Electrons Lewis model

The covalent, or shared electron pair, model of chemical bonding was first suggested by G N Lewis of the University of California m 1916 Lewis proposed that a sharing of two electrons by two hydrogen atoms permits each one to have a stable closed shell electron configuration analogous to helium... 

The Lewis model of the chemical bond assumes that each bonding electron pair is located between the two bonded atoms—it is a localized electron model. However, we know from the wave-particle duality of the electron (Sections 1.5-1.7) that the location of an electron in an atom cannot be described in terms of a precise position, but only in terms of the probability of finding it somewhere in a region of... 

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.

There is no clear rigorous definition of an atom in a molecule in conventional bonding models. In the Lewis model an atom in a molecule is defined as consisting of its core (nucleus and inner-shell electrons) and the valence shell electrons. But some of the valence shell electrons of each atom are considered to be shared with another atom, and how these electrons should be partitioned between the two atoms so as to describe the atoms as they exist in the molecule is not defined. 

The concept of a bond has precise meaning only in terms of a given model or theory. In the Lewis model a bond is defined as a shared electron pair. In the valence bond model it is defined as a bonding orbital formed by the overlap of two atomic orbitals. In the AIM theory a bonding interaction is one in which the atoms are connected by a bond path and share an interatomic surface. 

The theory as presented so far is clearly incomplete. The topology of the density, while recovering the concepts of atoms, bonds and structure, gives no indication of the localized bonded and non-bonded pairs of electrons of the Lewis model of structure and reactivity, a model secondary in importance only to the atomic model. The Lewis model is concerned with the pairing of electrons, information contained in the electron pair density and not in the density itself. Remarkably enough however, the essential information about the spatial pairing of electrons is contained in the Laplacian of the electron density, the sum of the three second derivatives of the density at each point in space, the quantity V2p(r) [44]. 

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. 

Of course, the Coulomb interaction appears in the Hamiltonian operator, H, and is often invoked for interpreting the chemical bond. However, the wave function, l7, must be antisymmetric, i.e., must satisfy the Pauli exclusion principle, and it is the only fact which explains the Lewis model of an electron pair. It is known that all the information is contained in the square of the wave function, 1I7 2, but it is in general much complicated to be analyzed as such because it depends on too many variables. However, there have been some attempts [3]. Lennard-Jones [4] proposed to look at a quantity which should keep the chemical significance and nevertheless reduce the dimensionality. This simpler quantity is the reduced second-order density matrix... 

Of all the concepts used in chemistry, that of the chemical bond is one of the most useful and, at the same time, one of the most difficult. It is useful because it helps us to understand the structures of compounds and their properties, and it is difficult because it is not easy to relate it to the physical theories, such as quantum mechanics, that underlie chemistry. This is not to say that people have not attempted to find a connection between the chemical bond and quantum mechanics. The Lewis (1923) electron pair model and the orbital overlap model (Coulson 1961) are, perhaps, among the better known attempts, but all are a posteriori rationalizations, trying to explain the properties of the empirical nineteenth-century chemical bond in terms of twentieth-century physical concepts. It is unlikely that, left to themselves, theoretical chemists in the twentieth century would have ever created the idea of a chemical bond had not the concept already been central to the language of structural chemistry. To this day the chemical bond remains largely an empirical concept. 

Although it is not obvious from its Lewis structure, molecular oxygen, 02, is also a biradical In fact, experiments have shown that the most plausible Lewis structure, 0=0, gives a false impression of the arrangement of electrons. In molecular oxygen, two of the electrons that the Lewis structure implies are responsible for the bonds do not in fact pair with one another. The molecule is really a biradical with an unpaired electron on each O atom. For this reason, its Lewis structure is often q. . q written as shown in (30). The Lewis model of bonding does not predict... 

The Laplacian of the electron density plays a dominant role throughout the theory.191 In addition, Bader has shown that the topology of the Laplacian recovers the Lewis model of the electron pair, a model that is not evident in the topology of the electron density itself. The Laplacian of the density thus provides a physical valence-shell electron pair repulsion (VSEPR) basis for the model of molecular geometry and for the prediction of the reaction sites and their relative alignment in acid-base reactions. This work is closely tied to earlier studies by Bader of the electron pair density, demonstrating that the spatial localization of electrons is a result of a corresponding localization of the Fermi correlation hole. 

Fig. 13 is a drawing of electron-domain models of some Group VI hexafluorides. Open circles represent the electron-pairs of four of the six bonds to fluorine atoms in a Lewis, single-bond formulation of these molecules. Solid circles represent the atomic cores of oxygen, sulfur, selenium, tellurium, tungsten, and uranium (core radii, in hundreths of A, 9, 29, 42, 56, 62, and 80 2>, respectively). These hexafluorides are, in order, non-existent, extra-ordinarily unreactive, hydrolyzed slowly, hydrolyzed completely at room temperature in 24 hours, hydrolyzed readily, and hydrolyzed very rapidly. 

Fig. 19. Saturation of primary affinity. Two-dimensional representation of an electron-domain model of the formation of a conventional chemical bond the reaction of a Lewis base (NHg) with a relatively strong Lewis acid (BH3).

A drawing of a two-dimensional, electron-domain model of a conventional Lewis lone pair is shown in Fig. 23. The lone pair and bonding pairs are structurally equivalent they have identical van der Waals envelopes. Such seems to be nearly the case for lone pairs in the valence-shells of small-core, non-octet-expanding atoms (carbon, nitrogen, oxygen and fluorine). 

Prompted by the structure of the periodic table of the elements, electrons were assumed to occur in concentric shells around the nucleus with a positive charge of Z units, equal to the number of extranuclear electrons. In any period of 8 elements, arranged in order of increasing Z, electrons are postulated to occupy an increasing number of sites (from 1 to 8) at the corners of a cube centred at the nucleus. Any vacancy in the shell of eight enables the relevant atom to share an electron with a neighbouring atom to form a covalent bond and to complete the octet of electrons for that shell. This view has now endured for almost hundred years and still forms the basis for teaching elementary chemistry. The simple planetary model, proposed by Bohr, allows for only one electron per orbit and has little in common with the Lewis model. 

In isolated atoms the electrons are in the atomic orbitals (AOs) of that atom. What happens to the electrons when atoms come together to form bonds In the simple Lewis model, some of the electrons are pictured as being shared between atoms. In the orbital model, these shared electrons are pictured as being in orbitals that extend around more than one atom. Such orbitals are called molecular orbitals (MOs). 

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