The Valence Bond Theory

From the point of view of the Valence Bond Theory (VBT) the conception of the chemical bonding is practically the same as that of R.N. Lewis. VBT may indeed be considered as representing a rationalization in terms of the wave mechanics of the idea of bonds by sharing electron pairs. 

When two atoms with appropriate orbitals-i.e. orbitals of not very different energy and of the same symmetry, and each with one electron-approach one another closely, electron pairing will be produced. In this model electron pair sharing is mathematically represented as a product of the atom wave functions. 

This product is associated with the probability of finding the electron of both atoms A and B in the space between the nuclei. Because of the indistinguishabi-lity of electrons (1) and (2) two wave functions and should be considered. 

However, this solution may be considerably improved by considering that there is also a finite chance that both electrons will be occasionally associated to the same atom A or B  

Thus the description of real atoms can then be obtained in an acceptable approximation by the hybrid function ab- 

The more recent treatment of the covalent bond, based on the application of the principles of wave mechanics, has developed in two distinct forms, usually termed the valence-bond and molecular-orbital theories, respectively. Although ultimately there is no inconsistency between these two theories, they do in fact approach the problem of chemical binding from different points of view, and we shall generally find that for our purposes the valence-bond treatment is the more suitable. This theory starts from concepts already familiar to the chemist and its conclusions can usually be expressed verbally in qualitative terms the molecular-orbital theory, on the other hand, is more mathematical in its approach and lends itself less readily to such an interpretation. We shall, therefore, first discuss the valency-bond theory, and refer only briefly to the molecular-orbital treatment later in the chapter. 

The valence-bond theory of covalent binding involves the reinterpretation of the Lewis picture of the chemical bond in terms of the more detailed description of the electronic structure of the elements discussed in chapter 2, and immediately new considerations arise. The bond is still conceived as due to a sharing of two electrons, or more precisely to an overlapping of their orbitals, but now sharing is possible only between electrons of opposite spin. It follows at once that electrons already paired in orbitals can play no part in covalent binding, so that for any given element it becomes important to consider which particular orbitals will be available for bond formation. 

In the hydrogen atom the single electron in the s orbital is of course unpaired, and it is a pairing of the two electrons in two atoms which is responsible for the H-H bond in the hydrogen molecule such a bond may therefore be termed an s-s bond. In fluorine, with the 

This distinctive spatial distribution of the bonds from an atom is a most important characteristic of the covalent link and one by means of which it may often be recognized in crystal structures. 

Carbon, with the configuration is2, 2s22p zpli presents an apparent difficulty although there are four electrons in the L shell, two of these are already paired in the 2s orbital and only two are available for bond formation, suggesting that carbon should be divalent. To 

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The concepts of directed valence and orbital hybridization were developed by Linus Pauling soon after the description of the hydrogen molecule by the valence bond theory. These concepts were applied to an issue of specific concern to organic chemistry, the tetrahedral orientation of the bonds to tetracoordinate carbon. Pauling reasoned that because covalent bonds require mutual overlap of orbitals, stronger bonds would result from better overlap. Orbitals that possess directional properties, such as p orbitals, should therefore be more effective than spherically symmetric 5 orbitals. 

McWeeny, R., Proc. Roy. Soc. London) A223, 306, The valence-bond theory of molecular structure. II. Reformulation of the theory."... 

For purely qualitative arguments, on the other hand, the former is quite convenient. The description of the theory up to this point has been, in fact, merely a statement of the qualitative con elusions of the valence bond theory. 

All lone pair orbitals have a node between the two atoms and, hence, have a slightly antibonding character. This destabilizing effect of the lone pair localized molecular orbitals corresponds to the nonbonded repulsions between lone pair atomic orbitals in the valence bond theory. In the MO theory all bonding and antibonding resonance effects can be described as sums of contributions from orthogonal molecular orbitals. Hence, the nonbonded repulsions appear here as intra-orbital antibonding effects in contrast to the valence-bond description. 

The VSEPR theory is only one way in which the molecular geometry of molecules may be determined. Another way involves the valence bond theory. The valence bond theory describes covalent bonding as the mixing of atomic orbitals to form a new kind of orbital, a hybrid orbital. Hybrid orbitals are atomic orbitals formed as a result of mixing the atomic orbitals of the atoms involved in the covalent bond. The number of hybrid orbitals formed is the same as the number of atomic orbitals mixed, and the type of hybrid orbital formed depends on the types of atomic orbital mixed. Figure 11.7 shows the hybrid orbitals resulting from the mixing of s, p, and d orbitals. 

The valence bond theory describes covalent bonding as the overlap of atomic orbitals to form a new kind of orbital, a hybrid orbital. 

In the valence bond theory, sigma bonds overlap on a line drawn between the two nuclei, while pi bonds result from the overlap of atomic orbitals above and below a line connecting the two atomic nuclei. 

According to the valence bond theory, if a total charge-transfer occurs between neutral starting partners, all acceptor molecules will have a negative charge and all donor molecules a positive charge131. 

The Hy-CI function used for molecular systems is based on the MO theory, in which molecular orbitals are many-center linear combinations of one-center Cartesian Gaussians. These combinations are the solutions of Hartree-Fock equations. An alternative way is to employ directly in Cl and Hylleraas-CI expansions simple one-center basis functions instead of producing first the molecular orbitals. This is a subject of the valence bond theory (VB). This type of approach, called Hy-CIVB, has been proposed by Cencek et al. (Cencek et.al. 1991). In the full-CI or full-Hy-CI limit (all possible CSF-s generated from the given one-center basis set), MO and VB wave functions become identical each term in a MO-expansion is simply a linear combination of all terms from a VB-expansion. Due to the non-orthogonality of one-center functions the mathematical formalism of the VB theory for many-electron systems is rather cumbersome. However, for two-electron systems this drawback is not important and, moreover, the VB function seems in this case more natural. 

The MO theory treats molecular bonds as a sharing of electrons between nuclei. Unlike the valence bond theory, which treats the electrons as locahzed balloons of electron density, the MO theory says that the electrons are delocalized. That means that they are spread out over the entire molecule. Now, when two atoms come together, their two atomic orbitals react to form two possible molecular orbitals. 

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. 

What is the composition of iron, cobalt, and nickel carbonyls Consider the structure of the carbonyls of these elements from the standpoint of the valence bond theory. 

Preparation of a Complex Ammonium Salt of Copper(II). Dissolve 0.5 g of finely triturated copper(II) sulphate pentahydrate in 12.5 ml of a 15% ammonia solution. If the solution is turbid, filter it. Slowly add 7.5 ml of ethanol to the filtrate and let it stand for a few hours in the cold. Filter off the formed crystals, wash them first with a mixture of ethanol and a concentrated ammonia solution (1 1), and then with ethanol and ether. Dry them at room temperature. Into what ions does the product dissociate in the solution Consider the structure of the complex ion from the viewpoint of the valence bond theory. 

In some respects the ligand field theory is closely related, at least qualitatively, to the valence-bond theory described in the preceding sections, and many arguments about the structure of the normal state of a complex or crystal can be carried out in either of the two ways, with essentially the same results.66... 

The principal innovations that have been made in the discussion of the theory of the chemical bond in this edition are the wide application of the electroneutrality principle and the use of an empirical equation (Sec. 7-10) for the evaluation of the bond numbers of fractional bonds from the observed bond lengths. A new theory of the structure of electron-deficient substances, the resonating-valence-bond theory, is described and used in the discussion of the boranes, ferrocene, and other substances. A detailed discussion of the valence-bond theory of the electronic structure of metals and intermetallic compounds is also presented. 

When this kind of interaction occurs between vibrational states instead of electronic states it is called Fermi resonance we shall discuss this later (Sect. 10.8). In fact, the whole qualitative concept of resonance stabilization as used in the valence bond theory is just the same principle in still another guise. 

As noted in Section 9.1, there are three closely related theories of the electronic structures of transition metal complexes, all making quite explicit use of the symmetry aspects of the problem but employing different physical models of the interaction of the ion with its surroundings as a basis for computations. These three theories, it will be recalled, are the crystal field, ligand field, and MO theories. There is also the valence bond theory, which makes less explicit use of symmetry but is nevertheless in accord with the essential symmetry requirements of the problem. We shall now briefly outline the crystal field and ligand field treatments and comment on their relationship to the MO theory. 

There is an implicit assumption contained in all of the above The two bonding electrons are of opposite spin. If two electrons are of parallel spin, no bonding occurs, but repulsion instead curve /, Fig. 5.1). This is a result of the Pauli exclusion principle. Because of the necessity for pairing in each bond formed, the valence bond theory is often referred to as the electron pair theory, and it forms a logical quantum-mechanical extension of Lewis s theory of electron pair formation. 

In the valence bond theory, hybridization of orbitals is an integral part of bond formation. As we shall see, the concept need not be explicitly considered in molecular orbital theory but may be helpful in visualizing the process of bond formation. 

Lewis s theory of the chemical bond was brilliant bul it was little more than guesswork inspired by insight. 1 ewis had no way of knowing why an electron pair, the essential feature of his approach, was so important. The valence-bond theory explained this point but could not explain the properties of some molecules. For example, the Lewis description of 02 is 0=0, with all the electrons paired. However, oxygen is a paramagnetic substance (Fig. 3.28 and Box 3.2), and paramagnetism is a property of unpaired electrons. The magnetism of O, therefore contradicts both the l wis structure and the valence-bond description of the molecule. 

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... 

According to the valence bond theory (Section 7.10), the bonding in metal complexes arises when a filled ligand orbital containing a pair of electrons overlaps a vacant hybrid orbital on the metal ion to give a coordinate covalent bond ... 

From the viewpoint of the valence bond theory, the excited states resulting from the transition (32) involve resonance between structures C—O and C—0 which, since the interaction between a lone electron and an electron pair is repulsive, is roughly the equivalent of a three-electron CO bond. Their structure can be represented approximately by the formula (3). The lone non-bonding electron confers intense chemical reactivity not unlike that possessed by a free alkoxy radical (see, e.g., de Mayo et al., 1961). 

Graphite has layers of hexagonal networks. Each C atom is bonded to three C atoms in the same plane (sp2 hybrids). There is one electron per C in delocalized tt orbitals extending throughout the layer or, in terms of the valence bond theory, there are alternating single and double bonds. Graphite conducts electricity within the plane and can be used as an electrode. 

McWeeny has written a tribute to the valence-bond theory pioneers of 1927-1935.362 Shavitt has outlined the history and evolution of Gaussian basis sets as employed in ah initio molecular orbital calculations.363 Hargittai has interviewed Roald Hoffmann (b. 1937)364 of Cornell University and Kenichi Fukui (1918-1998)365 of Kyoto University, who were jointly awarded the Nobel Prize in Chemistry in 1981. Fukui developed the concept of frontier orbitals and recognized the importance of orbital symmetry in chemical reactions, but his work was highly mathematical and its importance was not appreciated until Robert Woodward (1917-1979) and Hoffmann produced their rules for the conservation of orbital symmetry from 1965 onwards.366... 

Historically, molecular orbital theory was preceded by an alternative and successful description of the bonding in H2. In 1927, W. Heitler and F. London proposed the valence bond theory, in which each electron resides in an atomic orbital. In other words, in this model, the identity of the atomic orbital is preserved. There are two ways in which the two electrons in H2 can be accommodated in the pair of Is atomic orbitals ... 

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