Ionic bonding orbitals

Structure determines properties and the properties of atoms depend on atomic struc ture All of an element s protons are m its nucleus but the element s electrons are dis tributed among orbitals of varying energy and distance from the nucleus More than any thing else we look at its electron configuration when we wish to understand how an element behaves The next section illustrates this with a brief review of ionic bonding... 

How much can we bend this bond Well, the electrons of each ion occupy complicated three-dimensional regions (or orbitals ) around the nuclei. But at an approximate level we can assume the ions to be spherical, and there is then considerable freedom in the way we pack the ions round each other. The ionic bond therefore lacks directionality, although in packing ions of opposite sign, it is obviously necessary to make sure that the total charge (+ and -) adds up to zero, and that positive ions (which repel each other) are always separated by negative ions. 

Several methods of quantitative description of molecular structure based on the concepts of valence bond theory have been developed. These methods employ orbitals similar to localized valence bond orbitals, but permitting modest delocalization. These orbitals allow many fewer structures to be considered and remove the need for incorporating many ionic structures, in agreement with chemical intuition. To date, these methods have not been as widely applied in organic chemistry as MO calculations. They have, however, been successfully applied to fundamental structural issues. For example, successful quantitative treatments of the structure and energy of benzene and its heterocyclic analogs have been developed. It remains to be seen whether computations based on DFT and modem valence bond theory will come to rival the widely used MO programs in analysis and interpretation of stmcture and reactivity. 

As will become apparent as this chapter progresses, many of our basic ideas on the chemical bond were proposed by Ci. N. Lewis, one of the greatest of all chemists, in the early years of the twentieth century. Lewis devised a simple way to keep track of valence electrons when atoms form ionic bonds. He represented each valence electron as a dot and arranged the dots around the symbol of the element. A single dot represents an electron alone in an orbital a pair of dots represents two paired electrons sharing an orbital. Examples of the Lewis symbols of atoms are... 

In other cases, discussed below, the lowest electron-pair-bond structure and the lowest ionic-bond structure do not have the same multiplicity, so that (when the interaction of electron spin and orbital motion is neglected) these two states cannot be combined, and a knowledge of the multiplicity of the normal state of the molecule or complex ion permits a definite statement as to the bond type to be made. 

When the difference in electronegativities is great, the orbital may be so far over to one side that it barely covers the other nucleus. This is an ionic bond, which is seen to arise naturally out of the previous discussion, leaving us with basically only one type of bond in organic molecules. Most bonds can be considered intermediate between ionic and covalent. We speak of percent ionic character of a bond, which indicates the extent of electron-cloud distortion. There is a continuous gradation from ionic to covalent bonds. 

Chromium has a similar electron configuration to Cu, because both have an outer electronic orbit of 4s. Since Cr3+, the most stable form, has a similar ionic radius (0.64 A0) to Mg (0.65 A0), it is possible that Cr3+ could readily substitute for Mg in silicates. Chromium has a lower electronegativity (1.6) than Cu2+ (2.0) and Ni (1.8). It is assumed that when substitution in an ionic crystal is possible, the element having a lower electronegativity will be preferred because of its ability to form a more ionic bond (McBride, 1981). Since chromium has an ionic radius similar to trivalent Fe (0.65°A), it can also substitute for Fe3+ in iron oxides. This may explain the observations (Han and Banin, 1997, 1999 Han et al., 2001a, c) that the native Cr in arid soils is mostly and strongly bound in the clay mineral structure and iron oxides compared to other heavy metals studied. On the other hand, humic acids have a high affinity with Cr (III) similar to Cu (Adriano, 1986). The chromium in most soils probably occurs as Cr (III) (Adriano, 1986). The chromium (III) in soils, especially when bound to... 

Still another aspect of the Li and F valence orbitals is modified by ionic-bond formation. In an isolated ionic or neutral species, each NAO retains the characteristic angular shape of the pure s and p hydrogenic orbitals shown in Fig. 1.1, reflecting the full rotational symmetry of atoms. However, in the presence of another atom or ion this symmetry is broken, and the optimal valence orbitals acquire sp hybrid form (assumed for simplicity to include only valence s and p orbitals), as represented mathematically by... 

The following question remains Why are the sigma-type interactions weaker than the pi-type interactions in this case This is apparently a geometrical effect, enforced by the relative sizes of M and X valence and core orbitals in the ionic bonding environment, and illustrated in the NAO diagrams of Fig. 2.18. We may... 

Let us first consider the charge and spin distributions for atoms and ions of the first transition series (M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn). The neutral ground-state TM electron configurations are of generic form s2d , except at n = 4 (Cr sM5) and n = 9 (Cu s d1") where the well-known anomalies associated with the special stability of half-filled and filled d shells are manifested. The simplest picture of ionic bonding therefore involves metal ionization from an s orbital to give the... 

For Li—F, the quantal ionic interaction can be qualitatively pictured in terms of the donor-acceptor interaction between a filled 2pf. orbital of the anion and the vacant 2su orbital of the cation. However, ionic-bond formation is accompanied by continuous changes in orbital hybridization and atomic charges whose magnitude can be estimated by the perturbation theory of donor-acceptor interactions. These changes affect not only the attractive interactions between filled and unfilled orbitals, but also the opposing filled—filled orbital interactions (steric repulsions) as the ionic valence shells begin to overlap. 

For a normalized bond orbital, the relationship between polarization coefficients cA and cB and fractional ionicity zAB can be expressed as (cf. Eq. (1.41a))... 

In general, overlap of incompletely filled p orbitals results in large deviations from pure ionic bonding, and covalent interactions result. Incompletely filled / orbitals are usually well shielded from the crystal field and behave as essentially spherical orbitals. Incompletely filled d orbitals, on the other hand, have a large effect on the energetics of transition metal compounds and here the so-called crystal field effects become important. 

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