Orbitals localized electron model

The localized-electron model or the ligand-field approach is essentially the same as the Heitler-London theory for the hydrogen molecule. The model assumes that a crystal is composed of an assembly of independent ions fixed at their lattice sites and that overlap of atomic orbitals is small. When interatomic interactions are weak, intraatomic exchange (Hund s rule splitting) and electron-phonon interactions favour the localized behaviour of electrons. This increases the relaxation time of a charge carrier from about 10 s in an ordinary metal to 10 s, which is the order of time required for a lattice vibration in a polar crystal. 

Carbon occurs in the allotropes (different forms) diamond, graphite, and the fullerenes. The fullerenes are molecular solids (see Section 16.6), but diamond and graphite are typically network solids. In diamond, the hardest naturally occurring substance, each carbon atom is surrounded by a tetrahedral arrangement of other carbon atoms, as shown in Fig. 16.26(a). This structure is stabilized by covalent bonds, which, in terms of the localized electron model, are formed by the overlap of sp3 hybridized atomic orbitals on each carbon atom. 

Compare the description of the localized electron model (Lewis structure) with that of the molecular orbital model for the bonding in NO, NO+, and NO-. Account for any discrepancies between the two models. 

By this point in your study of chemistry, you no doubt recognize that the localized electron model, although very simple, is a very useful model for describing the bonding in molecules. Recall that a central feature of the model is the formation of hybrid atomic orbitals that are used for sharing electron pairs to form cr bonds between atoms. This same model can be used to account for the bonding in complex ions, but there are two important points to keep in mind. 

The main reason that the localized electron model cannot fully account for the properties of complex ions is that in its simplest form it gives no information about how the energies of the d orbitals are affected by complex ion formation. This is critical because, as we will see, the color and magnetism of complex ions result from changes in the energies of the metal ion d orbitals caused by the metal-ligand interactions. 

The simplest member of the saturated hydrocarbons, which are also called the alkanes, is methane (CH4). As discussed in Section 14.1, methane has a tetrahedral structure and can be described in terms of a carbon atom using an sp-J hybrid set of orbitals to bond to the four hydrogen atoms (see Fig. 22.1). The next alkane, the one containing two carbon atoms, is ethane (C2H6), as shown in Fig. 22.2. Each carbon in ethane is surrounded by four atoms and thus adopts a tetrahedral arrangement and sp3 hybridization, as predicted by the localized electron model. 

A special class of cyclic unsaturated hydrocarbons is known as the aromatic hydrocarbons. The simplest of these is benzene (C6H6), which has a planar ring structure, as shown in Fig. 22.11(a). In the localized electron model of the bonding in benzene, resonance structures of the type shown in Fig. 22.11(b) are used to account for the known equivalence of all the carbon-carbon bonds. But as we discussed in Section 14.5, the best description of the benzene molecule assumes that sp2 hybrid orbitals on each carbon are used to form the C—C and C—H a bonds, while the remaining 2p orbital on each carbon is used to form 77 molecular orbitals. The delocalization of these 1r electrons is usually indicated by a circle inside the ring [Fig. 22.11(c)]. 

The localized electron model assumes that the empty Zd orbitals can be used to accommodate extra electrons. Thus the sulfur atom in SF0 can have 12 electrons around it by using the Zs and 3p orbitals to hold 8 electrons, with the extra 4 electrons placed in the formerly empty orbitals. 

As we saw in Chapter 8, the localized electron model views a molecule as a collection of atoms bound together by sharing electrons between their atomic orbitals. The arrangement of valence electrons is represented by the Lewis structure (or structures, where resonance occurs), and the molecular geometry can be predicted from the VSEPR model. In this section we will describe the atomic orbitals used to share electrons and hence to form the bonds. 

In applying the localized electron model, we must remember not to overemphasize the characteristics of the separate atoms. It is not where the valence electrons originate that is important it is where they are needed in the molecule to achieve stability. In the same vein, it is not the orbitals in the isolated atom that matter, but which orbitals the molecule requires for minimum energy. 

It would seem that the ideal bonding model would be one with the simplicity of the localized electron model but with the delocalization characteristic of the molecular orbital model. We can achieve this by combining the two models to describe molecules that require resonance. Note that for species such as O3 and the double bond changes... 

Therefore, we conclude that the a bonds in a molecule can be described as being localized with no apparent problems. It is the tt bonding that must be treated as being delocalized. Thus, for molecules that require resonance, we will use the localized electron model to describe the a bonding and the molecular orbital model to describe the tt bonding. This allows us to keep the bonding model as simple as possible and yet give a more physically accurate description of such molecules. 

Very similar treatments can be applied to other planar molecules for which resonance is required by the localized electron model. For example, the NO3 ion can be described using the tt molecular orbital system shown In Fig. 9.48. In this molecule each atom is assumed to be sp hybridized, which leaves one p orbital on each atom perpendicular to the plane of the Ion. These p orbitals can combine to form the tt molecular orbital system. 

Molecules that require the concept of resonance in the localized electron model can be more accurately described by combining the localized electron and molecular orbital models... 

Describe the bonding in the CO ion using the localized electron model. How would the molecular orbital model describe the TT bonding in this species ... 

Localized electron model The central oxygen atom is sp hybridized, which is used to form the two cr bonds and hold the lone pair of electrons. An unchanged (unhybridized) p atomic orbital forms the tt bond with the neighboring oxygen atoms. The actual structure of O3 is an average of the two resonance structures. Molecular orbital model There are two localized cr bonds and a tt bond that is delocalized over the entire surface of the molecule. The delocalized TT bond results from overlap of a p atomic oribtal on each oxygen atom in O3. 59. 

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