Complex ions, symmetry

Finally, it seems appropriate to comment on evidence for complex ions afforded by the electronic spectra of 3d ions in view of the earlier discussion (Section III, A, 4) of the difficulty of assessing these from particularly thermodynamic data for melts with a common anion. The spectroscopic studies in LiCl-KCl, the most studied solvent to date, certainly seem to be as presumptive a collection of evidence for the formation of complex ions in the melt as are the similar results in inert solvents which are so frequently used as proof of their identity. At the very least, a discrete environment rather than a wide range of configurations is evidently present (see Wilmshurst, 1963), since broadening of transitions energies is no more than that which usually accompanies an increase in temperature. Even more powerful evidence has been accumulated for the correctness of the assignment of the spectral data for the melts to a given complex ion in that the data are in many cases substantially identical with those for accepted complexes in aqueous solution or in crystals of known structure, either pure or in dilute solid solution. It does not seem particularly important that the complex ion symmetry and stabffity can be accounted for at least quali-... 

The aluminium ion, charge -I- 3. ionic radius 0.045 nm, found in aluminium trifluoride, undergoes a similar reaction when a soluble aluminium salt is placed in water at room temperature. Initially the aluminium ion is surrounded by six water molecules and the complex ion has the predicted octahedral symmetry (see Table 2.5 ) ... 

In Section 4.2.1 it will be pointed out that hydrogen peroxide (Figure 4.1 la) has only one symmetry element, a C2 axis, and is therefore a chiral molecule although the enantiomers have never been separated. The complex ion [Co(ethylenediamine)3], discussed in Section 4.2.4 and shown in Figure 4.11(f), is also chiral, having only a C3 axis and three C2 axes. 

M Simulation of symmetry by molecules or complex ions in crystals has been discussed by Linus Pauling, Phys. Rev., 36, 430 (1930). 

Many complex ions, such as NH4+, N(CH3)4+, PtCle", Cr(H20)3+++, etc., are roughly spherical in shape, so that they may be treated as a first approximation as spherical. Crystal radii can then be derived for them from measured inter-atomic distances although, in general, on account of the lack of complete spherical symmetry radii obtained for a given ion from crystals with different structures may show some variation. Moreover, our treatment of the relative stabilities of different structures may also be applied to complex ion crystals thus the compounds K2SnCle, Ni(NH3)3Cl2 and [N(CH3)4]2PtCl3, for example, have the fluorite structure, with the monatomic ions replaced by complex ions and, as shown in Table XVII, their radius ratios fulfil the fluorite requirement. Doubtless in many cases, however, the crystal structure is determined by the shapes of the complex ions. 

Of particular importance in structural chemistry is the concept of hybridization, that is, the construction of linear combinations of atomic orbitals that transform according to the symmetry of the structure. For the present, a simple illustration is provided by the hybridization of atomic orbitals in a molecule or complex ion of trigonal structure. 

The environment of an ion in a solid or complex ion corresponds to symmetry transformations under which the environment is unchanged. These symmetry transformations constitute a group. In a crystalline lattice these symmetry transformations are the crystallographic point groups. In three-dimensional space there are 32 point groups. 

It was mentioned above that tris(chelate) complexes of the type (Co(en) ],+ lack an improper axis of rotation. As a result, such complexes can exist in either of two enantiomeric forms (or a racemic mixtire of the two). Figure 12.20 illustrates the complex ions (Co(en)j]3+ and (Crfoxy3-. each of which ts chiral with Di symmetry. 

For complexes of symmetry lower than cubic no general relationships which connect the parameters describing departure from cubic symmetry, Ds and Dt say, with features of M and L or their combination appear. For example, it is difficult to obtain a coherent account even of the signs of the splittings of the cubic field spectral bands of Cr(en)2X2+ ions using the parameters Aoct(Cr(en)33+) and Aoct(CrX63 ). The predictive power of the LFT parameterization scheme does not seem to extend to symmetries lower than cubic. 

Example 9.4-1 Determine the normal coordinates for the even parity modes of the ML6 molecule or complex ion with Oh symmetry. 

A d2 complex ion has D4 symmetry. It has the electronic configuration (b2)2 in the ground-state and excited-state configurations b2e, b2a, b2b. Determine the electronic states that arise from these configurations. Hence decide which of the possible El transitions from the ground state to excited states are spin- and symmetry-allowed. If any of the possible spin-allowed El transitions are symmetry-forbidden, are they allowed Ml transitions ... 

We pass next to the Ln(III) bis-dipicolinate complexes, shown in Fig. 6. There is no crystal structure for the complexes. Flowever detailed examination of the proton NMR spectra at room temperature shows that the shift ratios are again constant throughout the series and that absolute shifts follow Bleaney s predicted values, Table 3. The complexes must be isostructural and must have axial symmetry. Again the use of relaxation data gives an independent assessment of the relative distances of meta and para protons. We can put all the data together and give a structure for the complex ion as in Fig. 6 leaving three water molecules in the inner sphere. To prove that this is so we must analyse the proportions of the water, both bound and outer sphere. 

The second stmcture is preferred because it brings about a lesser symmetry in the complex ion and this deaeased symmetry is found to lead to an explanation of one of the characteristics of the spectra, the fact that they exhibit polarization, i.e., have differences in the spectra when the polarized light incident on the sample is in either the parallel or the vertical plane, respectively. Thus, polarization of the scattered Raman radiation is expected from the 2v but not from the Qv complex ion. 

More recently it has been shown that in addition to Pi the nephe-lauxetic ratio )3 [)3 = B/Bg, Bg is the B value for the free ion in the gas phase and is equal to 1120 cm for Co(III) (173) ] has an effect on the shielding experienced by the cobalt nucleus. Juranic (179, 180) and Bramley et al. (173) found that there is a linear relationship between the chemical shift and )3 vi. The correlation is rather good for cubic complexes (Oh symmetry of donor atoms) but does not hold as well for distorted complexes (such as the tris-chelates). Co NMR data are shown in Table III. 

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