Electron Pair Domains

We can see now why the static model of Lewis with four electron pairs in a tetrahedral arrangement is so useful even though electrons are in rapid motion and do not occupy fixed positions. Each electron pair occupies a reasonably well localized domain, and four domains have a tetrahedral arrangement. 

We have so far considered valence shells containing four pairs of electrons, but we can extend the same arguments to other numbers of valence shell electron pairs. The most probable arrangements of pairs of opposite spin electrons in the valence shell of an atom in a molecule are two pairs, collinear three pairs, equilateral triangular four pairs, tetrahedral five pairs, trigonal bipyramidal six pairs, octahedral. This is because, as we will now see, these are the arrangements that keep the electron pairs as far apart as possible. We discuss valence shells with more than six electron pairs in Chapter 9. 

Attempts have been made to put the VSEPR model on a quantitative basis by describing the interaction between electron pairs in terms of force law of the type 

Although the electron domain model is, as we shall see, a very useful model, we must remember that it is just that, a model—indeed a very approximate model. We cannot observe the individual domains of electrons but only the total electron density distribution. 

Number of particles Arrangement3 Number of particles Arrangement3 

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Two, Three, Four, and Six Electron Pair Domain Valence Shells 93... 

We discuss molecules with a valence shell containing five electron pair domains in Section 4.6. The preferred arrangements of five valence shell domains, the trigonal bipyramid and the square pyramid, are not regular polyhedra and therefore exhibit special features not found in tetrahedral and octahedral molecules. Molecules with seven and more electron pair domains in the valence shell of a central atom are not common, although they are of considerable interest. They are restricted to the elements of period 4 and higher periods, with very small ligands such as fluorine, and are discussed in Chapter 9. 

Figure 4.12 Representation of the bonding and nonbonding electron pair domains in the ammonia molecule, an AX3E molecule.

The nonequivalence in the size and shape of bonding and nonbonding electron pair domains can alternatively be expressed in terms of the relative magnitude of their mutual Pauli repulsions, which decrease in the following order ... 

Figure 4.16 Double bond (a) Lewis model of two tetrahedra sharing an edge, (b) Domain model the two single electron pair domains of the double bond are pulled in toward each other by the attraction of the two carbon cores forming one four-electron double-bond domain with a prolate ellipsoidal shape, thereby allowing the two hydrogen ligands to move apart.

Figure 4.17 Triple bonds (a) Lewis model of two tetrahedra sharing a face, (b) three electron pair domains, and (c) end-on view of the three electron pair domains forming the triple bond.

For AX molecules with no lone pairs in the valence shell of A, both the VSEPR model and the LCP model predict the same geometries, namely AX2 linear, AX3 equilateral triangular, AX4 tetrahedral, AX5 trigonal bipyramidal, and AX octahedral. Indeed Bent s tangent sphere model can be used equally as a model of the packing of spherical electron pair domains and as a model of the close packing of spherical ligands around the core of the central atom. 

Maxima are always observed in the VSCC of an atom in a molecule corresponding in number and geometrical arrangement to the nonbonding electron pair domains of the VSEPR model. 

Electrons in the core of an atom are fully localized into spherical shells but not into opposite-spin pairs. In an isolated atom the valence shell electrons are similarly localized into a spherical shell. The Laplacian shows that in each of these spherical shells there is a spherical region of charge concentration and a spherical region of charge depletion. But in these regions there is no localization of electrons of opposite spin into pairs. There are no Lewis pairs or electron pair domains in an inner shell. The domain of each electron is spherical and fully delocalized through the shell. 

Several methods have been used for analyzing the electron density in more detail than we have done in this paper. These methods are based on different functions of the electron density and also the kinetic energy of the electrons but they are beyond the scope of this article. They include the Laplacian of the electron density ( L = - V2p) (Bader, 1990 Popelier, 2000), the electron localization function ELF (Becke Edgecombe, 1990), and the localized orbital locator LOL (Schinder Becke, 2000). These methods could usefully be presented in advanced undergraduate quantum chemistry courses and at the graduate level. They provide further understanding of the physical basis of the VSEPR model, and give a more quantitative picture of electron pair domains. 

An analogy exists, also, between electron-pair-domain models and quantum mechanical models of molecules. 

Spherical-domain models of three-center bonds in localized-molecular-orbital models of a nonclassical carbonium ion, B4CI4, and TaeClfJ have been described 49,52) a drawing of a spherical-domain model of the methyl lithium tetramer, (LiCH, is shown in Fig. 31. Large, outer circles represent domains of electron-pairs of C—H bonds. Solid circles represent domains of Li+ ions. Shaded circles represent 4-center lithium-lithium-lithium-carbon bonds — i.e., electron-pair domains that touch, simultaneously, three lithium ions and the kernel of a carbon atom. The... 

Double and triple bond domains which are composed of two and three electron pairs, respectively, are larger than single-bond electron pair domains. 

Based upon Linnett s model, Gillespie begins by associating each unpaired electron with a region or domain in the atom, and then defines electron pair domains as regions of the atom in which there is a high probability of finding a pair of electrons of opposite spin, for example... 

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