Bond valences theory

The valence bond theory was developed by Professor Linus Pauling, of the California Institute of Technology, and made available in his excellent book. The Nature of the Chemical Bond, published in 1940, 1948, and 1960. Along with the late Marie Curie, Professor Pauling is one of the very few persons to have been awarded two Nobel prizes, the Nobel prize in chemistry in 1954 and the Nobel peace prize in 1962. Pauling s ideas have had an important impact on all areas of chemistry his valence bond theory has aided coordination chemists and has been extensively used. It can account reasonably well for the structure and magnetic properties of metal complexes. Extensions of the theory will account for other properties of coordination compounds such as absorption spectra, but other theories seem to do this more simply. Therefore, in recent years coordination chemists have favored the crystal field, ligand field, and molecular orbital theories. 

In six-coordinated systems, the hybrid orbitals involve the s, p py p, and atomic orbitals. The resulting six sp (f or cf sp hybrid orbitals point toward corners of an octahedron. For [CoFe] the d orbitals used have the same principal energy level as the s and p orbitals. A complex of the nsnp ruf type is called an outer-orbital complex because it uses outer d 

There must be at least one polar bond or one lone pair on the central atom. 

The polar bonds, if there are more than one, must be arranged so that their 

Put another way, if there are no polar bonds or lone pairs of electrons on the central atom, the molecule cannot be polar. Even if polar bonds or lone pairs are present, they may be arranged so that their polarities cancel one another, resulting in a nonpolar molecule. 

Carbon dioxide, CO2, is a three-atom molecule in which each carbon-oxygen bond is polar because of the electronegativity difference between C and O. But the molecule as a whole is shown by experiment (dipole moment measurement) to be nonpolar. This tells us that the polar bonds are arranged in such a way that the bond polarities cancel. Water, H2O, on the other hand, is a very polar molecule this tells us that the H—O bond polarities do not cancel one another. Molecular shapes clearly play a crucial role in determining molecular dipole moments. We will develop a better understanding of molecular shapes in order to understand molecular polarities. 

In Chapter 7 we described covalent bonding as electron pair sharing that results from the overlap of orbitals from two atoms. This is the basic idea of the valence bond (VB) theory—it describes how bonding occurs. In many examples throughout this chapter, we first use the VSEPR theory to describe the orientations of the electron 

The Lewis theory of chemical bonding provides a relatively simple way for us to visualize the arrangement of electrons in molecules. It is insufficient, however, to explain the differences beuveen the covalent bonds in compounds such as Hi, Fi, and HF. Although Lewis theory describes the bonds in these three molecules in exactly the same way, they really are quite different from one another, as evidenced by their bond lengths and bond enthalpies listed in Table 9.3. Understanding these differences and why covalent bonds form in the first place requires a bonding model that combines Lewis s notion of atoms sharing election pairs and the quantum mechanical descriptions of atomic orbitals. 

According to valence bond theory, atoms share electrons when an atomic orbital on one atom overlaps with an atomic orbital on the other. Each of the overlapping atomic orbitals must contain a single, unpaired electron. Furthermore, the two electrons shared by the bonded atoms must have opposite spins Section 6.6] nuclei of both atoms are attracted to the shared pair of electrons. It is this mutual attraction for the shared electrons that holds the atoms together. 

The H—H bond in Hi forms when the singly occupied Is orbitals of the two H atoms overlap  

Keep in mind that although there are still just two electrons, each atom thinks it owns them both, so when the sin occupied cxbitals overlap, both cxbitals end up dotiily cxixipied. 

Similarly, the F—F bond in Ft forms when the singly occupied 2p orbitals of the two F atoms overlap y y y 

The molecular orbital theory of the dihydrogen molecule is dealt with in detail above, and describes how the two electrons occupy a bonding molecular orbital so that they are equally shared between the two nuclei. This state of affairs can be written symbolically in the form  

The conclusion from this short discussion is that both valence bond and molecular orbital theories can describe the bonding of a system and 

The procedure of taking a linear combination of atomic orbitals, which we have considered with respect to the H2 molecule, is very fruitful when applied to other covalent bonds. Consider, for example, the hydrogen fluoride molecule, HF, formed from a hydrogen atom with one electron in the Is state and a fluorine atom with an electron configuration of ls 2s 2p. Fluorine has an unpaired 2p electron, and we can form a wave function of the Heitler-London type by making use of the atomic orbitals for this 2p electron and for the Is electron in the hydrogen atom  

This wave function could be improved by adding the contributions for ionic states  

Calculation of the bond energy on the basis of the variation treatment gives a reasonably good approximation to the experimental value. Better results are obtained if account is taken of the other electrons in the fluorine atom. Similar treatments can be applied to other covalent bonds. 

As with the hydrogen molecule, the calculations for hydrogen fluoride le ad to the conclusion that there is a piling-up of electron density between the nuclei. The H2 molecule is symmetrical, so that the electron cloud lies symmetrically between the nuclei. The quantum-mechanical calculations for hydrogen fluoride, on the other hand, lead to the result that the electron cloud lies more toward the fluorine atom. In other words, the last term in the wave function (1.56), in which both electrons are related to the fluorine atom, is more important than the third term, in which both are associated with the hydrogen atom (i.e., C4 c ). 

Two charges and -q. separated by a distance c/ the dipole moment is gd The direction of the moment is often represented by an arrow -t- , as shown. 

The VSEPR model is usually a satisfactory method for predicting molecular geometries. To understand bonding and electronic structure, however, you must look to quantum mechanics. We will consider two theories stemming from quantum mechanics valence bond theory and molecular orbital theory. Both use the methods of quantum mechanics but make different simplifying assumptions. In this section, we will look in a qualitative way at the basic ideas involved in valence bond theory, an approximate theory to explain the electron pair or covalent bond by quantum mechanics. 

The H—H bond forms when the Is orbitals,one from each atom, overlap. 

The bond forms by the overlap of a hydrogen Is orbital (blue) along the axis of a chlorine 3p orbital (green). 

Accx)rding to valence bond theory, a bond forms between two atoms when the following conditions are met  

An orbital on one atom comes to occupy a portion of the same region of space 

With the understanding that electrons occupy regions of space called orbitals, we can now turn our attention to a deeper understanding of covalent bonds. Specifically, a covalent bond is formed from the overlap of atomic orbitals. There are two commonly used theories for describing the nature of atomic orbital overlap valence bond theory and molecular orbital (MO) theory. The valence bond approach is more simphstic in its treatment of bonds, and therefore we will begin our discussion with valence bond theory. 

The overlap of the Is atomic orbitals of two hydrogen atoms, forming molecular hydrogen (H2). 

An illustration of a sigma bond, showing the circular symmetry with respect to the bond axis. 

Principles of Inorganic Chemistry, First Edition. Brian W. pfennig. 

A correction for the shielding of one electron from experiencing the full strength of either nuclear attraction by the presence of the other electron improves the curve, leading to a minimum at 74 pm and 365 kj/mol. Finally, curve (c) allows for the possibility of an ionic contribution to the bonding, where both of the electrons reside either on nucleus A or on nucleus 6. The probability of an ionic contribution in H2, where there is no difference in electronegativity between the two H atoms is very small, and so a weighting factor A is included as a coefficient in Equation (10.3) in front of each of the ionic terms (where A I). The minimum now occurs at 74.6 pm and 397 kj/mol. 

Artist s rendering of the theoretical potential energy curves (a)-(c) constructed using the data given by Equations (10.1)-(10.3), along with the experimentally observed attractive potential (c/) for the FI2 molecule. Curve (e) is the experimental repulsive term. [Blatt Communications.] 

According to VBT, the H-F bond forms as a resuit of the overlap of the Is orbital on H with the 2p orbitai on F so that the two nuclei can share a pair of electrons. In this and all subsequent figures, the hoiiow orbitai iobes indicate positive sign of the wavefunction while the shaded lobes indicate negative sign of the wavefunction. 

The process of hybridization itself does not consume any energy, because it simply involves a mathematical redistribution of the total electron density. However, the increased overlap and decreased electron-electron repulsion that result when the four sp -hybridized orbitals on C overlap with the four I s AOs on the H atoms more than compensate for the initial cost of electron promotion. Each C-H single bond in methane gains 435 kJ/mol of energy. The centrality of hybrid orbitals to 

The first and second combinations are the same (the terms are simply listed in different order), and the fifth and sixth combinations are exactly zero. The unique wavefunctions are, after some algebraic simplification  

Analogous steps will yield proper wavefunctions with A2, and symmetries. They ultimately yield, for the unique combinations, 

There are no nonzero linear combinations that can be labeled with the A2 symmetry species. Although most of the molecular wavefunctions are represented by a single atomic wavefimction in this case, this will not always be so. We get seven unique molecular orbitals from the seven atomic orbitals. 

Electron spins are not addressed explicitly by MO theory, but they are treated with respect to the Pauli principle just as atomic orbitals are Only two electrons can occupy any one orbital, and their spins must be opposite. Just as in atoms, electrons in molecules fill MOs starting with the lowest-energy MO, and in order of increasing energy. If two or more MOs are degenerate, one electron fills each MO before pairing of electrons in orbitals (Hund s rule). 

Previously, we have treated orbitals as covering the molecule as a whole, and have not from the start restricted the orbitals to any one atom. Many molecular orbitals can be approximated as linear combinations of atomic orbitals. Another way to consider molecular wavefunctions is in terms of products of atomic orbitals. This is valence bond theory, and ultimately it is very useful for describing the structures of molecules. Valence bond (or VB) theory dates from 1927, when W. Heftier and F. W. London constructed the first successful quantum-mechanical approximation of the hydrogen molecule, H2. It was developed further by J. C. Slater (of Slater determinant fame) and Linus Pauling. 

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Oxygen is a colourless gas which condenses to a pale blue liquid, b.p. 90 K, which is markedly paramagnetic indicating the presence of unpaired electrons (p. 229). Simple valence bond theory (as used in this book) would indicate the structure... 

One widely used valence bond theory is the generalised valence bond (GVB) method of Goddard and co-workers [Bobrowicz and Goddard 1977]. In the simple Heitler-London treatment of the hydrogen molecule the two orbitals are the non-orthogonal atomic orbitals on the two hydrogen atoms. In the GVB theory the analogous wavefunction is written ... 

Another approach is spin-coupled valence bond theory, which divides the electrons into two sets core electrons, which are described by doubly occupied orthogonal orbitals, and active electrons, which occupy singly occupied non-orthogonal orbitals. Both types of orbital are expressed in the usual way as a linear combination of basis functions. The overall wavefunction is completed by two spin fimctions one that describes the coupling of the spins of the core electrons and one that deals with the active electrons. The choice of spin function for these active electrons is a key component of the theory [Gerratt ef al. 1997]. One of the distinctive features of this theory is that a considerable amount of chemically significant electronic correlation is incorporated into the wavefunction, giving an accuracy comparable to CASSCF. An additional benefit is that the orbitals tend to be... 

T orbital for benzene obtained from spin-coupled valence bond theory. (Figure redrawn from Gerratt ], D L oer, P B Karadakov and M Raimondi 1997. Modem valence bond theory. Chemical Society Reviews 87 100.) figure also shows the two Kekule and three Dewar benzene forms which contribute to the overall wavefunction Kekuleform contributes approximately 40.5% and each Dewar form approximately 6.4%. 

Gerratt J, D L Cooper, P B Karadakov and M Raimondi 1997. Modem Valence Bond Theory. Chemical Society Reviews pp. 87-100. 

The characteristic feature of valence bond theory is that it pictures a covalent bond between two atoms in terms of an m phase overlap of a half filled orbital of one atom with a half filled orbital of the other illustrated for the case of H2 m Figure 2 3 Two hydrogen atoms each containing an electron m a Is orbital combine so that their orbitals overlap to give a new orbital associated with both of them In phase orbital overlap (con structive interference) increases the probability of finding an electron m the region between the two nuclei where it feels the attractive force of both of them... 

A vexing puzzle m the early days of valence bond theory concerned the fact that methane is CH4 and that the four bonds to carbon are directed toward the corners of a tetrahedron Valence bond theory is based on the overlap of half filled orbitals of the connected atoms but with an electron configuration of s 2s 2p 2py carbon has only two half filled orbitals (Figure 2 8a) How can it have bonds to four hydrogens ... 

In valence bond theory a covalent bond is described m terms of m phase overlap of a half filled orbital of one atom with a half filled orbital of another When applied to bonding m H2 the orbitals involved are the Is orbitals of two hydrogen atoms and the bond is a ct bond... 

Section 2 6 Bonding m methane is most often described by an orbital hybridization model which is a modified form of valence bond theory Four equiva lent sp hybrid orbitals of carbon are generated by mixing the 2s 2p 2py and 2p orbitals Overlap of each half filled sp hybrid orbital with a half filled hydrogen Is orbital gives a ct bond... 

Valence bond theory (Section 2 3) Theory of chemical bond mg based on overlap of half filled atomic orbitals between two atoms Orbital hybridization is an important element of valence bond theory... 

Structure. The straiued configuration of ethylene oxide has been a subject for bonding and molecular orbital studies. Valence bond and early molecular orbital studies have been reviewed (28). Intermediate neglect of differential overlap (INDO) and localized molecular orbital (LMO) calculations have also been performed (29—31). The LMO bond density maps show that the bond density is strongly polarized toward the oxygen atom (30). Maximum bond density hes outside of the CCO triangle, as suggested by the bent bonds of valence—bond theory (32). The H-nmr spectmm of ethylene oxide is consistent with these calculations (33). 

When activating substituents are present in the benzenoid ring, substitution usually becomes more facile and occurs in accordance with predictions based on simple valence bond theory. When activating substituents are present in the heterocyclic ring the situation varies depending upon reaction conditions thus, nitration of 2(177)-quinoxalinone in acetic acid yields 7-nitro-2(177)-quinoxalinone (21) whereas nitration with mixed acid yields the 6-nitro derivative (22). The difference in products probably reflects a difference in the species being nitrated neutral 2(177)-quinoxalinone in acetic acid and the diprotonated species (23) in mixed acids. 

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. 

Valence bond theory offers no immediare qualitative explanation since the a bond that is involved is cylindrically symmetrical. A steric argument based on repulsions between hydrogens also fails because on detailed examination of this hypothesis, it is found that the... 

The examples that have been presented in this section illustrate the approach that is used to describe structure and reactivity effects within the framework of MO description of structure. In the chapters that follow, both valence bond theory and MO theory will be used in the discussion of structure and reactivity. Qualitative valence bond terminology is normally most straightforward for saturated systems. MO theory provides useful insights into conjugated systems and into effects that depend upon the symmetry of the molecules under discussion. 

D. J. Klein and N. Trinajstic, eds.. Valence Bond Theory and Chemical Structure, Elsevier, Amsterdam, 1990. 

Several methods of quantitative description of molecular structure based on the concepts of valence bond theory have been developed. These methods employ orbitals similar to localized valence bond orbitals, but permitting modest delocalization. These orbitals allow many fewer structures to be considered and remove the need for incorporating many ionic structures, in agreement with chemical intuition. To date, these methods have not been as widely applied in organic chemistry as MO calculations. They have, however, been successfully applied to fundamental structural issues. For example, successful quantitative treatments of the structure and energy of benzene and its heterocyclic analogs have been developed. It remains to be seen whether computations based on DFT and modem valence bond theory will come to rival the widely used MO programs in analysis and interpretation of stmcture and reactivity. 

Both the language of valence bond theory and of molecular orbital theory are used in discussing structural effects on reactivity and mechanism. Our intent is to illustrate both approaches to interpretation. A decade has passed since the publication of the Third Edition. That decade has seen significant developments in areas covered by the text. Perhaps most noteworthy has been the application of computational methods to a much wider range of problems of structure and mechanism. We have updated the description of computational methods and have included examples throughout the text of application of computational methods to specific reactions. 

It is not possible to write down a single, satisfactory, classical bonding diagram for S4N4 and, in valence-bond theory, numerous resonance hybrids must be considered of which the following are typical ... 

In his valence bond theory (VB), L. Pauling extended the idea of electron-pair donation by considering the orbitals of the metal which would be needed to accommodate them, and the stereochemical consequences of their hybridization (1931-3). He was thereby able to account for much that was known in the 1930s about the stereochemistry and kinetic behaviour of complexes, and demonstrated the diagnostic value of measuring their magnetic properties. Unfortunately the theory offers no satisfactory explanation of spectroscopic properties and so was... 

The way in which oui pjesenl undeislanding of the stereochemical intricacies of Ni has evolved illustrates rather well the inteiplay of theory and cxpcruiicnt. On the basis of valence-bond theory, three types of complex of ions were anticipated. These were ... 

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