VSEPR electron distributions

Before discussing the AIM theory, we describe in Chapters 4 and 5 two simple models, the valence shell electron pair (VSEPR) model and the ligand close-packing (LCP) model of molecular geometry. These models are based on a simple qualitative picture of the electron distribution in a molecule, particularly as it influenced by the Pauli principle. 

Consider one beautifully symmetrical shape predicted by VSEPR theory the tetrahedron. Four equivalent pairs of electrons in the valence shell of an atom should distribute themselves into such a shape, with equal angles and an equal distance between each pair. But what sort of atom has four equivalent electron pairs in its valence shell Aren t valence electrons distributed between different kinds of orbitals, like s and p orbitals (We introduce these orbitals in Chapter 4.)... 

The VSEPR model of bonding treats all atoms the same. However, the identities of the atoms in a molecule affect how the electrons are distributed. This knowledge is important, because electron distribution affects the properties of the substance. Life itself depends on the locations of electrons for example, their distribution controls the shape of the DNA double helix and the way it unwinds in the course of reproduction. Electron distributions also control the shapes of our individual proteins and enzymes, and shape is crucial to their function. In fact, when proteins lose their shape—for instance, when we suffer burns—they cease to function and we may die. Knowledge about electron distributions is also essential for understanding less dramatic properties, such as the ability of water to dissolve ionic compounds. 

The VSEPR model works at its best in rationalizing ground state stereochemistry but does not attempt to indicate a more precise electron distribution. The molecular orbital theory based on 3s and 3p orbitals only is also compatible with a relative weakening of the axial bonds. Use of a simple Hiickel MO model, which considers only CT orbitals in the valence shell and totally neglects explicit electron repulsions can be invoked to interpret the same experimental results. It was demonstrated that the electron-rich three-center bonding model could explain the trends observed in five-coordinate speciesVarious MO models of electronic structure have been proposed to predict the shapes and other properties of non-transition element... 

The VSEPR theory allows chemists to successfully predict the approximate shapes of molecules it does not, however, say why bonds exist. The quantum mechanical valence bond theory, with its overlap of atomic orbitals, overcomes this difficulty. The resulting hybrid orbitals predict the geometries of molecules. A quantum mechanical graph of radial electron density (the fraction of electron distribution found in each successive thin spherical shell from the nucleus out) versus the distance from the nucleus shows maxima at certain distances from the nucleus—distances at which there are higher probabilities of finding electrons. These maxima correspond to Lewis s idea of shells of electrons. 

Most workers who have considered this question have concluded that there is. Crucial is the way that a single entity, the electron distribution in a molecule, is divided up to give distinct lone and bonding pairs. What has usually been done is to adopt some criterion which seems to lead to a division as close as possible to that made, more qualitatively, by the VSEPR model itself. 

The most stable shape for any molecule maximizes electron-nuclear attractive interactions while minimizing nuclear-nuclear and electron-electron repulsions. The distribution of electron density in each chemical bond is the result of attractions between the electrons and the nuclei. The distribution of chemical bonds relative to one another, on the other hand, is dictated by electrical repulsion between electrons in different bonds. The spatial arrangement of bonds must minimize electron-electron repulsion. This is accomplished by keeping chemical bonds as far apart as possible. The principle of minimizing electron-electron repulsion is called valence shell electron pair repulsion, usually abbreviated VSEPR. 

If the electronegativity of the ligands X is much less than the electronegativity of the central atom A, the electrons in the valence shell of A are not well localized into pairs and therefore have a small or zero effect on the geometry. In such molecules the bonds are very ionic in the sense A X+, and the central atom A is essentially an anion with a spherical electron density distribution. In this case the VSEPR model is not valid, and the geometry of the molecule is determined by ligand-ligand repulsions. 

This chapter is based on the VSEPR and LCP models described in Chapters 4 and 5 and on the analysis of electron density distributions by the AIM theory discussed in Chapters 6 and 7. As we have seen, AIM gives us a method for obtaining the properties of atoms in molecules. Throughout the history of chemistry, as we have discussed in earlier chapters, most attention has been focused on the bonds rather than on the atoms in a molecule. In this chapter we will see how we can relate the properties of bonds, such as length and strength, to the quantities we can obtain from AIM. 

Gillespie, R.J. (2000). Improving our understanding of molecular geometry and the VSEPR model through the ligand close-packing model and the analysis of electron density distributions. 

Chapters 8 and 9 are devoted to a discussion of applications of the VSEPR and LCP models, the analysis of electron density distributions to the understanding of the bonding and geometry of molecules of the main group elements, and on the relationship of these models and theories to orbital models. Chapter 8 deals with molecules of the elements of period 2 and Chapter 9 with the molecules of the main group elements of period 3 and beyond. 

Under the conditions of maximum localization of the Fermi hole, one finds that the conditional pair density reduces to the electron density p. Under these conditions the Laplacian distribution of the conditional pair density reduces to the Laplacian of the electron density [48]. Thus the CCs of L(r) denote the number and preferred positions of the electron pairs for a fixed position of a reference pair, and the resulting patterns of localization recover the bonded and nonbonded pairs of the Lewis model. The topology of L(r) provides a mapping of the essential pairing information from six- to three-dimensional space and the mapping of the topology of L(r) on to the Lewis and VSEPR models is grounded in the physics of the pair density. 

VSEPR Model valence shell electron pair repulsion model, model used to predict the geometry of molecule based on distribution of shared and unshared electron pairs distributed around central atom of a molecule... 

The table below contains examples of molecules that possess various total numbers of a electron pairs, and possess various numbers of bonding electron pairs. For each example, draw out a VSEPR thought experiment diagram and sketch the distribution of the g electron pairs. 

The electron-dot structures described in Sections 7.6 and 7.7 provide a simple way to predict the distribution of valence electrons in a molecule, and the VSEPR model discussed in Section 7.9 provides a simple way to predict molecular shapes. Neither model, however, says anything about the detailed electronic nature of covalent bonds. To describe bonding, a quantum mechanical model called valence bond theory has been developed. 

Bonds with r < dl < d[ become possible because of nuclear screening (increased bond order), which causes concentration of the bonding pair directly between the nuclei. The exclusion limit is reached at d = t and appears as a geometrical property of space. The distribution of molecular electron density is dictated by the local geometry of space-time. Model functions, such as VSEPR or minimum orbital angular momentum [65], that correctly describe this distribution, do so without dictating the result. The template is provided by the curvature of space-time which appears to be related to the three fundamental constants tt, t and e. 

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