Polyatomic ions symmetry

The solvation of polyatomic ions or polar neutral molecules is even more difficult to describe. There are two sources of additional problems first of all, the symmetry of the system under investigation is drastically reduced and hence the number of different configurations increases tremendously. Furthermore, the strength of the electric field is much smaller than in the case of monatomic ions with spherical symmetry and therefore the dynamic behavior of the solvation shell is even more important for a priori calculations of macroscopic properties. 

The so-called Coulumb explosion technique, in which ions with translational energies in the MeV regions are denuded of electrons by a thin carbon foil, also promises to provide information on structures and on the symmetries of polyatomic ions [325, 326, 327], as has already... 

For the chemist, the Jahn-Telkr effect is, in a way, the obverse side of the Tanabe-Kamimura theorem . The abstract formulation of the Jahn-Teller theorem is that two or more electronic states having identical energy in a definite symmetry of a non-linear molecule or polyatomic ion (with exception of Kramers doublets in the case of an odd number of electrons) spontaneously separate in energy, such that (at least) the state of... 

Thermodynamic and structural evidence points to the marked departure from spherical symmetry of polyatomic ions as one factor which strongly favours the formation of association complexes when the crystals are melted. General indications may be... 

Deviations of the absorption pattern from that expected for a free molecule can provide information on the crystal environment. A polyatomic ion containing n atoms has 3n-6 internal modes of vibration and six external modes, corresponding to rotary and translational vibrations of the ion as a whole. Thus, the carbonate and nitrate ions have six internal modes. Owing to the symmetry elements of such ions, one vibration (v. Figure 16) is inactive in the... 

The modes of vibration of polyatomic anions60 are primarily determined by the number of atoms present and the symmetry of the free ions (Table 1), and the IR frequencies of these high-symmetry free ions are well characterized (Figure 6a). 

Considerable difficulties arise when attempting to apply this expression to polyatomic molecules, owing to possible coupling between different modes of the same symmetry. Nevertheless, the data in Table 9 allow one to estimate the metal-metal bond dissociation energy in [M2X8]" ions (84) to be around 500kJmol, which is a very substantial value, exceeded among homonuclear units only by those of C C and N=N. 

In molecules and polyatomic complex ions, the equilibrium positions of the nuclei determine point-groups8) which are finite (one of the seven cubic groups, or belonging to one of the seven series Dnh, Dn(j, D , Cnh, Cnv, Cn and S2n including the isolated plane of symmetry Cs, the isolated centre of inversion C and, finally,... 

The ligand it orbitals may be simple pit orbitals, as in the Cl" ion, simple dn orbitals as in phosphines or arsines, or molecular orbitals of a polyatomic ligand as in CO, CN or pyridine. When they are simple pit or dn orbitals, it is quite easy to visualize how they combine to form the proper symmetry orbitals for overlapping with the metal-ion orbitals. This is illustrated for pit orbitals in Fig. 20-40. 

We can now consider the effect of the size and shape of the anion on the symmetry and dimensions of the unit cell. For minerals, the anion can vary widely. So far, we have talked only about monatomic (single atom) anions, but many minerals contains polyatomic anions such as carbonate, sulfate, phosphate, vanadate, and, of course, silicates. These are all oxy anions that is, they contain some central atom surrounded by oxygens. It is important to understand that in these anions the oxygens are attached to the central atom by covalent bonds (the bonds may, of course, contain some ionic character). The sulfate, phosphate, vanadate, and nesosilicate ions are tetrahedral in shape. For example, the snlfate ion contains a sulfur at the center of a tetrahedron, as shown below (remember the entire species has a charge of 2-, which is not shown in this structural representation) ... 

The MO model of C2 predicts a doubly bonded molecule, with all electrons paired, but with both highest occupied molecular orhitals (HOMOs) having tt symmetry. C2 is unusual because it has two tt bonds and no cr bond. Although C2 is a rarely encountered allotrope of carbon (carbon is significantly more stable as diamond, graphite, fullerenes and other polyatomic forms described in Chapter 8), the acetylide ion, C2 , is well known, particularly in compounds with alkali metals, alkaline earths, and lanthanides. According to the molecular orbital model, 2 should have a bond order of 3 (configuration TT TT a-g ). This is supported by the similar C—C distances in acetylene and calcium carbide (acetylide) . ... 

In the case of a crystal where the anion is a polyatomic one (e.g., the carbonate ion), the surface effect does not reveal itself just by ion relaxation. We have seen that the crystal field produces slight modifications in the ions (carbonate in calcite) however, in the infinite crystal the general symmetry is preserved. On the other hand, for ions on the surface, the crystal field is different and has either a much lower symmetry or even no symmetry, as happens in the case of a cleavage face of calcite. A special kind of deformation must thus take place for these ions. 

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