Valence bond theory Assumes that

Application of valence bond theory to more complex molecules usually proceeds by writing as many plausible Lewis structures as possible which correspond to the correct molecular connectivity. Valence bond theory assumes that the actual molecule is a hybrid of these canonical forms. A mathematical description of the molecule, the molecular wave function, is given by the sum of the products of the individual wave functions and weighting factors proportional to the contribution of the canonical forms to the overall structure. As a simple example, the hydrogen chloride molecule would be considered to be a hybrid of the limiting canonical forms H—Cl, H Cr, and H C1. The mathematical treatment of molecular structure in terms of valence bond theory can be expanded to encompass more complex molecules. However, as the number of atoms and electrons increases, the mathematical expression of the structure, the wave function, rapidly becomes complex. For this reason, qualitative concepts which arise from the valence bond treatment of simple molecules have been applied to larger molecules. The key ideas that are used to adapt the concepts of valence bond theory to complex molecules are hybridization and resonance. In this qualitative form, valence bond theory describes molecules in terms of orbitals which are mainly localized between two atoms. The shapes of these orbitals are assumed to be similar to those of orbitals described by more quantitative treatment of simpler molecules. 

Describe the bonding in H2O according to valence bond theory. Assume that the molecular geometry is the same as given by the VSEPR model. 

We said in Section 1.5 that chemists use two models for describing covalent bonds valence bond theory and molecular orbital theory. Having now seen the valence bond approach, which uses hybrid atomic orbitals to account for geometry and assumes the overlap of atomic orbitals to account for electron sharing, let s look briefly at the molecular orbital approach to bonding. We ll return to the topic in Chapters 14 and 15 for a more in-depth discussion. 

In valence-bond theory, we assume that bonds form when unpaired electrons in valence-shell atomic orbitals pair the atomic orbitals overlap end to end to form cr-bonds or side by side to form ir-bonds. 

The generally accepted theory of electric superconductivity of metals is based upon an assumed interaction between the conduction electrons and phonons in the crystal.1-3 The resonating-valence-bond theory, which is a theoiy of the electronic structure of metals developed about 20 years ago,4-6 provides the basis for a detailed description of the electron-phonon interaction, in relation to the atomic numbers of elements and the composition of alloys, and leads, as described below, to the conclusion that there are two classes of superconductors, crest superconductors and trough superconductors. 

Valence bond theory was initially the most widely accepted approach, probably because it depended on familiar concepts of mesomeric effects in conjugated systems. The theory assumed that the true wave function for the mesomeric state of a molecule is a linear sum of those of the contributing canonical forms. The technique was never successful for quantitative calculation of the absorption spectra of dyes, however, because of the difficulties encountered when introducing the numerous canonical structures necessary for computational precision. 

The exceptions to the octet rule described in the previous section, the xenon compounds and the tri-iodide ion, are dealt with by the VSEPR and valence bond theories by assuming that the lowest energy available d orbitals participate in the bonding. This occurs for all main group compounds in which the central atom forms more than four formal covalent bonds, and is collectively known as hypervalence, resulting from the expansion of the valence shell This is referred to in later sections of the book, and the molecular orbital approach is compared with the valence bond theory to show that d orbital participation is unnecessary in some cases. It is essential to note that d orbital participation in bonding of the central atom is dependent upon the symmetry properties of individual compounds and the d orbitals. 

The VSEPR theory assumes that the four electrons from the valence shell of the carbon atom plus the valency electrons from the four hydrogen atoms form four identical electron pairs which, at minimum repulsion, give the observed tetrahedral shape. To rationalize the tetrahedral disposition of four bond-pair orbitals with those of the 2s and three 2p atomic orbitals of the carbon atom, sp3 hybridization is invoked. 

We have used the concepts of the resonance methods many times in previous chapters to explain the chemical behavior of compounds and to describe the structures of compounds that cannot be represented satisfactorily by a single valence-bond structure (e.g., benzene, Section 6-5). We shall assume, therefore, that you are familiar with the qualitative ideas of resonance theory, and that you are aware that the so-called resonance and valence-bond methods are in fact synonymous. The further treatment given here emphasizes more directly the quantum-mechanical nature of valence-bond theory. The basis of molecular-orbital theory also is described and compared with valence-bond theory. First, however, we shall discuss general characteristics of simple covalent bonds that we would expect either theory to explain. 

A major difference between the valence-bond theory of chemical bonding and molecular orbital theory is that the former assumes, like the Lewis approach, that the electrons in a bond are localized between the two... 

It will now be clear that the accuracy that may be attained in crystal analysis depends on the number of observed reflections and on the precision with which their intensities can be measured. (We assume that the structure is not complicated by any randomness or disorder, and that the necessary absorption and extinction corrections can be made.) A very useful discussion of the requirements necessary for determining bond lengths to within a limit of error of 0-01 A has been given by Cruickshank (1960). This is, of course, a very ambitious limit, but if it could be achieved it would enable the predictions of the molecular-orbital and valence-bond theories in aromatic hydrocarbons to be distinguished. It is pointed out that at the 0-1% level of significance a bond length difference must be 3-3 times the standard deviation to be accepted as genuine, so the limit of error of 0-01 A would require an e.s.d. (estimated standard deviation) of 0-003 A or better in the bond difference, or a coordinate e.s.d. of 0-0015 A or better. 

This theory implies outer orbital involvement in the bonding. It assumes that each bond between the ligand and the central atom involves an electron pair. A double bond involves four electrons. Further, it assumes that all nonbonding valence electrons have a steric effect. These lone pairs repel other electron pairs more than do bonding electron pairs and have about the same steric requirements as a double bond. Gillespie predicted the shape of unknown species using this theory all later isolated species conformed to his predictions. 

Valence bond (VB) theory Assumes that covalent bonds are formed when atomic orbitals on different atoms overlap and electrons are shared. 

The valence bond and molecular orbital theories differ in how they use the orbitals of two hydrogen atoms to describe the orbital that contains the electron pair in H2. Both theories assume that electron waves behave much like more familiar waves, such as sound and light waves. One property of waves that is important here is called interference in physics. Constructive interference occurs when two waves combine so as to reinforce each other ( in phase ) destructive interference occurs when they oppose each other ( out of phase ) (Figure 1.15). In the valence bond model constructive interference between two electron waves is seen as the basis for the shared electron-pair bond. In the molecular orbital model, the wave functions of molecules are derived by combining wave functions of atoms. 

At present, two quantum mechanical theories are used to describe covalent bond formation and the electronic structure of molecules. Valence bond (VB) theory assumes that the electrons in a molecule occupy atomic orbitals of the individual atoms. It permits us to retain a picture of individual atoms taking part in the bond formation. The second theory, called molecular orbital (MO) theory, assumes the formation of molecular orbitals from the atomic orbitals. Neither theory perfectly explains aU aspects of bonding, but each has contributed something to our understanding of many observed molecular properties. 

It is well known that certain univalent metals (for example, lithium) form diatomic molecules in the vapour in which the interatomic binding is presumably covalent in character. On the valence-bond theory it is assumed that such bonds also operate in the solid state, but since the number of electrons available is inadequate to give rise to covalent bonds between each atom and all its neighbours (eight in lithium) resonance is assumed to take place throughout the solid in a way which may be symbolized, in two dimensions, thus ... 

Valence bond theory. Valence bond (VB) theory assumes that atoms form covalent bonds as they share pairs of electrons via overlapping valence shell orbitals. A single covalent bond forms when two atoms share a pair of electrons via the sigma overlap of two atomic orbitals—a valence orbital from each atom. A double bond forms when two atoms share two pairs of electrons, one pair via a sigma overlap of two atomic orbitals and one via a pi overlap. A triple bond forms by three sets of orbital overlap, one of the sigma type and two of the pi type, accompanied by the sharing of three pairs of electrons via those overlaps. (When a pair of valence shell electrons is localized at only one atom, that is, when the pair is not shared between atoms, it is called a lone or nonbonding pair.)... 

Again, the value of fi is assumed to be the same for the Hiickel and Mobius systems. Zimmerman advocated this approach as a general tool in organic chemistry and called it MO following, noting that it is the molecular orbital theory counterpart to electron pushing in valence bond theory. For a discussion, see reference 172c. 

In the previous chapters, we discussed various models of bonding for covalent and polar covalent molecules (the VSEPR and LCP models, valence bond theory, and molecular orbital theory). We shall now turn our focus to a discussion of models describing metallic bonding. We begin with the free electron model, which assumes that the ionized electrons in a metallic solid have been completely removed from the influence of the atoms in the crystal and exist essentially as an electron gas. Freshman chemistry books typically describe this simplified version of metallic bonding as a sea of electrons that is delocalized over all the metal atoms in the crystalline solid. We shall then progress to the band theory of solids, which results from introducing the periodic potential of the crystalline lattice. 

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