Quantum theory covalent bonds

This chapter provides a substantial introduction to molecular structure by coupling experimental observation with interpretation through simple classical models. Today, the tools of classical bonding theory—covalent bonds, ionic bonds, polar covalent bonds, electronegativity, Lewis electron dot diagrams, and VSEPR Theory—have all been explained by quantum mechanics. It is a matter of taste whether to present the classical theory first and then gain deeper insight from the... 

Lewis s theory of the chemical bond was brilliant, but it was little more than guesswork inspired by insight. Lewis had no way of knowing why an electron pair was so important for the formation of covalent bonds. Valence-bond theory explained the importance of the electron pair in terms of spin-pairing but it could not explain the properties of some molecules. Molecular orbital theory, which is also based on quantum mechanics and was introduced in the late 1920s by Mul-liken and Hund, has proved to be the most successful theory of the chemical bond it overcomes all the deficiencies of Lewis s theory and is easier to use in calculations than valence-bond theory. 

In molecular crystals, there are two levels of bonding intra—within the molecules, and inter—between the molecules. The former is usually covalent or ionic, while the latter results from photons being exchanged between molecules (or atoms) rather than electrons, as in the case of covalent bonds. The hardnesses of these crystals is determined by the latter. The first quantum mechanical theory of these forces was developed by London so they are known as London forces (they are also called Van der Waals, dispersion, or dipole-dipole forces). 

Molecular mechanics force fields rest on four fundamental principles. The first principle is derived from the Bom-Oppenheimer approximation. Electrons have much lower mass than nuclei and move at much greater velocity. The velocity is sufficiently different that the nuclei can be considered stationary on a relative scale. In effect, the electronic and nuclear motions are uncoupled, and they can be treated separately. Unlike quantum mechanics, which is involved in determining the probability of electron distribution, molecular mechanics focuses instead on the location of the nuclei. Based on both theory and experiment, a set of equations are used to account for the electronic-nuclear attraction, nuclear-nuclear repulsion, and covalent bonding. Electrons are not directly taken into account, but they are considered indirectly or implicitly through the use of potential energy equations. This approach creates a mathematical model of molecular structures which is intuitively clear and readily available for fast computations. The set of equations and constants is defined as the force... 

Molecular Orbital Theory Model. Oxygen and hydrogen atoms in H2O are held together by a covalent bond. According to the quantum molecular orbital theory of covalent bonding between atoms, electrons in molecules occupy molecular orbitals that are described, using quantum mechanical language, by a linear combination of... 

A second quantum mechanical bonding theory is molecular orbital theory. This theory is based on a wave description of electrons. The molecular orbital theory assumes that electrons are not associated with an individual atom but are associated with the entire molecule. Delocalized molecular electrons are not shared by two atoms as in the traditional covalent bond. For the hydrogen molecule, the molecular orbitals are formed by the addition of wave functions for each Is electron in each hydrogen atom. The addition leads to a bonding molecular... 

What he does not seem to realize is that a perfectly good explanation existed for chemical bonding prior to the advent of the quantum mechanical explanation, namely Lewis s theory whereby pairs of electrons form the bonds between the various atoms in a covalently bonded molecule. Although the quantum mechanical theory provides a more fundamental explanation in terms of exchange energy and so on is undeniable but it also retains the notion of pairs of electrons even if this notion is now augmented by the view that electrons have anti-parallel spins within such pairs. 

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. 

The electron-dot structures described in Sections 7.6 and 7.7 provide a simple way to predict the distribution of valence electrons in a molecule, and the VSEPR model discussed in Section 7.9 provides a simple way to predict molecular shapes. Neither model, however, says anything about the detailed electronic nature of covalent bonds. To describe bonding, a quantum mechanical model called valence bond theory has been developed. 

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. 

Quantum theory sheds more light on the character of such silicenium ion-Lewis base complexes, e.g. on the nature of the bonds formed. Are they covalent Do d-orbitals contribute Flow large are the complexation energies and how do they change upon substitution Can free tricoordinate silicenium ions be formed at all in 7r-donor or aromatic solvents ... 

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. 

The quantum theory of atoms in molecules (QTAIM) [25, 26] is based on analyses of the electron density distribution. The electron density of such systems such as simple molecules or ions, and also complexes, complex molecular and ionic aggregates, as well as crystals may be analyzed using this approach. QTAIM is a powerful tool that allows characterizing of various interactions covalent bonds, ionic bonds, van der Waals interactions and, what is the most important for this review, also HBs. The analysis of critical points of the electron density is very useful. For the critical points (CPs), the gradient of electron density, p(r), vanishes ... 

There are five chapters in Part I Introduction to quantum theory, The electronic structure of atoms, Covalent bonding in molecules, Chemical bonding in condensed phases and Computational chemistry. Since most of the contents of these chapters are covered in popular texts for courses in physical chemistry, quantum chemistry and structural chemistry, it can be safely assumed that readers of this book have some acquaintance with such topics. Consequently, many sections may be viewed as convenient summaries and frequently mathematical formulas are given without derivation. 

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