Bonding elementary concepts

Our aim in this chapter will be to establish the basic elements of those quantum mechanical methods that are most widely used in molecular modelling. We shall assume some familiarity with the elementary concepts of quantum mechanics as found in most general physical chemistry textbooks, but little else other than some basic mathematics (see Section 1.10). There are also many excellent introductory texts to quantum mechanics. In Chapter 3 we then build upon this chapter and consider more advanced concepts. Quantum mechanics does, of course, predate the first computers by many years, and it is a tribute to the pioneers in the field that so many of the methods in common use today are based upon their efforts. The early applications were restricted to atomic, diatomic or highly symmetrical systems which could be solved by hand. The development of quantum mechanical techniques that are more generally applicable and that can be implemented on a computer (thereby eliminating the need for much laborious hand calculation) means that quantum mechanics can now be used to perform calculations on molecular systems of real, practical interest. Quantum mechanics explicitly represents the electrons in a calculation, and so it is possible to derive properties that depend upon the electronic distribution and, in particular, to investigate chemical reactions in which bonds are broken and formed. These qualities, which differentiate quantum mechanics from the empirical force field methods described in Qiapter 4, will be emphasised in our discussion of typical applications. 

Some of the elementary concepts of free radical mechanisms were presented in Chapter 1. Reactions following free radical mechanisms have reactive intermediates containing unpaired electrons which are produced by homolytic cleavage of covalent bonds. A method of detecting free radicals was published in 1929, and it is based on the fact that metals such as lead react with free radicals. When heated, tetramethyl lead decomposes. 

Chemistry is an experimental subject whose results can be built into a pattern around quite elementary concepts. The role of quantum chemistry is to understand these concepts and to show what are the essential features of chemical behaviour. To say that the electronic computer shows that D(H-F) >> D(F-F) is not an explanation at all, but merely a confirmation of experiment. Any acceptable explanation must be in terms of repulsions between non-bonding electrons, dispersion forces between atomic cores and the like. 

Look again at Figure 16-1 If two NO2 molecules can form a bond when they collide, then that bond also can break apart when an N2 O4 molecule distorts. The concept of reversibility is a general principle that applies to all molecular processes. Every elementary reaction that goes in the forward direction can also go In the reverse direction. As a consequence of reversibility, we can write each step in a chemical mechanism using a double arrow to describe what happens at chemical equilibrium. 

Chapter 2 discusses the properties of bonds such as bond lengths and bond energies, which provide much of the experimental information on which bonding concepts and explanations of geometry have been mainly based. Again this is a brief summary at a fairly elementary level, serving mainly as a review. No attempt is made to deal with the experimental details of the many different experimental methods used to obtain the information discussed. 

Our principal goal has been to translate the deepest truths of the Schrodinger equation into a visualizable, intuitive form that makes sense even for beginning students, and can help chemistry teachers to present bonding and valency concepts in a manner more consistent with modern chemical research. Chemistry teachers will find here a rather wide selection of elementary topics discussed from a high-level viewpoint. The book includes a considerable amount of previously unpublished material that we believe to be of broad pedagogical interest, such as the novel Lewis-like picture of transition-metal bonding presented in Chapter 4. 

Elementary reactions on solid surfaces are central to heterogeneous catalysis (Chapter 8) and gas-solid reactions (Chapter 9). This class of elementary reactions is the most complex and least understood of all those considered here. The simple quantitative theories of reaction rates on surfaces, which begin with the work of Langmuir in the 1920s, use the concept of sites, which are atomic groupings on the surface involved in bonding to other atoms or molecules. These theories treat the sites as if they are stationary gas-phase species which participate in reactive collisions in a similar manner to gas-phase reactants. 

There is a twofold death the one indeed universally known, in which the body is liberated from the soul but the other peculiar to the philosophers [alchemists] in which the soul is liberated from the body nor does one entirely follow the other. That which nature binds, nature also dissolves that which the soul binds, the soul likewise can dissolve nature indeed, binds the body to the soul, but the soul binds herself to the body. Nature therefore liberates the body from the soul, but the soul may also liberate her self from the body. That is to say, if she know how, and have the right disposition awarded, she may dissolve her own conceptive vehicle, even the parental bond, and return consciously (the elementary principles remaining, nor yet... 

While many techniques have evolved to evaluate surface intermediates, as will be discussed below, it is equally important to also obtain information on gas phase intermediates, as well. While the surface reactions are interesting because they demonstrate heterogeneous kinetic mechanisms, it is the overall product yield that is finally obtained. As presented in a text by Dumesic et al. one must approach heterogeneous catalysis in the way it has been done for gas phase systems, which means using elementary reaction expressions to develop a detailed chemical kinetic mechanism (DCKM). DCKMs develop mechanisms in which only one bond is broken or formed at each step in the reaction scheme. The DCKM concept was promoted and used by numerous researchers to make great advances in the field of gas phase model predictions. 

Having been introduced to the concepts of operators, wavefunctions, the Hamiltonian and its Schrodinger equation, it is important to now consider several examples of the applications of these concepts. The examples treated below were chosen to provide the learner with valuable experience in solving the Schrodinger equation they were also chosen because the models they embody form the most elementary chemical models of electronic motions in conjugated molecules and in atoms, rotations of linear molecules, and vibrations of chemical bonds. 

Reaction dynamics on the femtosecond time scale are now studied in all phases of matter, including physical, chemical, and biological systems (see Fig. 1). Perhaps the most important concepts to have emerged from studies over the past 20 years are the five we summarize in Fig. 2. These concepts are fundamental to the elementary processes of chemistry—bond breaking and bond making—and are central to the nature of the dynamics of the chemical bond, specifically intramolecular vibrational-energy redistribution, reaction rates, and transition states. 

A basic understanding of the quantum theory is essential in many areas of chemistry, especially in connection with spectroscopy and with theories of atomic and molecular structure. The present book gives an introduction to the theory, and its application to elementary atomic structure, but chemical bonding is not discussed. I have tried to put the essential ideas in their historical context, but without retaining the historical introduction which has been traditional with this topic. With the crucial and difficult concepts of wave-particle duality, it seemed to me more important to give modem illustrations to show that they have current applications in chemistry. 

The BRC concept [99] allows the analysis of the elementary actions of chemical transformation at the level of active complexes, in which electron density is redistributed in accordance with bond multiplicity change. Generally, this is expressed by the rule of multiplicity alternating change ... 

The BOVB method is aimed at combining the qualities of interpretability and compactness of valence bond wave functions with a quantitative accuracy of the energetics. The fundamental feature of the method is the freedom of the orbitals to be different for each VB structure during the optimization process. In this manner, the orbitals respond to the instantaneous field of the individual VB structure rather than to an average field of all the structures. As such, the BOVB method accounts for the differential dynamic correlation that is associated with elementary processes like bond forming/breaking, while leaving the wave function compact. The use of strictly localized orbitals ensures a maximum correspondence between the wave function and the concept of Lewis structure, and makes the method suitable for calculation of diabatic states. 

This chapter has presented an overview of several important aspects of the chemistry of coordination compounds. In addition to the elementary ideas related to bonding presented here, there is an extensive application of molecular orbital concepts to coordination chemistry. However, most aspects of the chemistry of coordination compounds treated in this book do not require this approach, so it is left to more advanced texts. The references at the end of this chapter should be consulted for more details on bonding in complexes. 

Another way to define ionic charges consists in partitioning space into elementary volumes associated to each atom. One method has been proposed by Bader [240,241]. Bader noted that, although the concept of atoms seems to lose significance when one considers the total electron density in a molecule or in a condensed phase, chemical intuition still relies on the notion that a molecule or a solid is a collection of atoms linked by a network of bonds. Consequently, Bader proposes to define an atom in molecule as a closed system, which can be described by a Schrodinger equation, and whose volume is defined in such a way that no electron flux passes through its surface. The mathematical condition which defines the partitioning of space into atomic bassins is thus ... 

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