp] and [TiCl₂Cp₂], as the addition of Cp⁻ reduces the Ti-Cl p bonding, because Cp⁻ is a better p donor than Cl⁻ (E. V. Bryukhova, G. K. Semin, I. M. Alimov, A. N. Nesmeyanov, O. V. Nogina, V. A. Dubovitsky and S. I. Kuznetsov, J. Organomet. Chem. 81 195 (1974)). The observation of a reduction in Ti-Cl p bonding in [TiCl₂Cp₂] compared to [TiCl₃Cp] has been confirmed by more recent quantum chemical calculations (A. J. Rossini, R. W. Mills, G. A. Briscoe, E. L. Norton, S. J. Geier, I. Hung, S. Zheng, J. Autschbach and R. W. Schurko, J. Am. Chem. Soc. 131 3317 (2009)). The EFG at the chlorine is also increased by addition of Cp⁻ as the two chlorine orbitals involved in p bonding are different, compared to TiCl₄.

10.5 Use the NQR and NMR data in Table 10.5P to determine the structures of PCl₃F₂ and PCl₂F₃. 

Compound	35Cl NQR /MHz	19F NMR /ppm
PCl3F2	31.57	-123.0
PCl2F3	31.49	-67.4, +41.5

Table 10.5P ³⁵Cl NQR data and ¹⁹F NMR data for PCl₃F₂ and PCl₂F₃. (Holmes, R. P. Carter and G. E. Peterson, Inorg. Chem., 3, 1748 (1964), R. P. Carter and R. R. Holmes, Inorg. Chem., 4, 738 (1965), H. Chihara, N. Nakamura, S. Seki, Bull. Chem. Soc. Jpn., 40, 50 (1967)

The ³⁵Cl NQR data indicates that there is only one Cl environment in both PCl₃F₂ and PCl₂F₃. The ¹⁹F NMR data indicates that there is only one ¹⁹F environment in PCl₃F₂, but two ¹⁹F environments in PCl₂F₃. If there is only one chlorine environment in PCl₃F₂ the chlorine atoms must be in the equatorial position with the fluorine atoms in the axial positions. In Example 10.5 equatorial chlorines were associated with an NQR frequency of 32.54 MHz, and axial chlorines with resonance at 28.99 MHz. The observation of the ³⁵Cl NQR resonance at 31.57 MHz is consistent with the chlorine atoms being in the equatorial plane, as shown in Figure 10.5ST.

Figure 10.5ST Structures of PCl₃F₂ and PCl₂F₃ consistent with NQR and NMR data.

The NQR data for PCl₂F₂ with one resonance at 31.49 MHz indicates that the two chlorine atoms are both in the equatorial plane. The ¹⁹F NMR data indicate two fluorine environments, suggesting that one of the fluorine atoms is in the equatorial position and the other two in the axial positions as shown in Figure 10.5ST.

These are both examples of the Muetterties rule that states that in a trigonal bipyramidal structure the most electropositive ligands occupy the axial (apical) positions, and the more electropositive ligands occupy the equatorial positions. 

10.6 The NQR spectrum of [Co(NH₃)₆]³⁺ only has features from ¹⁴N (I = 1) and none from ⁵⁹Co (I = ⁷/₂) and the ¹⁴N quadrupole coupling constant in the complex is less than half that found for free NH₃. Explain these observations. 

The observation of an NQR signal is dependent on the quadrupole energy levels being split by an electric field gradient (EFG) to give an energy separation proportional to the quadrupole coupling constant, QCC. If the QCC is zero, there will be no observable transitions. The larger the QCC, the larger the NQR frequency

For octahedral [Co(NH₃)₆]³⁺ there is no geometric contribution to the EFG, and as it is low-spin d⁶, the electronic contribution is also zero. Therefore, there will be no ⁵⁹Co NQR spectrum observed for [Co(NH₃)₆]³⁺. In the case of lower symmetry cobalt complexes such as [CoCl(NH₃)₅]²⁺, and trans-[CoCl₂(NH₃)₄]⁺, the QCC is now modest (31.74 MHz and 59.23 MHz, respectively) and ⁵⁹Co NQR spectra are observed.

For the ¹⁴N NQR resonances in [Co(NH₃)₆]³⁺ and NH₃, the EFG, and hence QCC is largest in NH₃ as this is pyramidal, whereas in the complex the N atom is four coordinate in an approximately tetrahedral environment.