Valence-bond structure-resonance theory

Various reactivity indices have been derived for benzenoid hydrocarbons from the following purely topological approaches the Huckel model (HMO), first-order perturbation theory (PMO), the free electron MO model (FEMO), and valence-bond structure resonance theory (VBSRT). Since many of the indices that have been known for a long time (index of free valence Fr, self-atom polarizability ir , superdelocalizability Sr, Brown s index Z, cation localization energy Lr+, Dewar reactivity number Nt, Brown s para-localization energy Lp) have been described in detail by Streitwieser in his well-known volume [23] we will refer here only to some more recent developments. 

The perturbational MO method of Longuet-Higgins (11) and Dewar (12), which was thoroughly reviewed by Dewar and Dougherty (6), has been the pencil-and-paper method of choice in numerous applications. More recently, a modified free-electron (MFE) MO approach (13-15) and a valence-bond structure-resonance theory (VBSRT) (7, 16, 17) have been applied to several PAH structure and reactivity problems. A new perturbational variant of the free-electron MO method (PMO F) has also been derived and reported (8, 18). Both PMO F and VBSRT qualify as simple pencil-and-paper procedures. When applied to a compilation of electrophilic substitution parameters (ct+) (19-23), the correlation coefficients of calculated reactivity indexes with cr+ for alternant hydrocarbons are 0.973 and 0.959, respectively (8). In this case, the performance of the PMO F method rivals that of the best available SCF calculations for systems of this size, and that of VBSRT is sufficient for most purposes. 

In this book the discussion has been restricted to the structure of the normal states of molecules, with little reference to the great part of chemistry dealing with the mechanisms and rates of chemical reactions. It seems probable that the concept of resonance can be applied very effectively in this field. The activated complexes which represent intermediate stages in chemical reactions are, almost without exception, unstable molecules which resonate among several valence-bond structures. Thus, according to the theory of Lewis, Olson, and Polanyi, Walden inversion occurs in the hydrolysis of an alkyl halide by the following mechanism ... 

Resonance theory [15] contains essentially three assumptions beyond those of the valence bond method. Perhaps the most serious assumption is the contention that only unexcited canonical forms, non-polar valence bond structures or classical structures need be considered. Less serious, but no more than intuitive, is the proposition that the molecular geometry will take on that expected for the average of the classical structures. This is extended to the measurement of stability being greater the greater the number of classical structures. These concepts are still widely used in chemistry in very qualitative ways. 

Une of the most interesting and useful applications of the theory of resonance is in the discussion of the structure of molecules for which no one valence-bond structure is satisfactory. An introduction to this discussion is presented in the following sections. The chapter ends with a reply to some critical comments that have been made about the theory. 

The theory of resonance has been applied to many problems in chemistry. In addition to its use in the discussion of the normal covalent bond (involving the interchange of two electrons, with opposed spins, between two atoms) and to the structure of molecules for which a single valence-bond structure does not provide a satisfactory description, it has rendered service to chemistry by leading to the discovery of several... 

Now let us consider benzene. There is no single valence-bond structure that accounts satisfactorily for the properties of benzene. The simple description of benzene that is given by the theory of resonance involves two valence-bond structures, the two Kekul6 structures... 

I feel that the greatest advantage of the theory of resonance, as compared with other ways (such as the molecular-orbital method) of discussing the structure of molecules for which a single valence-bond structure is not enough, is that it makes use of structural elements with which the chemist is familiar. The theory should not be assessed as inadequate because of its occasional unskillful application. 11 becomes more and more powerful, just as does classical structure theory, as the chemist develops a better and better chemical intuition about it. 

Carbon Dioxide and Related Molecules.—It is not surprising that so unconventional a molecule as carbon monoxide should have a resonating structure but recognition of the faci, that the carbon dioxide molecule, for which the valence-bond formula 0—C---0 has been written ever since the development of valence theory, is not well represented by this structure alone and that other valence-bond structures also make important contributions must have come as a surprise to everyone. 

The method of averaging for all valence-bond structures, asTdescribed above for diborane, is extremely laborious for any except very simple molecules. A statistical theory of resonating valence bonds that can be easily applied to complex as well as simple molecules has been developed.87 It can be illustrated by application to B6H9. Let us begin by assigning the probability 1 to the nonbridging B—II bonds and to the other bonds in the molecule ... 

Recognition has been made of some rather strongly worded criticism, from various sides, of the treatment of resonance of molecules among alternative valence-bond structures, as presented in earlier editions of this book, on the basis of its idealistic and arbitrary character, by the introduction of a section (Sec. 6-6) in which it is pointed out that the theory of resonance involves only the same amounts of idealization arid arbitrariness as the classical valence-bond theory. 

The resonance theory is very useful in accounting for, and in many cases predicting, the behavior of substances with tt bonds. However, it is not omnipotent. One example where it fails is cyclobutadiene, for which we can write two equivalent valence-bond structures corresponding to the Kekule structures for benzene ... 

Why is the excited state of a conjugated system of double bonds stabilized more, relative to the ground state, than for a nonconjugated system Resonance theory provides an explanation (see Section 6-5). Of the several conventional valence-bond structures that can be written for 1,3-butadiene, four of which are shown here, 2a-2d, only structure 2a has a low enough energy to be dominant for the ground state of 1,3-butadiene ... 

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. 

In the preceding section, we discussed the electron pair (2c-2e) bond and how it can be influenced by Pauli repulsion of the SOMOs with other electrons. In the three-electron (2c-3e) bond, Pauli repulsion plays an even more fundamental role, as we will see.72 The idea of the three-electron bond was introduced in the early 1930s by Pauling in the context of the valence bond (VB) model of the chemical bond.70 71 Since then, it has been further developed both in VB and in MO theory and has become a standard concept in chemistry.118-129 In VB theory,7°>71 118 123 the two-center, three-electron (2c-3e) bond between two fragments A and B is viewed as arising from a stabilizing resonance between two valence bond structures in which an electron pair is on fragment A and an unpaired electron on B (13a), or the other way around (13b) ... 

Canonical valence-bond structures of benzene according to the theory of resonance by Slater (1929)... 

It is important to stress the difference between resonance and tauto-merism. The concept of resonance has been introduced to describe the delocalization of electrons in all the different forms of the molecule as represented by valence bond structures, among which resonance is said to occur, the configuration of the nuclei is the same. In tautomerism, on the other hand, the atoms are arranged in different ways and tautomeric changes, in which one form is changed into the other, occur as the result of chemical reactions. The tautomeric forms are in fact different chemical entities and in theory and frequently in practice, each can be isolated. 

In order to apply the resonance theory of the transitional type of bond it is necessary to reconsider the electronic states of the atoms of the elements and to consider the valence bond structures of certain of their compounds, which may make an appreciable contribution to the state of the molecule. 

GH3GF3, /i=Q-27 D, might appear to contradict the theory of the mutual suppression of ionic structures developed above however in these compounds resonance can occur, since valence bond structures of the type... 

The top panel in the accompanying figure depicts valence bond structures for the two major resonance contributors of benzene. Contrary to earlier notions of two rapidly fluctuating structures, Pauling s resonance theory, developed with his student George W. Wheland (1907-74), viewed benzene as represented by two idealized but fictional resonance... 

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