Limitations of the Lewis Model

We should note that hydrogen never has more than two electrons in its valence shell in the Lewis diagram of any of its molecules because its valence shell is filled by just two electrons. Thus the octet rule is not applicable to hydrogen. 

The relationships between bond length, stretching force constant, and bond dissociation energy are made clear by the potential energy curve for a diatomic molecule, the plot of the change in the internal energy AU of the molecule A2 as the internuclear separation is increased until the molecule dissociates into two A atoms  

At 298 K AU includes vibrational, rotational, and translational energy changes that total 25 kJ mol-1, of which the most important is the vibrational energy, so that the quantity AU29 that is measured at 298 K is 

AU298 = Af/e - Af/vib. coi, leans = 458 - 25 = 433 kJ mol 1 This is the quantity called the bond dissociation energy or bond energy. 

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So, honest disagreements exist among chemists as to the best Lewis structures for molecules that, at least at first glance, appear to exceed the octet rule. This uncertainty shows the limitations of the Lewis model with its localized electron pairs. Note, however, that even with its limitations, it is still very useful because of its simplicity. The ability to obtain a reasonable bonding picture with a back-of-the-envelope model has led to the enduring influence of the Lewis model. ... 

We will see in Chapter 5 that the treatment of water via molecular orbital tiieory results in an electronic structure in which each of these electron pairs has a unique energy. This model is supported by spectroscopic evidence, and indicates one limitation of the Lewis model. 

The term resonance does not mean that the molecule physically oscillates back and forth from one of these bonding structures to the other. Rather, within the limitations of the Lewis dot model of bonding, the best representation of the actual bonding is a hybrid diagram that includes features of each of the acceptable individual diagrams. This awkwardness can be avoided by using molecular orbital theory to describe chemical bonding (see Chapter 6). 

The extent to which individual electron pairs are localized in distinct spatial regions has been carefully analyzed by Bader and Stephens (1975) using the minimum fluctuation criterion. These authors arrive at the conclusion that the model of spatially localized pairs is appropriate for LiH, BeH2, BH3, and BH-r, it is borderline for CH4, but in NHj, OH2, FH, Ne, N2, and F2, the motions of the valence electrons are so strongly inter-correlated, the localized pair model ceases to afford a suitable description. Moreover, their results provide no physical basis for the view that there are two separately localized pairs of nonbonded electrons in H20. This clearly shows the limit of the Lewis electron pair concept which otherwise has practically disappeared in Linnett s theory. 

Chapter 1 discusses classical models up to and including Lewis s covalent bond model and Kossell s ionic bond model. It reviews ideas that are generally well known and are an important background for understanding later models and theories. Some of these models, particularly the Lewis model, are still in use today, and to appreciate later developments, their limitations need to be clearly and fully understood. 

Where then to look for the Lewis model, a model which in the light of its ubiquitous and constant use throughout chemistry must most certainly be rooted in the physics governing a molecular system If one reads the introductory chapter on fields in Morse and Feshbach s book Methods of theoretical physics (1953), one finds a statement to the effect that the Laplacian of a scalar field is a very important property, for it determines where the field is locally concentrated and depleted. The Laplacian of the charge density at a point r in space, the quantity V p(r), is defined in eqn (2.3). This property of the Laplacian of determining where electronic charge is locally concentrated and depleted follows from its definition as the limiting difference between the two first derivatives which bracket the point in question as defined in eqn (2.2) and illustrated in Fig. 2.2. 

The large-dimension limit has recently resolved at least some of the difficulties of the molecular model. The molecule-like structure falls out quite naturally from the rigid bent triatomic Lewis configuration obtained in the limit D — oo [5], and the Langmuir vibrations at finite D can be analyzed in terms of normal modes, which provide a set of approximate quantum numbers [6,7]. These results are obtained directly from the Schrodinger equation, in contrast to the phenomenological basis of some of the earlier studies. When coupled with an analysis of the rotations of the Lewis structure, this approach provides an excellent alternative classification scheme for the doubly-excited spectrum [8]. Furthermore, an analysis [7] of the normal modes offers a simple explanation of the connection between the explicitly molecular approaches of Herrick and of Briggs on the one hand, and the hyperspherical approach, which is rather different in its formulation and basic philosophy. 

The discussion above has indicated some of the limitations of the original Lewis/ Kossel descriptiOTi of chemical bonding and the manner in which it has been adapted to assimilate the multitude of new compounds being reported from chemical laboratories during the last century. Central to the model is the definition of the chemical bond as a pair of electrons and the adherence to the octet rule. 

However, this cannot be the only role of the Lewis acid, since only redox-active compounds are active as cocatalysts and non redox-active Lewis acids show at best a limited promoting activity. Note that, despite its wide acceptance, the promoting role of a Lewis acid in the CO insertion into a metal-imido bond has never been directly observed for any model compound. 

We know from Chapter 7 that representing electrons with dots, as we do in the Lewis model, is a drastic oversimplification. As we have already discussed, this does not invah-date the Lewis model—which is an extremely useful theory— but we must recognize and compensate for its inherent limitations. One limitation of representing electrons as dots, and covalent bonds as two dots shared between two atoms, is that the shared electrons always appear to be equally shared. Such is not the case. For example, consider the Lewis structure of hydrogen fluoride ... 

In the very first chapter of this book, we described the scientific approach and put a special emphasis on scientific models or theories. In this chapter, we looked carefully at a model for chemical bonding (the Lewis model). Why is this theory successful What are some of the limitations of the theory ... 

Limiting L ws. Simple laws that tend to describe a narrow range of behavior of real fluids and substances, and which contain few, if any, adjustable parameters are called limiting laws. Models of this type include the ideal gas law equation of state and the Lewis-RandaH fugacity rule (10). 

The parameters and Ca are associated with the Lewis acid, and Eg and Cb with the base. a and b are interpreted as measures of electrostatic interaction, and Ca and Cb as measures of covalent interaction. Drago has criticized the DN approach as being based upon a single model process, and this objection applies also to the — A/y fBFs) model. Drago s criticism is correct, yet we should be careful not to reject a simple concept provided its limits are appreciated. Indeed, many very useful chemical quantities are subject to this criticism for example, p o values are measures of acid strength with reference to the base water. 

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