Quantum Mechanics Of Chemical Bonding

Type of physical science: Chemistry

Field of study: Chemistry of molecules: structure

The diversity observed in chemistry is a result of the large number of ways in which atoms can bond together to form new chemical substances. An understanding of chemical bonding makes it possible to predict the properties of chemical compounds.

Overview

All the millions of chemical compounds that exist in the world can be decomposed into elements, or substances that cannot themselves be broken down into simpler substances by chemical means. There are less than one hundred naturally occurring elements, with a handful of additional synthetic, or man-made, elements that have been produced by nuclear reactions. The diversity of chemical compounds that exists is a result of the different ways in which the atoms, or particles composing elements, can be combined to form new substances with new physical and chemical properties. The forces of attraction that hold atoms together and allow them to combine to form compounds are called chemical bonds. The study of bonding in compounds is the fundamental topic of chemistry.

Chemical bonds can be divided into two main categories, ionic and covalent. Both ionic and covalent bonding involve the outermost, or valence, electrons in an atom. It is the valence electrons that are least strongly attracted to the atomic nucleus, and are therefore most easily rearranged to form chemical bonds. In contrast, the inner, or core, electrons of an atom are strongly attracted to the nucleus, and are therefore usually unable to participate in chemical bond formation.

In an ionic bond, one or more electrons are transferred from one atom or group of atoms to another. This results in the formation of positively charged ions (cations) and negatively charged ions (anions). The electrostatic force of attraction that exists between cations and anions is the basis for the bonding.

The ability of an atom to gain or lose electrons and form an ionic bond is in large part determined by the electronegativity of the atom, or relative tendency of the atom to attract electrons. Since metal atoms have low values of electronegativity in comparison to nonmetals, ionic compounds usually consist of a metal cation ionically bonded to a nonmetal anion. For example, table salt is an ionic compound formed of the elements sodium and chlorine, and is called sodium chloride. In this compound, one electron is transferred from each sodium atom to a chlorine atom, resulting in the formation of sodium and chloride ions. It is also possible for ionic bonding to involve groups of atoms that act in the same way as an individual atomic ion.

The number of electrons an atom gains or loses to form an ionic compound depends on the number of electrons originally present in the valence shell. The general tendency is for an atom to gain or lose electrons in order to fill completely or empty the valence shell. For example, alkali earth metals such as beryllium, magnesium, and calcium have two valence electrons, and therefore form cations by donating two electrons to a more electronegative nonmetal. Transition metals often can form cations with different values of charge. For instance, iron can form two different ionic compounds with chlorine: iron (II) chloride, with a +2 charge on the iron cation; and iron (III) chloride, with a +3 charge on the iron cation. In cases such as these, the charge of the cation is indicated in the name of the compound by a Roman numeral.

Because the electrostatic attractive force between cations and anions is isotropic, or the same in all directions, cations in ionically bonded compounds generally surround themselves with anions, and vice versa. In the solid phase, individual subunits, or molecules, of an ionic compound do not exist. Instead, a regular arrangement of cations and anions called a crystal lattice forms. The structure of the crystal lattice for a particular ionic compound is determined by the relative sizes of the cations and anions making up the compound.

In contrast to ionic bonding, covalent bonding involves the sharing of one or more pairs of electrons between atoms. Covalent bonds usually form between two atoms, with each atom contributing one electron per covalent bond, although occasionally both electrons can come from the same atom and form a dative covalent bond. The bonding that occurs when a pair of electrons is shared between two atoms arises from the attraction between the positively charged atomic nuclei and the negative charge of the electrons located between the atoms bonded together.

The Pauli exclusion principle explains the phenomenon that covalent bonds form from pairs of electrons. Each electron in an atom or molecule can be labeled by a set of quantum numbers that specify the properties of the electron. The exclusion principle states that no two electrons in the same atom or molecule can have the same set of quantum numbers. Since there are two possible values for the spin quantum number describing the rotation of an electron about its axis, it is possible to put up to two electrons into a covalent bond and still satisfy the exclusion principle.

The sharing of electrons in a covalent bond will occur when the electronegativities of the two atoms involved in the bond are similar, preventing the transfer of an electron from one atom to the other that takes place in ionic bonding. Covalent bonds are usually found between atoms of nonmetallic elements, although exceptions to this rule exist. Covalent bonds are not isotropic, but are oriented in particular directions. Also, covalently bonded compounds form distinct units of atoms chemically united, called molecules. The forces of interaction between different molecules in a covalently bonded compound are weak, and tend to short range.

Most chemical bonding is a combination of ionic and covalent bonding. In general, as the difference in electronegativity between two atoms in a bond increases, the amount of ionic character in the bond also increases. One consequence of this is that covalent bonds between atoms of different elements will have a nonsymmetrical distribution of electron density, with the more electronegative atom having a partial negative charge and the less electronegative atom having a partial positive charge. Such a bond is defined as a polar covalent bond. A molecule containing one or more polar bonds will have an overall separation between the center of positive and negative charge, and is therefore called a polar molecule, unless the effects of the polar bonds in the molecule cancel as a result of the symmetry of the molecule.

The strength of a covalent bond is related to the bond order, or number of electron pairs in the bond. A covalent bond is classified as a single bond if one pair of electrons is shared, a double bond if two pairs of electrons are shared, and a triple bond if three pairs of electrons are shared. Higher-order bonds are also possible but are rare. In general, double bonds are stronger than single bonds, and triple bonds are stronger than double bonds.

As in ionic bonding, atoms that are covalently bonded together tend to form valence shells that are completely filled or completely empty. The electrons in the valence shell can be divided into two categories. Lone pairs of electrons are not shared between atoms, and are therefore not involved in covalent bonding. Bonding pairs of electrons are shared between adjacent atoms and are responsible for the bonding in a molecule.

Atoms in covalently bonded molecules often form bonds until their valence shell is completely filled with electrons. For many atoms, particularly those in the first few rows of the periodic table, it takes eight electrons to fill the valence shell. This is the origin of the octet rule, which states that an atom will form covalent bonds until it has eight valence electrons. For example, a nitrogen atom has five valence electrons, and therefore must form three covalent bonds to obtain a filled valence shell. In the compound nitrogen trichloride, for example, the nitrogen atom fills its valence shell by forming a single bond with each of the three chlorine atoms. For atoms of elements further down in the periodic table, exceptions to the octet rule can occur. Phosphorus, which like nitrogen has five valence electrons, can combine with chlorine to form the compound phosphorus trichloride, satisfying the octet rule. Nevertheless, phosphorus and chlorine can also combine to form phosphorus pentachloride, a compound violating the octet rule.

Since electrons repel one another, it is reasonable to expect that the lone pair and bonding electrons about an atom will arrange themselves in such a way as to be as far apart from one another as possible. This is the origin of a simple model of covalent bonding called valence shell electron pair repulsion theory (VSEPR theory). VSEPR theory can be used to predict the geometric arrangement of atoms in a molecule. For example, in carbon dioxide, the central carbon atom forms double bonds with two oxygen atoms. VSEPR theory predicts that this molecule should be linear, as is confirmed by experiment. In contrast, a methane molecule contains a central carbon atom covalently bonded to four hydrogen atoms. The predicted geometry for methane is tetrahedral, again in agreement with experiment.

A more sophisticated theory of covalent bonding begins with the idea that electrons in an atom are localized in particular regions of space, called atomic orbitals. Each orbital in an atom can hold a maximum of two electrons, a consequence of the exclusion principle. In valence bond theory, bonding occurs as a result of the overlap of atomic orbitals between adjacent atoms.

Often, instead of using the original atomic orbitals to describe the chemical bonding taking place, a new set of hybrid orbitals, constructed from the original set of atomic orbitals, is created. In this case, it is overlap of the hybrid orbitals of an atom with atomic orbitals or hybrid orbitals of an adjacent atom that results in formation of covalent bonds. The larger the degree of overlap of the atomic or hybrid orbitals, the stronger the covalent bond that is formed.

The valence bond theory makes predictions concerning the geometry and electronic properties of molecules that are in large part confirmed by experiment. It also represents a convenient picture for bonding in molecules. While qualitatively correct, however, valence bond theory cannot calculate exact values for molecular properties such as bond strength and electron charge distribution.

An alternative to valence bond theory is molecular orbital theory. In the simple version of the theory, combinations of atomic orbitals are used to construct molecular orbitals for the electrons. The molecular orbitals responsible for bonding can extend over the entire molecule instead of being localized between adjacent atoms, as in valence bond theory. Electrons are added to the molecular orbitals in the same way that electrons can be added to the atomic orbitals of an atom. The accuracy of molecular orbital calculations can be improved by increasing the number of atomic orbitals used in the construction of the molecular orbitals. Accuracy also can be improved by using experimental information as a guide to the construction of molecular orbitals, a semiempirical approach. In contrast, ab initio molecular orbital theory is carried out starting from principles, with no use of experimental data.

Molecular orbital theory is particularly useful in describing covalent bonds extending over more than two atoms. Such bonds are called delocalized bonds, or multicenter covalent bonds. Delocalization of electron density in a bond can give additional strength to the bond and result in more stable molecules. Aromatic molecules, for example, contain one or more rings of carbon atoms held together by delocalized covalent bonds. The extra stability from delocalization makes aromatic compounds more stable than the corresponding carbon compounds in which delocalization does not occur.

While the formation of most chemical compounds can be explained in terms of ionic or covalent bonding, there are some exceptions. In particular, the attractive forces holding a metal together are best described by treating the metal as a collection of cations surrounded by a sea of electrons. In this case, it is the attractive forces between the electrons and metal cations that are responsible for bonding in the metal.

Applications

The physical properties of chemical substances are determined by the attractive forces that bond the atoms of the substance together. Since there are large differences between ionic and covalent bonding, it is expected that ionically bonded and covalently bonded compounds should have distinct characteristics, and that these characteristics can be predicted from the type of bonding taking place.

Ionic compounds are, in general, good electrical conductors in the molten (liquid) phase or when dissolved in solution. This is because the individual ions making up the compound are mobile and can be used to transport electrical charge. In the solid phase, in which the positions of the ions are fixed by the crystal structure of the solid, ions cannot be used to carry charge. Solid ionic compounds are therefore usually good electrical insulators. Ionic compounds dissolve well in polar liquids because of the attractive forces acting between polar molecules and ions, but do not dissolve well in nonpolar liquids. Finally, because electrostatic interactions between ions are long-range and isotropic, ionically bonded compounds tend to have high melting points.

In contrast to ionic compounds, covalent compounds are usually poor electrical conductors in all phases. This is true since covalent compounds exist as neutral molecules, and cannot carry electrical charge. Exceptions occur with covalently bonded molecules that ionize, as is the case with acetic acid and other organic acids. Covalently bonded molecules tend to dissolve well in nonpolar solvents but not in polar solvents, although exceptions to this behavior can occur in molecules with strong polar bonds. Because the forces of attraction acting between different covalently bonded molecules are weak, such molecules, in general, have low melting and boiling points.

As well as making it possible to predict the general properties of ionic and covalent compounds, an understanding of bonding theory provides a means of determining specific properties of individual compounds. These properties include the strength of individual bonds in a molecule, the structure of molecules and crystals, the interaction of molecules with light and other electromagnetic radiation, the magnetic and electrical properties of compounds, and the reactivity of chemical substances toward other compounds.

A specific example of the connection between bonding and reactivity is the use of covalent compounds of boron in organic synthesis. For example, in boron trifluoride, there are only six electrons in the valence shell of the boron atom. It is therefore possible to add an additional pair of electrons to the boron atom by forming a dative bond with another molecule containing an atom with one or more lone pairs of electrons. Boron trifluoride will readily bond to other compounds such as alcohols, ethers, amines, and phosphines, and can be used to synthesize organic compounds and to initiate reactions forming polymers.

Bonding theory, particularly molecular orbital theory, has been used to predict properties of molecules or ions that cannot be produced in the laboratory easily due to their instability or high reactivity. These include reaction intermediates important in combustion of hydrocarbons and other fuels, trace components of the atmosphere responsible for the formation and disappearance of pollutants, and exotic molecules found in interstellar space.

Since the structure of a molecule is determined by the orientations of the bonds between the atoms within the molecule, bonding theory is also useful for understanding the relationship between structure and activity in biological molecules such as hormones and enzymes. It also can be used to aid in the design of pharmaceutical drugs by identifying the atom or group of atoms in a molecule responsible for the activity of the drug, and in suggesting ways in which a molecule can be modified to enhance drug activity or to minimize harmful side effects.

The application of bonding theory to solids has provided an explanation for the way in which different solids act as electrical conductors, semiconductors, and insulators. It also has been used to predict which substances are likely to behave as superconductors at high temperatures. Such superconducting materials can be used in computers and in medical and scientific instrumentation.

Context

The idea that substances are composed of atoms held together by chemical bonds dates back to speculations by Leucippus, Democritus, and other Greek philosophers of the fifth century B.C. Observations by Joseph Proust and John Dalton in the late eighteenth and early nineteenth centuries gave experimental support to this idea, but did not provide any evidence of how the atoms in a chemical compound were held together. Experimental work by Joseph John Thompson on electrons, Eugen Goldstein on positive ions, and Ernest Rutherford on nuclear structure in the late nineteenth and early twentieth centuries demonstrated that atoms themselves are composed of charged particles, and suggested that the forces holding atoms together in compounds were electrical in nature.

The development of quantum mechanics in the 1920's provided a quantitative theory that could be applied to bonding in molecules, and that gave an underlying explanation for the octet rule and other observations on covalent bonding previously formulated by the American chemists Gilbert Newton Lewis and Irving Langmuir. In 1927, Walter Heitler and Fritz London presented the first quantum mechanical treatment of the hydrogen molecule. Linus Pauling and others used this work as the basis for valence bond theory. Pauling also developed the idea of electronegativity as a means of predicting the polarity of covalent bonds, and proposed various ways of defining electronegativity using experimental data.

Molecular orbital theory developed more slowly than valence bond theory, in large part because of the difficulty in carrying out molecular orbital calculations. Douglas Hartree and Vladimir Fock developed one of the first numerical methods for molecular orbital calculations.

In the 1950's, when high-speed computers first became available, accurate molecular orbital calculations on polyatomic molecules were first performed. Further developments in molecular orbital theory, along with advances in the size and speed of computers, made it possible by the early 1970's to use molecular orbital theory to describe bonding in large molecules, including molecules of interest to biologists, and to describe extended systems such as ionic and molecular crystals.

Principal terms

BOND ORDER: the number of pairs of electrons being shared in a covalent bond

COVALENT BOND: a bond formed when one or more pairs of electrons are shared between two or more atoms

ELECTRONEGATIVITY: the relative tendency of an atom or group of atoms to attract electrons

IONIC BOND: a bond formed when one or more electrons are transferred from one atom or group of atoms to another

LONE PAIR ELECTRONS: pairs of electrons in an atom in a covalently bonded compound that do not participate in the bonding

OCTET RULE: the observation that atoms tend to add electrons by forming covalent bonds until they achieve a filled valence shell containing eight electrons

VALENCE BOND THEORY: a theory stating that covalent bonds form by the sharing of pairs of electrons in overlapping atomic orbitals of adjacent atoms

VALENCE ELECTRON: an electron in the outer, or valence, shell of an atom

Bibliography

Lagowski, J. J. THE CHEMICAL BOND. Boston: Houghton Mifflin, 1966. Develops concepts of molecular bonding from a historical perspective. Good presentation of the origins of modern bonding theory and their role in the development of chemistry.

Linnett, J. W. STRUCTURE OF MOLECULES. New York: Wiley, 1964. A discussion of bonding in molecules, beginning with simple diatomic molecules and proceeding in order to cover triatomic and larger molecules. The presentation is at a simple level.

Pauling, Linus. THE NATURE OF THE CHEMICAL BOND. Ithaca, N.Y.: Cornell University Press, 1960. The classic book on bonding in molecules, originally published in 1933, by one of the major developers of valence bond theory and other fundamental concepts of chemical bonding including electronegativity. The book is technical in nature, although Pauling has an ability to present complicated ideas in a simple manner.

Pauling, Linus, and Roger Hayward. THE ARCHITECTURE OF MOLECULES. San Francisco: W. H. Freeman, 1964. A pictorial approach to bonding and structure of molecules, at a simple level, directed at nonscientists. After a brief introduction, the authors discuss the bonding and structure of a number of common molecules.

Salem, Lionel. MARVELS OF THE MOLECULE. Translated by James Wuest. New York: VCH Publishers, 1987. A good introduction to molecular bonding and structure for the nonscientist. Salem makes extensive use of figures to illustrate his discussion of molecular bonding and structure, and their relation to chemical reactivity. The book begins at a simple level and progresses to more sophisticated concepts in bonding theory.

Speakman, J. C. MOLECULES. New York: McGraw-Hill, 1968. A discussion of bonding in molecules from the perspective of quantum mechanics. Some mathematical background is required to understand some of the material; however, there are good qualitative discussions of bonding and of atomic and molecular orbitals.

Chemical Bond Angles and Lengths

Electrons and Atoms

Calculations of Molecular Structure

Quantum Mechanics of Molecules

The Periodic Table and the Atomic Shell Model