CHEMICAL BONDING

any of the interactions that account for the association of atoms into molecules, ions, crystals, and other stable species. When atoms approach one another, their nuclei and electrons interact and tend to distribute themselves in space in such a way that the total energy is lower than it would be in any alternative arrangement. If the total energy of a group of atoms is lower than the sum of the energies of the component atoms, then they bond together and the energy lowering is the bonding energy. The number of bonds that an atom can form is referred to as its valence, or valency. For example, oxygen has a valence of two, and hydrogen has a valence of one; thus, two atoms of hydrogen combine with one atom of oxygen to form a water molecule, or two atoms of hydrogen combine with two atoms of oxygen to form a molecule of hydrogen peroxide. The valence number of an atom comprises the number of unpaired electrons in its valence shell, that is, its outer shell of electrons. Early theories of chemical bonding recognized that the valence of an atom could be explained by the fact that it ordinarily acquired the stable configuration of the electrons present in the nearest noble gas when it became part of a compound. The simplest type of chemical bond is the ionic, or electrovalent, bond. In such bonds, an electron is transferred from one neutral atom to another, and the resulting charged species are held together by electrostatic attraction. Sodium chloride (common table salt) provides an example of ionic bonding. The sodium atom, which has one more electron than the stable neon atom, gives up this extra electron to chlorine, which requires one further electron to resemble the stable argon atom. The resulting ions (charged species) Na+ and Cl- are held together by electrostatic forces. The sulfur atom requires two electrons to attain the electron configuration of argon. It can get these by combining with two sodium atoms to form the salt sodium sulfide (Na 2S) or by combining with one calcium atom, which has two valence electrons, forming calcium sulfide (CaS). Other compounds are held together by covalent bonds, in which an electron pair is shared between two atoms. This is the case, for example, in the chlorine molecule (Cl2). Each chlorine atom has seven valence electrons. The stability of the chlorine molecule is attributable to the sharing of a pair of electrons by the two atoms so that each of them acquires the stable configuration of argon. Atoms may also share more than one electron pair. By sharing two pairs of electrons, for example, two oxygen atoms (each with a valence of two) can form two covalent bonds and each attain a stable neon configuration. The oxygen molecule (O2) therefore has a double bond. The carbon atom has four unpaired valence electrons. In the acetylene molecule (C2H2) a covalent bond is formed between each of the carbon atoms and a hydrogen atom, and the carbon atoms share three pairs of electrons; acetylene contains a carbon-carbon triple bond: H-CC-H. Very strong forces unite the atoms in most crystalline metals. The metallic bond is recognized as a third major type of bond, alongside ionic and covalent bonds. Hydrogen bonds are relatively weak bonds, having about one-tenth the strength of a covalent bond, and involve an interaction between hydroxyl groups (OH) and amino groups (NH2). Hydrogen bonding plays a vital role in the exact manner of folding of the long polypeptide chains in proteins and in the base-pairing in the double strand of the DNA helix. The bonding in molecules explains their shapes. The four unpaired electrons in the carbon atom form four covalent bonds with hydrogen atoms in the methane molecule, and the four bonding pairs of electrons thus formed adjust their positions in space so that their mutual repulsions are minimized. Methane is thus a tetrahedral molecule with bond angles of 109. The ammonia molecule (NH3) has three bonding pairs of electrons and one lone, or nonbonding, pair of electrons; these pairs of electrons are oriented approximately tetrahedrally. Because the hydrogen atoms pull the electrons participating in a given bond away from the nitrogen atom, however, the repulsions between the bonding electron pairs are less than the repulsions between the lone pair and the bonding pairs; the H-N-H bond angle in the ammonia molecule (107) is somewhat less than the tetrahedral angle. In the water molecule there are two bonding electron pairs and two lone pairs in the valence shell; since lone-pair interactions are greater than lone-pairbond-pair interactions, the H-O-H bond angle (104) is less than the H-N-H bond angle in ammonia. A rigorous description of the bonding in molecules requires the use of quantum mechanical methods. Unfortunately, the quantum mechanical equations that govern the structure of molecules are too complicated to be readily solved. Two approximate methods are employed: valence bond (VB) theory and molecular orbital (MO) theory. Valence bond theory provides a quantum mechanical explanation of the electron pair-bond as resulting from the overlap (merging) of two atomic orbitals from two atoms. (An atomic orbital is a quantum mechanical function for the distribution of electrons within an atom.) A simple single bond, known as a sigma (s) bond, results from head-to-head overlap and is symmetrical about the line between the two bonded atoms. A second type of bond, known as the pi (p) bond, results from sideways overlap. A double bond consists of one s bond and one p bond, while a triple bond is made up of one s bond and two p bonds. An important concept in valence bond theory is hybridization, which is the merging of atomic orbitals on the same atom to form equivalent hybridized atomic orbitals available for forming bonds with other atoms. Molecular orbital theory treats bonding in terms of the overlap of molecular orbitals, which are functions describing the distribution of electrons over all the nuclei of a molecule. Each molecular orbital is formed by combining the atomic orbitals of the atoms in a molecule in an approximation known as the linear combination of atomic orbital (LCAO) approximation. Computational studies of the structures of molecules investigate the distribution of electrons according to MO theory. The chemical bonding in some molecules cannot be explained in terms of electron-pair bonds between pairs of atoms, that is, two-centre bonds. Many-centre bonds are required to explain the bonding in many of the boron hydrides. For example, diborane (B2H6) contains four normal covalent bonds and two B-H-B three-centre bonds, in which one pair of electrons is associated with three atoms; in this way the boron atoms achieve the stable electron configuration of the neon atom. any of the interactions that account for the association of atoms into molecules, ions, crystals, and other stable species that make up the familiar substances of the everyday world. When atoms approach one another, their nuclei and electrons interact and tend to distribute themselves in space in such a way that the total energy is lower than it would be in any alternative arrangement. If the total energy of a group of atoms is lower than the sum of the energies of the component atoms, they then bond together and the energy lowering is the bonding energy. The ideas that helped to establish the nature of chemical bonding came to fruition during the early 20th century after the electron had been discovered and quantum mechanics had provided a language for the description of the behaviour of electrons in atoms. However, even though chemists need quantum mechanics to attain a detailed quantitative understanding of bond formation, much of their pragmatic understanding of bonds is expressed in simple, intuitive models. These models treat bonds as primarily of two kindsnamely, ionic and covalent. The type of bond that is most likely to occur between two atoms can be predicted on the basis of the location of the elements in the periodic table, and to some extent the properties of the substances so formed can be related to the type of bonding. A key concept in a discussion of chemical bonding is that of the molecule. Molecules are the smallest units of compounds that can exist. One feature of molecules that can be predicted with reasonable success is their shape. Molecular shapes are of considerable importance for understanding the reactions that compounds can undergo, and so the link between chemical bonding and chemical reactivity is discussed briefly in this article. Although simple models of bonding are useful as rules of thumb for rationalizing the existence of compounds and the physical and chemical properties and structures of molecules, they need to be justified by appealing to more sophisticated descriptions of bonding. Moreover, there are some aspects of molecular structure that are beyond the scope of the simple theories. To achieve this insight, it is necessary to resort to a fully quantum mechanical description. In practice, these descriptions entail heavy reliance on computers. Such numerical approaches to the chemical bond provide important information about bonding. This article begins by describing the historical evolution of the current understanding of chemical bonding and then discusses how modern theories of the formation of chemical bonds have emerged and developed into a powerful description of the structure of matter. After the historical introduction, qualitative models of bonding are discussed, with particular attention given to the formation of ionic and covalent bonds and the correlation of the latter with molecular shapes. The more sophisticated quantum mechanical approaches to bond formation are then described, followed by a survey of a number of special cases that raise interesting problems or lead to important insights. For a detailed discussion of the structure and properties of atoms, see the article atom. Chemical compounds are surveyed in the article chemical compound, and the elements are described in the article chemical element. Additional reading An elementary introduction to chemical bonding is found in P.W. Atkins and J.A. Beran, General Chemistry, 2nd ed. (1992). Pictorial interpretations of many of the quantum mechanical concepts mentioned in this article are available in P.W. Atkins, Quanta: A Handbook of Concepts, 2nd ed. (1992). R.J. Puddephatt and P.K. Monaghan, The Periodic Table of the Elements, 2nd ed. (1986), provides an introduction to the basis of chemical periodicity. Duward F. Shriver, P.W. Atkins, and Cooper H. Langford, Inorganic Chemistry, 2nd ed. (1994), includes descriptions of atomic structure and bonding in complexes, clusters, and electron-deficient compounds. Two authoritative monographs on bonding are Linus Pauling, The Nature of the Chemical Bond and the Structure of Molecules and Crystals, 3rd ed. (1960, reissued 1989); and C.A. Coulson, Coulson's Valence, 3rd ed. by Roy McWeeny (1979). A more physical view of chemical bonding than presented in this article is given by John C. Morrison et al., Electronic Structure of Atoms and Molecules, in George L. Trigg (ed.), Encyclopedia of Applied Physics, vol. 6 (1993), pp. 4598. Other accounts include Roger L. DeKock and Harry B. Gray, Chemical Structure and Bonding (1980); Brian Webster, Chemical Bonding Theory (1990); and Ahmed Zewail (ed.), The Chemical Bond: Structure and Dynamics (1992). Applications to pharmacologically active molecules are introduced in W.G. Richards, Quantum Pharmacology, 2nd ed. (1983). Computational aspects of the chemical bond are described in Alan Hinchliffe, Computational Quantum Chemistry (1988). Peter W. Atkins Atomic structure and bonding To understand bond formation, it is necessary to know the general features of the electronic structure of atomsthat is, the arrangement of electrons around the central nucleus. For background information about this subject and further details, see the article atom. Atomic structure The modern version of atomic structure begins with Ernest (later Lord) Rutherford's recognition that an atom consists of a single, central, massive, positively charged nucleus surrounded by electrons. The number of protons in the nucleus is the atomic number, Z, of the element. (For hydrogen Z = 1, and for carbon Z = 6.) A proton is positively charged, and an electron carries an equal but opposite negative charge. For an atom to be electrically neutral, it must contain the same number of extranuclear electrons as there are protons in the nucleus. Hence, the number of electrons in a neutral atom of atomic number Z is also Z. A hydrogen atom consequently has one electron, and a carbon atom has six electrons. The quantum mechanics of bonding The preceding discussion has outlined the general approach to covalent bonding and has shown how it is still widely employed for a qualitative understanding of molecules. It is incomplete in many respects, however. First, the role of the electron pair remains unexplained but appears to be the hinge of both Lewis' theory and the VSEPR theory. Second, there is evidence that suggests that Lewis' theory overemphasizes the role of electron pairs. More fundamentally, little has been said about the distribution of bonding electrons in terms of orbitals, although it has been shown that in atoms the distributions of electrons are described by wavefunctions. Finally, the models that have been described have little quantitative content: they do not lead to bond lengths or precise bond angles, nor do they give much information about the strengths of bonds. A full theory of the chemical bond needs to return to the roots of the behaviour of electrons in molecules. That is, the role of the electron pair and the quantitative description of bonding must be based on the Schrdinger equation and the Pauli exclusion principle. This section describes the general features of such an approach. Once again, the discussion will be largely qualitative and conceptual rather than mathematical and numerical. However, the character of the presentation here should not be taken to imply that the current understanding of molecules is not rigorous, quantitative, and precise. Several difficulties are encountered at the outset of the application of the Schrdinger equation to molecules. Even the simplest molecules consist of two nuclei and several electrons, and interesting molecules may contain a thousand atoms and tens of thousands of electrons. So that any progress of a generally applicable kind can be made, approximations are necessary. One approximation is common to all discussions of molecules. The Born-Oppenheimer approximation, which was introduced by Max Born and J. Robert Oppenheimer in 1927, separates the motion of the electrons in a molecule from the motion of the nuclei. The separation is based on the fact that the nuclei are much heavier than the electrons and move more slowly. Hence, even though nuclei do move, the electrons can respond to their new positions almost instantaneously. That being the case, it is permissible to consider the nuclei as stationary in a given arrangement and then to solve the Schrdinger equation for the electrons in that stationary framework of nuclei. In order to explore how the energy of the molecule changes as the nuclei change their positions, a series of static nuclear arrangements can be selected, and the Schrdinger equation solved for the electrons in each stationary arrangement. Figure 10: A molecular potential energy curve. The strength of the bond is indicated by the The data obtained from such a procedure can be used to construct a molecular potential energy curve, a graph that shows how the energy of the molecule varies as bond lengths and bond angles are changed. A typical curve for a diatomic molecule, in which only the internuclear distance is variable, is shown in Figure 10. The energy minimum of this curve corresponds to the observed bond length of the molecule. The depth of the minimum is (apart from a small correction for the vibrational properties of the bond) equal to the bond dissociation energy and hence indicates the tightness with which the two atoms are held together. The steepness of the walls of the curve, which shows how rapidly the energy changes as the nuclear separation changes, indicates the rigidity of the bond. Thus, quantitative information can be obtained from such an approach. Even the Born-Oppenheimer approximation is only one of the approximations needed for the study of the molecule. It separates out the nuclear motion and leaves untouched the need to solve the Schrdinger equation for several (and perhaps tens of thousands) of electrons. Two major alternative approximations beyond the Born-Oppenheimer approach have been devised to tackle this aspect of the problem. The first to be proposed (by Walter Heitler and Fritz London in 1927 and substantially developed by John Slater and Linus Pauling in the 1930s) is valence bond (VB) theory. This theory introduced language into chemistry that is still widely used, particularly in the discussion of organic compounds, but it has been somewhat overshadowed in quantitative investigations by its rival. The latter, molecular orbital (MO) theory, was introduced in 1927 by Robert S. Mulliken and Friedrich Hund. It has undergone considerable development and is the principal model for the calculation of molecular properties and for general discussions of compounds. Valence bond theory The basis of VB theory is the Lewis concept of the electron-pair bond. Broadly speaking, in VB theory a bond between atoms A and B is formed when two atomic orbitals, one from each atom, merge with one another (the technical term is overlap), and the electrons they contain pair up (so that their spins are ). The merging of orbitals gives rise to constructive interferencei.e., an enhancement of amplitudebetween the wavefunctions in the areas where they overlap, and hence an enhanced amplitude results in the internuclear region. As a consequence of the formation of this region of heightened amplitude, there is an increased probability of finding he electrons in the internuclear region (so echoing Lewis' conception of the bond) and, by implication, a lowering of the energy of the molecule. The VB theory can be put in the broader context of quantum mechanics by drawing on the superposition principle and the Pauli exclusion principle (see quantum mechanics). The two principles establish more precisely the type of orbital merging that is required and also show that, to achieve that merging, the two electrons must pair their spins. The technical justification will not be presented here.