chemical bond

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chemical bond,

mechanism whereby atomsatom
[Gr.,=uncuttable (indivisible)], basic unit of matter; more properly, the smallest unit of a chemical element having the properties of that element. Structure of the Atom
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 combine to form moleculesmolecule
[New Lat.,=little mass], smallest particle of a compound that has all the chemical properties of that compound. A single atom is usually not referred to as a molecule, and ionic compounds such as common salt are not made up of molecules.
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. There is a chemical bond between two atoms or groups of atoms when the forces acting between them are strong enough to lead to the formation of an aggregate with sufficient stability to be regarded as an independent species. The number of bonds an atom forms corresponds to its valencevalence,
combining capacity of an atom expressed as the number of single bonds the atom can form or the number of electrons an element gives up or accepts when reacting to form a compound.
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. The amount of energy required to break a bond and produce neutral atoms is called the bond energy. All bonds arise from the attraction of unlike charges according to Coulomb's law; however, depending on the atoms involved, this force manifests itself in quite different ways. The principal types of chemical bond are the ionic, covalent, metallic, and hydrogen bonds. The ionic and covalent bonds are idealized cases, however; most bonds are of an intermediate type.

The Ionic Bond

The ionic bond results from the attraction of oppositely charged ions. The atoms of metallic elements, e.g., those of sodium, lose their outer electrons easily, while the atoms of nonmetals, e.g., those of chlorine, tend to gain electrons. The highly stable ions that result retain their individual structures as they approach one another to form a stable molecule or crystal. In an ionic crystal like sodium chloride, no discrete diatomic molecules exist; rather, the crystal is composed of independent Na+ and Cl ions, each of which is attracted to neighboring ions of the opposite charge. Thus the entire crystal is a single giant molecule.

The Covalent Bond

A single covalent bond is created when two atoms share a pair of electrons. There is no net charge on either atom; the attractive force is produced by interaction of the electron pair with the nuclei of both atoms. If the atoms share more than two electrons, double and triple bonds are formed, because each shared pair produces its own bond. By sharing their electrons, both atoms are able to achieve a highly stable electron configuration corresponding to that of an inert gasinert gas
or noble gas,
any of the elements in Group 18 of the periodic table. In order of increasing atomic number they are: helium, neon, argon, krypton, xenon, and radon. They are colorless, odorless, tasteless gases and were once believed to be entirely inert, i.e.
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. For example, in methane (CH4), carbon shares an electron pair with each hydrogen atom; the total number of electrons shared by carbon is eight, which corresponds to the number of electrons in the outer shell of neon; each hydrogen shares two electrons, which corresponds to the electron configuration of helium.

In most covalent bonds, each atom contributes one electron to the shared pair. In certain cases, however, both electrons come from the same atom. As a result, the bond has a partly ionic character and is called a coordinate link. Actually, the only purely covalent bond is that between two identical atoms.

Covalent bonds are of particular importance in organic chemistry because of the ability of the carbon atom to form four covalent bonds. These bonds are oriented in definite directions in space, giving rise to the complex geometry of organic molecules. If all four bonds are single, as in methane, the shape of the molecule is that of a tetrahedron. The importance of shared electron pairs was first realized by the American chemist G. N. Lewis (1916), who pointed out that very few stable molecules exist in which the total number of electrons is odd. His octet rule allows chemists to predict the most probable bond structure and charge distribution for molecules and ions. With the advent of quantum mechanics, it was realized that the electrons in a shared pair must have opposite spin, as required by the Pauli exclusion principleexclusion principle,
physical principle enunciated by Wolfgang Pauli in 1925 stating that no two electrons in an atom can occupy the same energy state simultaneously. The energy states, or levels, in an atom are described in the quantum theory by various values of four different
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. The molecular orbital theorymolecular orbital theory,
detailed explanation of how electrons are distributed in stable molecules. In the simpler valence theory of the chemical bond, each atom in a molecule is assumed to retain its own electrons.
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 was developed to predict the exact distribution of the electron density in various molecular structures. The American chemist Linus PaulingPauling, Linus Carl
, 1901–94, American chemist, b. Portland, Oreg. He was one of the few recipients of two Nobel Prizes, winning the chemistry award in 1954 and the peace prize in 1962.
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 introduced the concept of resonance to explain how stability is achieved when more than one reasonable molecular structure is possible: the actual molecule is a coherent mixture of the two structures.

Metallic and Hydrogen Bonds

Unlike the ionic and covalent bonds, which are found in a great variety of molecules, the metallic and hydrogen bonds are highly specialized. The metallic bond is responsible for the crystalline structure of pure metals. This bond cannot be ionic because all the atoms are identical, nor can it be covalent, in the ordinary sense, because there are too few valence electrons to be shared in pairs among neighboring atoms. Instead, the valence electrons are shared collectively by all the atoms in the crystal. The electrons behave like a free gas moving within the lattice of fixed, positive ionic cores. The extreme mobility of the electrons in a metal explains its high thermal and electrical conductivity.

Hydrogen bonding is a strong electrostatic attraction between two independent polar molecules, i.e., molecules in which the charges are unevenly distributed, usually containing nitrogen, oxygen, or fluorine. These elements have strong electron-attracting power, and the hydrogen atom serves as a bridge between them. The hydrogen bond, which plays an important role in molecular biology, is much weaker than the ionic or covalent bonds. It is responsible for the structure of ice.


See L. Pauling, The Nature of the Chemical Bond (3d ed. 1960); A. L. Companion, Chemical Bonding (2d ed. 1979).

bond, chemical:

see chemical bondchemical bond,
mechanism whereby atoms combine to form molecules. There is a chemical bond between two atoms or groups of atoms when the forces acting between them are strong enough to lead to the formation of an aggregate with sufficient stability to be regarded as an
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Chemical Bond


the attraction of atoms for one another, leading to the formation of molecules and crystals. It is customary to say that chemical bonds are formed between adjacent atoms in a molecule or crystal.

The valence of an atom, discussed in detail below, is a measure of the number of bonds formed by an atom with neighboring atoms (see alsoVALENCE). The British chemist E. Frankland proposed the concept of valence in 1852, stating that each element forms compounds by uniting with a definite number of equivalents of other elements, an equivalent being the amount involving one valence. F. A. Kekulé and A. W. H. Kolbe (1857) extended the concept of valence to carbon and stated that carbon usually has the valence 4, forming four bonds with other atoms. The Scottish chemist A. S. Couper pointed out (1858) that carbon atoms can be bonded to one another to form chains. He wrote chemical formulas much like the modern ones, using a line between the symbols of atoms to represent the valence bond. The term “chemical structure” was used for the first time in 1861 by the Russian chemist A. M. Butlerov, who stated that it is essential to express the structure by a single formula, which shows how each atom is linked to other atoms in the molecule of the substance. According to Butlerov, all properties of a compound are determined by the molecular structure of the substance, and therefore it should be possible to find the correct structural formula by studying the ways in which the substance can be synthesized. The next step, that of assigning structures in three-dimensional space to the molecules, was taken in 1874 by the Dutch chemist J. H. Van’t Hoff and the French chemist J. A. Le Bel.

In the 19th century the valence bond was represented by a line drawn between the symbols of two chemical elements. The nature of the bond was completely unknown. After the discovery of the electron, numerous attempts were made to develop an electronic theory of the chemical bond. This effort culminated in the work of G. N. Lewis, who in 1916 discussed the formation of a chemical bond, now called the covalent bond, by the sharing of two electrons between two atoms. A deeper understanding of the nature of the chemical bond came about as a result of the development of quantum mechanics in 1925 and the use of many experimental methods, such as molecular spectroscopy, X-ray diffraction by crystals, electron diffraction by gas molecules, and the study of magnetic properties, to determine bond lengths (interatomic distances), bond angles, the number of unpaired electrons, and other structural features of molecules and crystals.

Electronic structure of atoms. The electrons in an atom are assigned to various orbitals, which are characterized by the total quantum number n, the angular momentum quantum number l, and the magnetic quantum number ml. There is one, most stable, orbital with n = 1, constituting the K shell. The L shell, with n = 2, contains one orbital with l = 0 and ml = 0 and three orbitals with l = 1 and ml = –1, 0, or + 1. These are called the 1s orbital, the 2s orbital, and the three 2p orbitals. The M shell contains a 3s orbital, three 3p orbitals, and five 3d orbitals. The electron has a spin, with spin quantum number s = ½, which can orient itself with respect to a particular direction in two ways, with the component given by the spin magnetic quantum number ms = + ½ or – ½. No two electrons in an atom can have the same value of all quantum numbers. Accordingly, the 1s orbital, constituting the K shell, can be occupied by only one electron, with either positive or negative spin, or by two electrons (an electron pair), one with positive and one with negative spin.

The completion of certain shells and subshells corresponds to a special stability of atoms, observed in the argonons (the inert gases), whose electronic structures are shown in Table 1. In these stable structures, each orbital is occupied by a pair of electrons.

Table 1. Shells and subshells of electrons
Name of shellSymbol for shell1
1Symbol shows electron configuration of completed shell, indicating subshells
Helium shell ...............1s2
Neon shell ...............2s122p6
Argon shell ...............3s23p6
Krypton shell ...............3d104s24p6
Xenon shell ...............4d105s25p6
Radon shell ...............4f145d106s26p6
Eka-radon shell ...............5f146d107s27p6

Covalent bond. In 1927 a quantum-mechanical treatment of the hydrogen molecule ion, H2+, was carried out by the Danish physicist O. Burrau, who showed that the single electron in the ion occupies an orbital, called a molecular orbital, that extends around both of the protons. The theoretical treatment led to a value of 255 kJ · mole–1 for the bond energy of the molecule ion, that is, for the difference in energy of a separated hydrogen atom and proton and the molecule ion in its normal state. This value is in excellent agreement with experiment. It was soon noted that the electronic structure of the hydrogen molecule ion can be discussed by consideration of the wave function for the normal state of the hydrogen atom. As the hydrogen atom and the proton approach each other, there is the possibility that the electron will move from the region surrounding one nucleus to the region surrounding the second nucleus, occupying a 1s orbital in each case. The molecular orbital formed as the sum of the two 1s orbitals is a good approximation of the molecular orbital obtained by Burrau by way of the Schrödinger wave equation. If a wave function is formed by taking the difference of the two 1s orbitals, it is found to lead to repulsion rather than attraction. The first wave function—the symmetric combination of the two 1s functions—corresponds to stability and the formation of a one-electron covalent bond, whereas the second wave function—the antisymmetric combination of the same 1s functions—corresponds to instability. It is sometimes said that the formation of the one-electron covalent bond in the hydrogen molecule corresponds to the resonance of the electron between the two atomic orbitals or between the two hydrogen atoms.

Also in 1927, two quantum-mechanical discussions of the chemical bond in the hydrogen molecule, H2, were carried out. The American physicist E. U. Condon made use of a molecular orbital method, assigning to the hydrogen molecule a structure based on the H2+ orbital as evaluated by Burrau and placing both electrons in this orbital with opposite spins. The German physicists W. Heitler and F. London assigned the electron with positive spin to the 1s orbital of one hydrogen atom and the electron with negative spin to the 1s orbital of the second hydrogen atom. The wave function for the molecule was the sum of this function and the function in which the two electrons change places, with the electron with positive spin going to the second atom and the electron with negative spin to the first atom. Condon’s treatment and Heitler and London’s treatment both lead to stability for the hydrogen molecule, whose bond energy is about 1.7 times that of the hydrogen molecule ion. The bond between the two hydrogen atoms in the hydrogen molecule is the prototype of Lewis’ shared-electron-pair bond, usually called a covalent bond.

The formal results of the quantum-mechanical treatment of the chemical bond can be simply stated as follows: An atom can form an electron-pair covalent bond for each stable orbital occupied by one electron, the bond being of the type described for the hydrogen molecule and owing its stability to the same resonance phenomenon. In other words, for the formation of a covalent bond, two electrons with opposite spins and a stable orbital of each of the two bonded atoms are needed.

The hydrogen atom, with only one stable orbital (1s), is thus limited to the formation of one covalent bond. The carbon atom and other atoms of the second period (boron, nitrogen, oxygen) are limited to four covalent bonds, with use of the four orbitals of the L shell. The quantum-mechanical treatment also leads to the conclusion that in general each additional bond formed within a molecule stabilizes the molecule further, so that the most stable electronic structures of a molecule are those in which all of the stable orbitals of an atom are used either in bond formation or for occupancy by an unshared pair of electrons.

The valence-bond structure assigned to methane, CH4, for example, is

The dashes represent shared electron pairs. The shared electron pair can be said to occupy the 1s orbital of each hydrogen atom and one of the four orbitals in the L shell of the carbon atom. In this way, the hydrogen atom has achieved the completed K-shell structure, that is, the helium structure, and the carbon atom, which also has an unshared pair of 1s electrons, has a completed L-shell structure, that is, the neon structure.

The concept of hybrid bond orbitals provides the solution to a problem that had puzzled chemists and physicists during the early years of quantum theory. The four orbitals of the L shell are of two kinds, a 2s orbital and three 2p orbitals, while the four bonds about a carbon atom, as indicated by the chemical properties of carbon compounds, prove to be equivalent to one another. In fact, in place of the 2s orbital and three 2p orbitals, a set of equivalent sp3 hybrid orbitals can be formed, called tetrahedral orbitals, which are directed toward the corners of a regular tetrahedron and have greater bond-forming power than either an s orbital or a p orbital (L. Pauling, 1931).

For the water molecule, H20, the following valence-bond structure is written:

The oxygen atom is surrounded by two unshared electron pairs and two shared pairs. The 2s orbital has somewhat greater stability than the 2p orbitals, so much so that the unshared electron pairs use most of the 2s orbital. If the two bonds of the water molecule were formed by the p orbitals of the oxygen atom, then the bond angle would be predicted to be 90°, because p orbitals have their maximum bond-forming power in directions at 90” to one another. Calculations show that maximum stability results when the bond orbitals in the water molecule have a small amount of s character, corresponding to bond angles somewhat larger than 90°. The observed bond angle is 104.5°, and the bond angles for the hydrides H2S, H2Se, and H2Te are 92°, 91°, and 90°, respectively.

There is a double covalent bond between the carbon atoms in ethylene, C2H4, and a triple bond in acetylene, C2H2. The valence-bond structures for these molecules are

Two shared electron pairs are involved in the formation of the double bond, and three in the triple bond. With each of these structures, the carbon atom has achieved the neon electronic structure, being surrounded by four shared electron pairs. The carbon atoms can be described as forming four single bonds, directed toward the corners of a tetrahedron. In the double bond and the triple bond, there are two or three single bonds that are bent. It is interesting that the observed carbon-carbon distances, 133 picometers (pm) and 120 pm, respectively, lie within 1 pm of the values corresponding to bent bonds with the length 154 pm, which is the carbon-carbon distance in ethane. This agreement supports the idea that the double bond and the triple bond can be described in terms of bent bonds.

The bond energy of a carbon-carbon double bond is 73 kJ · mole–1 less than the sum of the bond energies for two single bonds, and that of the triple bond is 220 kJ · mole–1 less than the sum for three single bonds. These differences in stability can be attributed to the strain of the bent bonds. The strain energy favors the conversion of the multiple bonds to single bonds, so that substances with multiple bonds undergo easy reaction with addition of hydrogen. Such substances are said to be unsaturated, whereas the corresponding substances containing only single bonds, such as ethane, C2H6, are said to be saturated.

Resonance and the structure of benzene. The rules about the assignment of valence-bond structures, involving shared electron pairs with the use of a stable orbital for each of the two atoms connected by a covalent bond, permit the formulation of a satisfactory structural formula for a great number of substances; however, there are some substances for which a single valence-bond structure does not provide a completely satisfactory representation of the properties of the substance. Ozone, O3, is one such substance. Spectroscopic studies of ozone have shown that the molecule has a bond angle of 117° at the central oxygen atom, and each of the two oxygen-oxygen bond lengths is 128 pm. We can assign a reasonable valence-bond structure to the ozone molecule as follows:

This structure is a satisfactory one in that each of the oxygen atoms is surrounded by four electron pairs, some shared and some unshared. If we assign formal charges to the atoms by dividing shared electron pairs equally between the two atoms, the central atom has a positive charge and the atom to which it is attached by a single bond has a negative charge. This electronic structure is not, however, completely satisfactory, in that the interatomic distance corresponding to the double bond should be about 21 pm less than the distance corresponding to the single bond, whereas they are observed to be equal. The explanation of this discrepancy is that there is another valence-bond structure that can be written for the molecule, namely,

The two valence-bond structures shown here are equivalent. In the quantum-mechanical treatment of the ozone molecule, a wave function is assigned that is the sum of the wave functions for these two valence-bond structures. It is found that such a wave function corresponds to an intermediate value of the bond length, the same for the two bonds, and moreover, that it corresponds to greater stability than either of the individual valence-bond functions. This additional stability is described as the resonance energy corresponding to the resonance of the molecule between the two structures. Accordingly, for ozone there is no single valence-bond structure, of the ordinary type, that is satisfactory, but a combination of two structures of the valence-bond type does provide a satisfactory description of the molecule in its normal state.

This fact is not in conflict with the basic principle enunciated in 1861 by Butlerov that every substance has a definite molecular structure, which determines the properties of the substance. The ozone molecule, in its normal state, has a definite structure, a single structure, and we can represent it by a single formula:

The arrows in this formula indicate that the double bond and the single bond can change places. The structure with a double bond in one position and a single bond in the other does not represent any state of the ozone molecule, but the two structures together or the structural formula in which there is a symbol showing that the double bond and the single bond change places does provide an acceptable representation of the actual single structure of the normal state of the ozone molecule.

Benzene provides a similar case, which puzzled chemists until the theory of resonance (also called mesomerism) was developed in the period 1928–33. Kekulé had pointed out that the carbon quadrivalence of benzene can be preserved by assigning to it a structure in which single bonds and double bonds alternate. There are, however, two such structures:

Efforts were made to find isomers of substances such as orthodichlorobenzene, with a double bond between the carbon atoms and chlorine attached in one isomer and a single bond in this position in the other. All such efforts were, however, unsuccessful, and it was recognized that the six carbon-carbon bonds in the benzene ring are equivalent to one another. Detailed quantum-mechanical treatments of benzene have shown that the molecule has hexagonal symmetry, with all six carbon-carbon bonds equivalent. This fact can be represented by saying that the normal state of the benzene molecule can be represented by the two Kekulé structures, superimposed on one another or in resonance with one another. The quantum-mechanical treatment requires that the benzene molecule actually be more stable, by about 150 kJ · mole–1, than the hypothetical form of the substance corresponding to a single Kekulé structure. This additional stability makes benzene more resistant to hydrogenation than ordinary unsaturated substances.

The benzene molecule in its normal state can be represented by a single formula, such as

The circle within the hexagon means that the structure is the one found by experiment for benzene—that is, a structure with greater stability than the one corresponding to one Kekulé structure and with the six carbon-carbon bonds equivalent. There is, however, an advantage to writing the two Kekulé structures for benzene and then saying that the actual structure of the molecule corresponds to resonance between these two structures. We know what the properties are for single bonds and double bonds and accordingly can predict properties corresponding to a Kekulé structure and to the superposition of two Kekulé structures. The carbon-carbon single-bond length is 154 pm, and the double-bond length, 133 pm. For superposition of the two Kekulé structures, an intermediate value is expected, somewhat closer, because of resonance stabilization, to the double-bond value than to the single-bond value. The observed value is 140 pm, in agreement with expectation. Moreover, if we assign to each carbon atom a tetrahedral structure, with bent bonds in the double-bond positions (a shared edge of two tetrahedrons), the prediction can be made that the benzene molecule is planar, with the carbon atoms at the corners of a regular hexagon and the hydrogen atoms at the corners of a larger coplanar regular hexagon. These predictions are verified by experiment.

Ionic bond. Molten sodium chloride is a good conductor of electricity. It can be described as consisting of positive sodium ions, Na+, and negative chloride ions, Cl, in a moderately compact aggregate, in which, because of thermal agitation, each ion is free to move around slowly. Under the influence of an applied electrical field, the sodium ions move toward the negative electrode and the chloride ions toward the positive electrode, thus carrying the electric current.

A sodium ion is a sodium atom that has lost one electron, to become Na+, with the stable neon structure, and a chloride ion is a chlorine atom that has gained one electron and assumed the stable argon structure. The formula of sodium chloride is NaCl because of the stability of these ions and the necessity that the substance be electrically neutral. The metals in the first column of Mendeleev’s periodic table form unipositive ions and are said to have ionic valence +1, those in the second column form bipositive ions and have ionic valence +2, and so on. Similarly, the halogens, the elements of group VII, pick up an electron to form uninegative ions and are said to have ionic valence –1, oxygen and its congeners can pick up two electrons to form binegative ions, with the argonon structure, and are said to have ionic valence –2, and so on. The composition of salts is determined by ionic valences of the cations and anions that constitute the salt in such a way as to give electrical neutrality to the compound.

The Coulomb forces between ions, such as Na+ and Cl–1, cause each ion to attract neighboring ions of opposite sign and to tend to coordinate them about itself. For sodium chloride this leads to a stable spatial arrangement, reflecting the crystal structure, in which each ion has six nearest neighbors of the opposite sign and 12 neighbors of the same sign at a distance 2½ times larger. The total Coulomb energy for this arrangement is found by summation over pairs of ions to be –1.7476e2/R for each Na+Cl ion pair, in which R is the distance between the center of one ion and the center of one of its six nearest neighbors and e is the ionic charge. Consequently, the crystal is stabilized by the Coulomb attraction by an energy quantity 75 percent greater than the Coulomb energy of a positive charge and a negative charge, located at a distance R from one another. The Coulomb energy of the NaCl crystal is large, amounting to about 860 kJ · mole–1. It is large enough, with the help of the electron affinity of chlorine, to provide the energy to sublime sodium metal to separate atoms, to ionize the atoms, and to dissociate chlorine molecules into chlorine atoms; the remaining energy of 410 kJ · mole–1. corresponds to the heat of formation of sodium chloride from the elements.

The forces of attraction of ions of opposite charge are called ionic valence forces. We may say that in the sodium chloride crystal, in which the sodium ion has a coordination number (ligancy) of 6 (that is, is surrounded by six nearest neighbors), the total ionic valence +1 of the sodium ion is divided between the six neighbors, and each of the six bonds between sodium and the adjacent chlorine can be said to be an ionic bond with strength 1/6. The negative charge of the chloride ion is satisfied by the six ionic bonds, each with strength 1/6, that reach it from its six sodium ion neighbors. According to a valence rule of considerable importance in inorganic chemistry, the sums of the ionic valences reaching each negative ion should equal the ionic valence of the negative ion or at least approximate it closely.

In ionic crystals, the bonds are in fact not pure ionic bonds. Instead, they have some covalent character, as discussed in the following section.

Electronegativity and partial ionic character of bonds. In the 1920’s, when the concepts of ionic valence and covalence had been developed but the basic principles of the electronic structure of atoms and molecules were not yet known, there was much discussion about whether to describe a molecule such as HC1 as involving a covalent bond or an ionic bond. The structure H+C1 seemed satisfactory in that the ions are known to exist and the chloride ion has the stable argon structure. Furthermore, the structure Chemical Bond is satisfactory in that it involves a shared electron pair, giving the stable helium structure to hydrogen and the stable argon structure to chlorine. Hydrogen chloride ionizes into hydrogen ions and chloride ions when it is dissolved in water, suggesting that the ionic structure may also occur in the gas molecule. The dielectric constant of the gas, however, corresponds to an electric dipole moment only 19 percent as great as expected for separated ions, at the known interatomic distance of 127 pm. The resolution of this difficulty was provided by the general quantum-mechanical theory of molecular structure. It is that the actual structure of the normal state of the molecule can be described in terms of a wave function that is a sum of the functions corresponding to the ionic structure and the covalent structure. In the case of the HC1 molecule, the bond can be described as an ionic bond with considerable covalent character, or, better, as a covalent bond with little, 19 percent, ionic character.

The molecule in its normal state has, of course, a single structure, which may be represented by the single formula H—Cl. In the case of a covalent bond between like atoms, as in H—H or Cl—Cl, the bonding electron pair is shared equally between the two atoms. An ideal covalent bond may be defined as one in which the electron pair is shared equally by the two atoms, even when they are unlike. If an ideal covalent bond were present in HCl, we could expect that the bond energy would be the average of those in H2 and Cl2. It is, in fact, found that for some single bonds between like atoms, the bond energy is the average of the corresponding bonds between like atoms. An example is HI, with a bond energy of 299 kj · mole–1, which is only 5 kj · mole–1 greater than the average for H2 (436) and I2 (151). The electric dipole moment of the HI molecule is also close to zero, indicating that the shared electron pair is divided about equally between the two atoms. The bond in the HI molecule can be described as a covalent bond with very little ionic character. When the bond has considerable ionic character, it is found that the bond energy is significantly greater than the value corresponding to the ideal covalent bond; for HCl it is 92 kj · mole–1 greater. This quantity, which is the enthalpy of formation of HCl from the elementary substances, is the resonance energy associated with 19 percent of partial ionic character, that is, the energy corresponding to the resonance between the ionic structure and the ideal covalent structure for HCl.

It has been found that single bonds between unlike atoms are generally somewhat stronger than the average of the corresponding bonds between like atoms and that this difference, the enthalpy of formation, is approximately proportional to the square of the difference in the electronegativity of the atoms. Values of the electronegativity (x) can be assigned to the elements in this way, as shown in Table 2. The additional energy of a single bond between unlike atoms is approximately equal to 100 kJ · mole–1 times the square of the electronegativity difference. Somewhat greater reliability is obtained by introducing a biquadratic term; the approximate equation for the energy of a single bond A—B (in kJ · mole–1) between unlike atoms A and B is then

E(A—B) = ½[E(A—A) + E(B—B)] + 100(xAxB)2 – 6.5(xAxB)4

For H—Cl, for example, this equation, with E(H—H) = 436, E(Cl—Cl) = 243, and xHxCl = 0.9, gives the value 417 kj · mole–1, which is 4 percent less than the experimental value of 432 kJ · mole–1.

Observed values of electric dipole moments of molecules show that the amount of ionic character of a bond A—B increases with increase in Δx = xAxB, being about 22 percent for Δx = 1.0, 63 percent for Δx = 2.0, and 89 percent for Δx = 3.0. For HCl, for example, the observed value of the electric dipole moment is 19 percent of the value corresponding to charges +2 and –2 at the molecule’s internuclear distance, 127 pm, corresponding to the value x = 0.9 for H and Cl.

Electroneutrality principle. The electroneutrality principle, which was first formulated by the American chemist I. Langmuir in 1920, states that the electronic structures of stable molecules and crystals are such as to give each atom an electric charge close to zero and are essentially always in the range –1 to +1. For example, the O—H bond is about 40 percent ionic, so that in the water molecule, H2O, the resultant charges are H2+0.4O–0.8 and in the hydronium ion, [H3O]+, they are [H3+0.4O–0.2]+. For the nitrous oxide molecule, the following three structures are acceptable in that they give each atom the neon structure:

The third structure, however, is incompatible with the electroneutrality principle, since the formal charge –2 on the end nitrogen atom is not counterbalanced by ionic character of the N—N bond. The conclusion that the normal state of the molecule corresponds to the resonance between the valence-bond structures A and B with little or no contribution from C is supported by the observed bond lengths and vibrational frequencies.

Oxidation number. After the concepts of ionic valence and co-valence had been introduced and detailed electronic structures of molecules began to be written, it was recognized that a simple representation of the oxidation states of elements in a compound was needed. The oxidation number came into use for this purpose.

The oxidation number of an element in a substance is the electrical charge assigned to the atoms of the element according to certain rules. These rules are simple but not completely unambiguous, and their application requires some chemical insight. The rules are the following:

Table 2. The complete electronegativity scale1
1Pauling type. The values given in the table refer to the common oxidation states of the elements. Forsome elements, variation of the electronegativity with oxidation number is observed; for example, FeII 1.8, FeIII 1.9; CuI 1.9, CuII 2.0; SnII 1.8, SnIV 1.9.
LiBeB          CNOF
NaMgAI          SiPSCl

(1) The oxidation number of a monatomic ion in an ionic substance is equal to its electrical charge.

(2) The oxidation number of atoms in an elementary substance is 0.

(3) In a covalent compound of known structure, the oxidation number of each atom is equal to the charge remaining on the atom when each shared electron pair is assigned completely to the more electronegative of the two atoms sharing it. A pair shared by two atoms of the same element is usually split between them.

(4) The oxidation number of one element in a compound of uncertain structure may be calculated from a reasonable assignment of oxidation numbers to the other elements in the compound.

For example, in hydrogen peroxide, H2O2, the hydrogen atoms are assigned the oxidation number of +1; the neutrality of the molecule then requires that oxygen be given the oxidation number of –1. The state of oxidation of oxygen in H2O2 is thus midway between that in H2O, –2, and that in O2, 0.

The word “valence” when used in the field of inorganic chemistry ordinarily refers to the state of oxidation of an element as expressed by its oxidation number, whereas in organic chemistry it usually refers to the covalence of the element.

Hydrogen bond. A structural feature that has an important effect on the properties of many substances is the hydrogen bond. A hydrogen atom under certain circumstances may be bonded to two other atoms with significant strength. Hydrogen can form only one covalent bond, because it has only one stable orbital. Its one bond may, however, resonate between two positions. The most important hydrogen bonds are those formed between two strongly electronegative atoms, especially nitrogen, oxygen, and fluorine. In a few substances, such as the hydrogen difluoride ion, FHF, the hydrogen atom is approximately midway between two electronegative atoms, forming a half-bond with each. Most hydrogen bonds are unsymmetrical, with one interatomic distance about 50 to 80 pm longer than the other, corresponding to a ratio of bond strengths of around 10. The bond energy of the weaker bond is usually about 20 to 40 kJ · mole–1; this is called the energy of the hydrogen bond.

The hydrogen bonds formed by water molecules are responsible for the surprisingly high melting point of ice and the boiling point of water, for the existence of a maximum density of water, and for the expansion of water on freezing. Many special properties of inorganic and organic molecules, such as the dimerization of fatty acids, are caused by hydrogen-bond formation. The hydrogen bond is an especially important feature of the structure of proteins and of nucleic acids.

Bonds involving d orbitals. In 1893 the Swiss chemist A. Werner developed a new concept in chemistry. It had been recognized that many metallic salts have the ability to combine with other salts or with water or ammonia or other molecules; for example, potassium chloride and platinum (IV) chloride form a well-crystallized salt 2KCl · PtCl4, and cobalt (III) iodide adds ammonia to form CoI3 · 6NH3. The compounds formed in this way had not been fitted into any theory of valence, however, and their existence had been attributed to the action of weak residual forces, inferior to the forces of ordinary chemical bonds. By studying an immense number of these compounds, Werner demonstrated that their compositions and properties could be systematized on the basis of the new assumption that a metal atom has the ability to combine with a definite number (usually four or six) of other atoms, ions, or molecules and to coordinate, or ligate, them into a definite geometrical arrangement about itself. Werner was able to present solid evidence, consisting mainly of the existence of isomers, to support his proposal that most complexes with a coordination number of 6, such as the hexachloroplatinate ion, PtCl62–, and the cobaltic hexammine ion, Co(NH3)63+, have an octahedral configuration, the six attached groups being arranged at the corners of a regular octahedron about the central atom. He also showed that some complexes with a coordination number of 4 have a tetrahedral configuration, such as Zn(NH3)42+, and some, a square, planar configuration, such as PtCl42– and other complexes of bipositive palladium and platinum. The general acceptance of Werner’s theory came in 1911, after his prediction and the experimental verification of the existence of the optical isomerism of some octahedral coordination complexes. In 1920, R. W. G. Wyckoff and R. G. Dickinson completely verified the octahedral and square planar configurations by the X-ray diffraction determination of the crystal structure of K2PtCl6, K2Pt(CN)4, and other coordination complexes.

A theory of these complexes was developed in 1931 by Pauling, who pointed out that, whereas an s orbital and three p orbitals hybridize to form a set of four tetrahedral orbitals, the hybridization of these four orbitals with two d orbitals leads to a set of six hybrid spd orbitals that are directed toward the corners of a regular octahedron, while with only one d orbital available, four hybrid sp2d orbitals are formed directed toward the corners of a square in one plane. The numbers of electrons in palladium (IV) and platinum (IV) are such as to permit two d orbitals to be involved in bond formation, and accordingly the octahedral complexes, with a coordination number of 6, are formed, whereas palladium (II) and platinum (II), with two additional electrons, have only one d orbital available and can form only square planar complexes. This consideration led to the prediction that covalent complexes of nickel (II) should have the square planar configuration and should also be diamagnetic, whereas most compounds of nickel are paramagnetic. These predictions were immediately verified by the measurement of the magnetic properties and by the determination of the crystal structure of nickel coordination compounds.

Chemical bonds in metals. The nature of chemical bonds in metals and intermetallic compounds has not yet been completely elucidated (1981). It seems certain, however, that metals and intermetallic compounds can be described as aggregates of metal cations bound together by valence electrons, which have considerable freedom of motion through the metal, and it is reasonable to call the number of electrons of an atom that help bind the metallic crystal together the “metallic valence” of the atom.

The metallic valence of the alkali metals is 1, and that of the alkaline-earth metals, 2. Values for the transition metals are somewhat uncertain, but the strength, hardness, and melting points of these metals suggest values increasing from 3 for scandium to about 6 for chromium and succeeding elements and then decreasing for copper and zinc. The magnetic properties of the lantha-nides provide evidence that the metallic valence is 3 for all of them except europium and ytterbium, for which it is 2; the paramagnetic susceptibility of these two metals is the same as for their bivalent salts, whereas for the other lanthanides it is the same as for their tervalent salts.

In general, the coordination number of an atom in a metal is greater than the number of bonding electrons. The bonds in metals can be described as covalent bonds, resonating among a larger number of interatomic positions. For example, aluminum has a cubic closest-packed structure, in which each atom is surrounded by 12 neighbors. The valence of aluminum is 3, and accordingly the bond to each of the neighbors can be described as a ⅓ bond.

In order that the covalent bonds be able to resonate among the alternative positions, it is necessary that many or most of the atoms have a suitable bond orbital that is usually not occupied by an electron. This bond orbital may be called the metallic orbital. Possession of such an orbital by most atoms is the criterion for a metal. For example, tin, with four electrons in the outermost s and p orbitals, can distribute the four electrons among the four sp3 orbitals and thus form four covalent bonds. It then would not have an extra orbital, and consequently the resulting structure should not be metallic. The modification of tin called gray tin has, in fact, the diamond structure, in which each atom is bonded to four neighbors, tetrahedrally arranged, and is not metallic. The bond length is the same as for a single bond. In white tin, the metallic modification of tin, each atom has six neighbors, with bond lengths corresponding to a valence of about 2.5 for the tin atom. If two of the four outer electrons of the tin atom form an unshared pair, occupying the 5s orbital, the other two electrons can occupy two of the three p orbitals and be involved in bond formation. This leaves one p orbital free, which can serve as the metallic orbital. The observation that the bond length in white tin corresponds to metallic valence 2.5 rather than 2 indicates that there is resonance, to the extent of 25 percent, to the quadrivalent structure of tin.

When more d orbitals are available, hybrid spd orbitals can be formed, which are still better suited to bond formation since they have a larger concentration in the bond direction. Whereas the best sp orbitals that can be formed make the tetrahedral angle, 109°28′, with one another, the best spd orbitals are at angles of 73° and 133°.

Covalence of transition metals. The transition metals, with five d orbitals, one s orbital, and three p orbitals in the outer shell, can form as many as nine hybrid spd bond orbitals (at angles near 73° and 133° with one another) and accordingly can form nine covalent bonds, should the atom have nine electrons in its outer shell. An example is Os4O4(CO)12, whose structure may be described as having the four osmium atoms at four alternating corners of a cube, with oxygen atoms at the other four corners. Each oxygen atom transfers an electron to an osmium atom, so that the oxygen atom has five valence electrons and can form three covalent bonds and the osmium atom has nine valence electrons and can form nine covalent bonds. Each osmium atom forms three bonds with adjacent oxygen atoms and a double bond with the carbon atom of each of the three attached carbonyl groups, thus completing its enneacovalence.

For most carbonyls of the transition metals, the chemical formulas correspond to using all nine outer spd orbitals either for bond formation or for unshared electron pairs. For example, the nickel atom has ten outer electrons. In Ni(CO)4, eight of them are used to form double bonds with the four carbonyl groups. These four double bonds use eight of the nine spd orbitals, and the remaining one is occupied by an unshared pair. In Fe(CO)5, the iron atom gains an electron by transfer from one carbonyl group, with which it forms a single bond, Fe—C≡O; it uses the eight remaining orbitals and electrons to form double bonds with the carbon atoms of the four other carbonyls. In Cr(CO)6, the chromium atom gains three electrons from three carbonyl groups, giving it nine valence electrons. It then forms single bonds with these three and double bonds with the other three carbonyl groups. The partial ionic character of the chromium-carbon and carbon-oxygen bonds, as determined by the differences in electronegativity of the elements, is great enough to transfer most of the excess negative electron charge from chromium to oxygen, so that the atoms are nearly neutral, satisfying the electroneutrality principle.

Quadruple bonds. Carbon atoms can form triple bonds but not quadruple bonds, because the fourth bond of carbon extends in the opposite direction from the other three. Transition metals, however, can form quadruple bonds, because four spd orbitals at 73° with respect to one another (about 133° for two pairs) extend on one side of the atom. The first evidence for the existence of quadruple bonds was obtained by the Soviet chemists B. G. Kuznetsov and P. A. Kaz’min in 1963, when they reported that an X-ray diffraction study of a compound of rhenium showed the presence of Re2 groups with the Re—Re distance of 222 pm, each rhenium atom also having four chlorine atoms about it at a distance of 243 pm. The observed Re—Re distance is about 46 pm less than the single-bond value. It is evident that a quadruple bond is present, as was pointed out in 1964 by the American chemist F. A. Cotton, who found similar interatomic distances in many other crystals, showing the presence of Cr≣Cr, Re≣Re, Tc≣Tc, and Mo≣Mo.


Pauling, L. Obshchaia khimiia. Moscow, 1974. (Translated from English.)
Pauling, L. Priroda khimicheskoi sviazi. Moscow-Leningrad, 1947. (Translated from English.)
Pauling, L. The Nature of the Chemical Bond and the Structure of Molecules and Crystals, 3rd ed. Ithaca, N. Y., 1960.


chemical bond

[′kem·i·kəl ¦bänd]

chemical bond

A bond obtained as a result of cohesion between layers of similar crystalline materials, owing to the formation and the interlocking of crystals.
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