Covalent bonds quantum mechanical concept

The concepts which we need for understanding the structural trends within covalently bonded solids are most easily introduced by first considering the much simpler system of diatomic molecules. They are well described within the molecular orbital (MO) framework that is based on the overlapping of atomic wave functions. This picture, therefore, makes direct contact with the properties of the individual free atoms which we discussed in the previous chapter, in particular the atomic energy levels and angular character of the valence orbitals. We will see that ubiquitous quantum mechanical concepts such as the covalent bond, overlap repulsion, hybrid orbitals, and the relative degree of covalency versus ionicity all arise naturally from solutions of the one-electron Schrodinger equation for diatomic molecules such as H2, N2, and LiH. 

Because nonmetals do not form monatomic cations, the nature of bonds between atoms of nonmetals puzzled scientists until 1916, when Lewis published his explanation. With brilliant insight, and before anyone knew about quantum mechanics or orbitals, Lewis proposed that a covalent bond is a pair of electrons shared between two atoms (3). The rest of this chapter and the next develop Lewis s vision of the covalent bond. In this chapter, we consider the types, numbers, and properties of bonds that can be formed by sharing pairs of electrons. In Chapter 3, we revisit Lewis s concept and see how to understand it in terms of orbitals. 

Quantum mechanics has made important contributions to the development of theoretical chemistry, e.g. the concept of quantum mechanical resonance in the interpretation of the perturbation in the excited states of polyelectronic systems, the concept of exchange in the formation of a covalent bond, the concept of non-localized bonds (though, in my view, unsatisfactory and only arising from a neglect of electronic repulsions), the concept of dispersion forces etc., but it is noteworthy that all these ideas owe their success and justification to their ability to account qualitatively for previously unexplained experimental facts rather than to their quantitative mathematical aspect. 

All of these early studies, however, contained, in addition to suggestions that have since been incorporated into the present theory, many others that have been discarded. The refinement of the electronic theory of valence into its present form has been due almost entirely to the development of the theory of quantum mechanics, which has not only provided a method for the calculation of the properties of simple molecules, leading to the complete elucidation of the phenomena involved in the formation of a covalent bond between two atoms and dispersing the veil of mystery that had shrouded the bond during the decades since its existence was first assumed, but has also introduced into chemical theory a new concept, that of resonance, which, if not entirely unanticipated in its applications to chemistry, nevertheless had not before been clearly recognized and understood. 

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. 

To introduce some of the basic ideas of molecular orbital theory, let s look again at orbitals. The concept of an orbital derives from the quantum mechanical wave equation, in which the square of the wave function gives the probability of finding an electron within a given region of space. The kinds of orbitals that we ve been concerned with up to this point are called atomic orbitals because they are characteristic of individual atoms. Atomic orbitals on the same atom can combine to form hybrids, and atomic orbitals on different atoms can overlap to form covalent bonds, but the orbitals and the electrons in them remain localized on specific atoms. 

The chief content of the isomorphism displayed in Table 1 is embodied in the phrase "electride ion . By introducing at the outset in the electronic interpretation of chemistry the wave-like character of electrons and the Exclusion Principle through the concept of van der Waals-like electron-domains or electride ions , whose sizes indicate the magnitudes of the electrons kinetic energies, whose impenetrability8) simulates, at least approximately, the operation of the Exclusion Principle, and whose charges yield within the framework of the model easily foreseeable effects, one transforms the complex treatment of the covalent bond in quantum mechanics into a simpler, if less precise, exercise in classical electrostatics. 

Hammett s view of the scope of the subject is summarized in the rarely mentioned sub-title of his book Reaction Rates, Equilibria, and Mechanisms . His conception of the subject still defines its core, but requires amplifying certain other topics are now usually deemed part of physical organic chemistry. Thus the rationalization of the experimental results of studies of reaction rates, equilibria, and mechanisms involves the application of the electronic theory of the structures and reactions of organic molecules, either in its early forms as developed by Robinson, Ingold, and others on the basis of the electron-pair covalent bond, or in its later forms involving quantum mechanical treatments. 

Empirically measured parameters are additional solvent properties, which have been developed through the efforts of physical chemists and physical organic chemists in somewhat different, but to some extent related, directions. They have been based largely on the Lewis acid base concept, which was defined by G. N. Lewis. The concept originally involved the theory of chemical bonding which stated that a chemical bond must involve a shared electron pair. Thus, an atom in a molecule or ion which had an incomplete octet in the early theory, or a vacant orbital in quantum mechanical terms, would act as an electron pair acceptor (an acid) from an atom in a molecule or ion which had a complete octet or a lone pair of electrons (a base). Further developments have included the concepts of partial electron transfer and a continuum of bonding from the purely electrostatic bonds of ion-ion interactions to the purely covalent bonds of atoms and molecules. The development of the concept has been extensively described (see Ref. 11 for details). 

It is important to say, from the start, that covalent bonding and other molecular properties can be studied quantum mechanically without reference to molecular orbitals. We are referring to valence bond theory which, being based on the orbital concept for atoms, was, in fact, the first quantum-mechanical theory of the chemical bond. In Chapter 8, we will make a more detailed reference to this method. Our main concern in this and the coming chapters is molecular orbital theory. 

Soon after the development of the quantum mechanical model of the atom, physicists such as John H. van Vleck (1928) began to investigate a wave-mechanical concept of the chemical bond. The electronic theories of valency, polarity, quantum numbers, and electron distributions in atoms were described, and the valence bond approximation, which depicts covalent bonding in molecules, was built upon these principles. In 1939, Linus Pauling s Nature of the Chemical Bond offered valence bond theory (VBT) as a plausible explanation for bonding in transition metal complexes. His application of VBT to transition metal complexes was supported by Bjerrum s work on stability that suggested electrostatics alone could not account for all bonding characteristics. 

Valence bond theory is one of the two quantum mechanical approaches that explain bonding in molecules. It accounts, at least qualitatively, for the stability of the covalent bond in terms of overlapping atomic orbitals. Using the concept of hybridization, valence bond theory can explain molecular geometries predicted by the VSEPR model. However, the assumption that electrons in a molecule occupy atomic orbitals of the individual atoms can only be an approximation, since each bonding electron in a molecule must be in an orbital that is characteristic of the molecule as a whole. 

There is no quantum-mechanical evidence for spatially directed bonds between the atoms in a molecule. Directed valency is an assumption, made in analogy with the classical definition of molecular frameworks, stabilized by rigid links between atoms. Attempts to rationalize the occurrence of these presumed covalent bonds resulted in the notion of orbital hybridization, probably the single most misleading concept of theoretical chemistry. As chemistry is traditionally introduced at the elementary level by medium of atomic orbitals, chemists are conditioned to equate molecular shape with orbital hybridization, and reluctant to consider alternative models. Here is another attempt to reconsider the issue in balanced perspective. 

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