RESONATING VALENCE BOND THEORY molecular structure

In Chapter 7, we used valence bond theory to explain bonding in molecules. It accounts, at least qualitatively, for the stability of the covalent bond in terms of the overlap of atomic orbitals. By invoking hybridization, valence bond theory can account for the molecular geometries predicted by electron-pair repulsion. Where Lewis structures are inadequate, as in S02, the concept of resonance allows us to explain the observed properties. 

Heterocyclic systems have played an important role in this historical development. In addition to pyridine and thiophene mentioned earlier, a third heterocyclic system with one heteroatom played a crucial part protonation and methylation of 4//-pyrone were found by J. N. Collie and T. Tickle in 1899 to occur at the exocyclic oxygen atom and not at the oxygen heteroatom, giving a first hint for the jr-electron sextet theory based on the these arguments.36 Therefore, F. Arndt, who proposed in 1924 a mesomeric structure for 4//-pyrone, should also be considered among the pioneers who contributed to the theory of the aromatic sextet.37 These ideas were later refined by Linus Pauling, whose valence bond theory (and the electronegativity, resonance and hybridization concepts) led to results similar to Hiickel s molecular orbital theory.38... 

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. 

The yellow to orange compounds 804(118207)2, 864(84 013)2, and 8e4(8b2Fii)2 have been prepared. Crystallographic studies on 804(118207)2 have shown that the cation 8c4 + has square-planar D h) geometry. The structure can be described by valence bond theory in terms of four resonance structures equivalent to (la), or by simple molecular orbital theory in which three of the four n molecular orbitals are filled. " The 8e4 + ions are examples of six-jr-electron systems, and they are thus examples of inorganic aromatic compounds (lb). 

This process of constructing functions for the various resonant formulae, followed by an adequate combination of them, is mathematically more complex than the mathematics of molecular orbital theory. It is therefore understandable that, after the initial preference of chemists for the v.b. bond theory which has a closer relation to Lewis structures - especially due to the contribution of Linus Pauling - m.o. theory became increasingly popular. In addition, m.o. theory leads directly, not only to fundamental states (through the occupied m.o.), but also to excited states (through vacant m.o.) of molecules. In recent years, however, a new form of valence-bond theory has been developed that is more amenable to computation (spin-coupled valence-bond theory) in which the molecular wavefunction is expressed as a linear combination of all the coupling schemes of the various electrons corresponding to the same resultant spin (ref. 97). 

We can now state that each carbon-to-carbon linkage in benzene contains a sigma bond and a partial pi bond. The bond order between any two adjacent carbon atoms is therefore between 1 and 2. Thus molecular orbital theory offers an alternative to the resonance approach, which is based on valence bond theory. (The resonance structures of benzene are shown on p. 349.)... 

Despite its successes, the application of valence bond theory to the bonding in polyatomic molecules leads to conceptual difficulties. The method dictates that bonds are localized and, as a consequence, sets of resonance structures and bonding pictures involving hybridization schemes become rather tedious to establish, even for relatively small molecules (e.g. see Figure 4.10c). We therefore turn our attention to molecular orbital (MO) theory. 

Fig. 14.15 (a) The gas-phase planar structure of HNO3, and appropriate resonance structures, (b) The molecular structure of the planar [NOj]" anion the equivalence of the three N—O bonds can be rationalized by valence bond theory (one of three resonance structures is shown) or by MO theory (partial rr-bonds are formed by overlap of N and O 2p atomic orbitals and the TT-bonding is delocalized over the N03-framework as was shown in Figure 4.25). Colour code N, blue O, red H, white. 

Langmuir s conclusion is correct but, I think, incomplete. Saying that we often choose between two models does not mean that we must, from the time of that choice forward, use only the model that we accept. Instead, we must continually make selections, consciously or subconsciously, among many complementary models. Our choice of models is usually shaped by the need to solve the problems at hand. For example, Lewis electron dot structures and resonance theory provide adequate descriptions of the structures and reactions of organic compounds for some purposes, but in other cases we need to use molecular orbital theory or valence bond theory. Frequently, therefore, we find ourselves alternating between these models. Furthermore, consciously using complementary models to think about organic chemistry reminds us that our models are only human constructs and are not windows into reality. 

Both the language of valence bond theory and resonance and that of molecular orbital theory are used in the discussion of structural effects on reactivity. Our intention is to illustrate the use of both typesr of interpretation, with the goal of facilitating the student s ability to understand and apply both of these viewpoints of structure. Nearly all reaction types and concepts are illustrated by specific examples from the chemical literature. Such examples, of course, cannot provide breadth of coverage, and those that are cited have been selected merely to illustrate the mechanism or interpretation. Such illustrations are not meant to suggest any... 

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. 

For a classical presentation of resonance theory, see G. W. Wheland, Resonance Theory in Organic Chemistry, Wiley, New York, 1955. Models of molecular structure based on mathematical descriptions of valence bond theory have been developed F. W. Bodrowicz and W. A. Goddard III, in Modern Theoretical Chemistry, Methods of Electronic Structure Theory, H. F. Schaefer III (ed.). Plenum Press, New York, 1977, Vol. 3, Chapter 4 A. Voter and W. A. Goddard III, Chem. Phys. 57, 253 (1981) N. D. Epiotis, Unified Valence Bond Theory of Electronic Structure, Springer-Verlag, Berlin, 1983. 

Computer programs have been developed which can transform the results of molecular orbital calculations into NBOs. An optimal Lewis structure can be defined as that one with the maximum amount of electronic charge in Lewis orbitals (Lewis charge). A low amount of electronic charge in Lewis orbitals indicates strong effects of electron delocalisation [226-228]. In resonance structures, major and minor contributing structures may exist. These analyses provide results which are similar to modem valence bond theory methods. 

Resonance between imaginary structures having localised bond (valence bond theory) or delocalization of it orbitals (molecular orbital theory) have both been found to explain the bonding state of benzene. The benzene molecule may be represented either as a hybrid of Kekule structures (valence bond theory) or as a regular carbon hexagon having an inscribed circle or dotted circle that symbolizes the three delocalized n orbitals. 

We have noted several times in this book that resonance structures are inherently a valence bond theory (VBT) concept. Molecular orbital theory (MOT) does not require such structures. Hence, there are MOT bonding concepts that describe the bonding pictures given above for alkenes, alkynes, and CO. A simple MOT picture is given in the following Going Deeper highlight. 

Although satisfactory for allyl cation. Figure 10.1 is insufficient for species with more than two tt electrons because the tt orbital in (c) can accommodate only two electrons. Molecular orbital (MO) theory, however, offers an alternative to resonance and valence-bond theory for understanding the structure and reactions of not only allylic cations, but radicals (three rr electrons) and anions (four tt electrons) as well. In a simplification known as the Hiickel, or ir-electron, approximation the tt MOs are considered as separate from... 

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