MOLECULES

CONCEPT

Prior to the nineteenth century, chemists pursued science simply by taking measurements, before and after a chemical reaction, of the substances involved. This was an external approach, rather like a person reaching into a box and feeling of the contents without actually being able to see them. With the evolution of atomic theory, chemistry took on much greater definition: for the first time, chemists understood that the materials with which they worked were interacting on a level much too small to see. The effects, of course, could be witnessed, but the activities themselves involved the interactions of atoms in molecules. Just as an atom is the most basic particle of an element, a molecule is the basic particle of a compound. Whereas there are only about 90 elements that occur in nature, many millions of compounds are formed naturally or artificially. Hence the study of the molecule is at least as important to the pursuit of modern chemistry as the study of the atom. Among the most important subjects in chemistry are the ways in which atoms join to form molecules—not just the numbers and types of atoms involved, but the shape that they form together in the molecular structure.

HOW IT WORKS

Introduction to the Molecule

Sucrose or common table sugar, of course, is grainy and sweet, yet it is made of three elements that share none of those characteristics. The formula for sugar is C₁₂H₂₂O₁₁, meaning that each molecule is formed by the joining of 12 carbon atoms, 22 hydrogens, and 11 atoms of oxygen. Coal is nothing like sugar—for one thing, it is as black as sugar is white, yet it is almost pure carbon. Carbon, at least, is a solid at room temperature, like sugar. The other two components of sugar, on the other hand, are gases, and highly flammable ones at that.

The question of how elements react to one another, producing compounds that are altogether unlike the constituent parts, is one of the most fascinating aspects of chemistry and, indeed, of science in general. Combined in other ways and in other proportions, the elements in sugar could become water (H₂O), carbon dioxide (CO₂), or even petroleum, which is formed by the joining of carbon and hydrogen.

Two different compounds of hydrogen and oxygen serve to further illustrate the curiosities involved in the study of molecules. As noted, hydrogen and oxygen are both flammable, yet when they form a molecule of water, they can be used to extinguish most fires. On the other hand, when two hydrogens join with two oxygens to form a molecule of hydrogen peroxide (H₂O₂), the resulting compound is quite different from water. In relatively high concentrations, hydrogen peroxide can burn the skin, and in still higher concentrations, it is used as rocket fuel. And whereas water is essential to life, pure hydrogen peroxide is highly toxic.

THE QUESTION OF MOLECULAR STRUCTURE.

It is not enough, however, to know that a certain combination of atoms forms a certain molecule, because molecules may have identical formulas and yet be quite different substances. In English, for instance, there is the word "rose." Simply seeing the word, however, does not tell us whether it is a noun, referring to a flower, or a verb, as in "she rose through the ranks." Similarly, the formula of a compound does not necessarily tell what it is, and this can be crucial.

For instance, the formula C₂H₆O identifies two very different substances. One of these is ethyl alcohol, the type of alcohol found in beer and wine. Note that the elements involved are the same as those in sugar, though the proportions are different: in fact, some aspects of the body's reaction to ethyl alcohol are not so different from its response to sugar, since both lead to unhealthy weight gain. In reasonable small quantities, of course, ethyl alcohol is not toxic, or at least only mildly so; yet methyl ether—which has an identical formula—is a toxin.

But the distinction is not simply an external one, as simple as the difference between beer and a substance such as methyl ether, sometimes used as a refrigerant. To put it another way, the external difference reflects an internal disparity: though the formulas for ethyl alcohol and methyl ether are the same, the arrangements of the atoms within the molecules of each are not. The substances are therefore said to be isomers.

In fact C₂H₆O is just one of three types of formula for a compound: an empirical formula, or one that shows the smallest possible whole-number ratio of the atoms involved. By contrast, a molecular formula—a formula that indicates the types and numbers of atoms involved—shows the actual proportions of atoms. If the formula for glucose, a type of sugar (C₆H₁₂O₆), were rendered in empirical form, it would be CH₂O, which would reveal less about its actual structure. Most revealing of all, however, is a structural formula—a diagram that shows how the atoms are bonded together, complete with lines representing covalent bonds. (Structural formulas such as those that apply the Couper or Lewis systems are discussed in the Chemical Bonding essay, which also examines the subject of covalent bonds.)

Chemists involved in the area of stereo-chemistry, discussed below, attempt to develop three-dimensional models to show how atoms are arranged in a molecule. Such models for ethyl alcohol and methyl ether, for instance, would reveal that they are quite different, much as the two definitions of rose mentioned above illustrate the two distinctly different meanings. Because stereochemistry is a highly involved and complex subject, it can only be touched upon very briefly in this essay; nonetheless, an understanding of a molecule's actual shape is critical to the work of a professional chemist.

MOLECULES AND COMPOUNDS.

A molecule can be most properly defined as a group of atoms joined in a specific structure. A compound, on the other hand, is a substance made up of more than one type of atom—in other words, more than one type of element. Not all compounds are composed of discrete molecules, however. For instance, table salt (NaCl) is an ionic compound formed by endlessly repeating clusters of sodium and chlorine that are not, in the strictest sense of the word, molecules.

Salt is an example of a crystalline solid, or a solid in which the constituent parts are arranged in a simple, definite geometric pattern repeated in all directions. There are three kinds of crystalline solids, only one of which has a truly molecular structure. In an ionic solid such as table salt, ions (atoms, or groups of atoms, with an electric charge) bond a metal to a nonmetal—in this case, the metal sodium and the nonmetal chlorine. Another type of crystalline solid, an atomic solid, is formed by atoms of one element bonding to one another. A diamond, made of pure carbon, is an example. Only the third type of crystalline solid is truly molecular in structure: a molecular solid—sugar, for example—is one in which the molecules have a neutral electric charge.

Not all solids are crystalline; nor, of course, are all compounds solids: water, obviously, is a liquid at room temperature, while carbon dioxide is a gas. Nor is every molecule composed of more than one element. Oxygen, for instance, is ordinarily diatomic, meaning that even in its elemental form, it is composed of two atoms that join in an O₂ molecule. It is obvious, then, that the defining of molecules is more complex than it seems. One can safely say, however, that the vast majority of compounds are made up of molecules in which atoms are arranged in a definite structure.

In the essay that follows, we will discuss the ways atoms join to form molecules, a subject explored in more depth within the Chemical Bonding essay. (In addition, compounds themselves are examined in somewhat more detail within the Compounds essay.) We will also briefly examine how molecules bond to other molecules in the formation of solids and liquids. First, however, a little history is in order: as noted in the introduction to this essay, chemists did not always possess a clear understanding of the nature of a molecule.

A Brief History of the Molecule

In ancient and medieval times, early chemists—some of whom subscribed to an unscientific system known as alchemy—believed that one element could be transformed into another. Thus many an alchemist devoted an entire career to the vain pursuit of turning lead into gold. The alchemists were at least partially right, however: though one element cannot be transformed into another (except by nuclear fusion), it is possible to change the nature of a compound by altering the relations of the elements within it.

Modern understanding of the elements began to emerge in the seventeenth century, but the true turning point came late in the eighteenth century. It was then that French chemist Antoine Lavoisier (1743-1794) defined an element as a simple substance that could not be separated into simpler substances by chemical means. Around the same time, another French chemist, Joseph-Louis Proust (1754-1826) stated that a given compound always contained the same proportions of mass between elements. The ideas of Lavoisier and Proust were revolutionary at the time, and these concepts pointed to a substructure, invisible to the naked eye, underlying all matter.

In 1803, English chemist John Dalton (1766-1844) defined that substructure by introducing the idea that the material world is composed of tiny particles called atoms. Despite the enormous leap forward that his work afforded to chemists, Dalton failed to recognize that matter is not made simply of atoms. Water, for instance, is not just a collection of "water atoms": clearly, there is some sort of intermediary structure in which atoms are combined. This is the molecule, a concept introduced by Italian physicist Amedeo Avogadro (1776-1856).

AVOGADRO AND THE IDEA OF THE MOLECULE.

French chemist and physicist Joseph Gay-Lussac (1778-1850) had announced in 1809 that gases combine to form compounds in simple proportions by volume. As Gay-Lussac explained, the ratio, by weight, between hydrogen and oxygen in water is eight to one. The fact that this ratio was so "clean," involving whole numbers rather than decimals, intrigued Avogadro, who in 1811 proposed that equal volumes of gases have the same number of particles if measured at the same temperature and pressure. This, in turn, led him to the hypothesis that water is not composed simply of atoms, but of molecules in which hydrogen and oxygen combine.

For several decades, however, chemists largely ignored Avogadro's idea of the molecule. Only in 1860, four years after his death, was the concept resurrected by Italian chemist Stanislao Cannizzaro (1826-1910). Of course, the understanding of the molecule has progressed enormously in the years since then, and much of this progress is an outcome of advances in the study of subatomic structure. Only in the early twentieth century did physicists finally identify the electron, the negatively charged subatomic particle critical to the bonding of atoms.

REAL-LIFE APPLICATIONS

Molecular Mass

Just as the atoms of elements have a definite mass, so do molecules—a mass equal to that of the combined atoms in the molecule. The figures for the atomic mass of all elements are established, and can be found on the periodic table; therefore, when one knows the mass of a hydrogen atom and an oxygen atom, as well as the fact that there are two hydrogens and one oxygen in a molecule of water, it is easy to calculate the mass of a water molecule.

Individual molecules cannot easily be studied; therefore, the mass of molecules is compared by use of a unit known as the mole. The mole contains 6.022137 × 10²³ molecules, a figure known as Avogadro's number, in honor of the man who introduced the concept of the molecule. When necessary, it is possible today to study individual molecules, or even atoms and subatomic particles, using techniques such as mass spectrometry.

Bonding Within Molecules

Note that the mass of an atom in a molecule does not change; nor, indeed, do the identities of the individual atoms. An oxygen atom in water is the same oxygen atom in sugar, or in any number of other compounds. With regard to compounds, it should be noted that these are not the same thing as a mixture, or a solution. Sugar or salt can be dissolved in water at the appropriate temperatures, but the resulting solution is not a compound; the substances are joined physically, but they are not chemically bonded.

Chemical bonding is the joining, through electromagnetic force, of atoms representing different elements. Each atom possesses a certain valency, which determines its ability to bond with atoms of other elements. Valency, in turn, is governed by the configuration of valence electrons at the highest energy level (the shell) of the atom.

While studying noble gases, noted for their tendency not to bond, German chemist Richard Abegg (1869-1910) discovered that these gases always have eight valence electrons. This led to the formation of the octet rule: most elements (with the exception of hydrogen and a few others) are inclined to bond in such a way that they end up with eight valence electrons.

When a metal bonds to a nonmetal, this is known as ionic bonding, which results from attractions between ions with opposite electric charges. In ionic bonding, two ions start out with different charges and form a bond in which both have eight valence electrons. Nonmetals, however, tend to form covalent bonds. In a covalent bond, two atoms start out as most atoms do, with a net charge of zero. Each ends up possessing eight valence electrons, but neither atom "owns" them; rather, they share electrons.

ELECTRONEGATIVITY.

Not all elements bond covalently in the same way. Each has a certain value of electronegativity—the relative ability of an atom to attract valence electrons. Elements capable of bonding are assigned an electronegativity value ranging from a minimum of 0.7 for cesium to a maximum of 4.0 for fluorine. The greater the electronegativity value, the greater the tendency of an element to attract valence electrons.

When substances of differing electronegativity values form a covalent bond, this is described as polar covalent bonding. Water is an example of a molecule with a polar covalent bond. Because oxygen has a much higher electronegativity (3.5) than hydrogen (2.1), the electrons tend to gravitate toward the oxygen atom. By contrast, molecules of petroleum, a combination of carbon and hydrogen, tend to be nonpolar, because carbon (2.5) and hydrogen have very similar electronegativity values.

A knowledge of electronegativity values can be used to make predictions concerning bond polarities. Bonds that involve atoms whose electronegativities differ by more than 2 units are substantially ionic, whereas bonds between atoms whose electronegativities differ by less than 2 units are polar covalent. If the atoms have the same or similar electronegativity values, the bond is covalent.

Attractions Between Molecules

The energy required to pull apart a molecule is known as bond energy. Covalent bonds that involve hydrogen are among the weakest bonds between atoms, and hence it is relatively easy to separate water into its constituent parts, hydrogen and oxygen. (This is sometimes done by electrolysis, which involves the use of an electric current to disperse atoms.) Double and triple covalent bonds are stronger, but strongest of all is an ionic bond. The strength of the bond energy in salt, for instance, is reflected by its melting point of 1,472°F (800°C), much higher than that of water, at 32°F (0°C).

Bond energy relates to the attraction between atoms in a molecule, but in considering various substances, it is also important to recognize the varieties of bonds between molecules—that is, intermolecular bonding. For example, the polar quality of a water molecule gives it a great attraction for ions, and thus ionic substances such as salt and any number of minerals dissolve easily in water. On the other hand, we have seen that petroleum is essentially nonpolar, and therefore, an oil molecule offers no electric charge to bond it with a water molecule. For this reason, oil and water do not mix.

The bonding between water molecules is known as a dipole-dipole attraction. This type of intermolecular bond can be fairly strong in the liquid or solid state, though it is only about 1% as strong as a covalent bond within a molecule. When a substance containing molecules joined by dipole-dipole attraction is heated to become a gas, the molecules spread far apart, and these bonds become very weak. On the other hand, when hydrogen bonds to an atom with a high value of electronegativity (fluorine, for example), the dipole-dipole attraction between these molecules is particularly strong. This is known as hydrogen bonding.

Even a nonpolar molecule, however, must have some attraction to other nonpolar molecules. The same is true of helium and the other noble gases, which are highly nonattractive but can be turned into liquids or even solids at extremely low temperatures. The type of intermolecular attraction that exists in such a situation is described by the term London dispersion forces. The name has nothing to do with the capital of England: it is a reference to German-American physicist Fritz Wolfgang London (1900-1954), who in the 1920s studied the molecule from the standpoint of quantum mechanics.

Because electrons are not uniformly distributed around the nucleus of an atom at every possible moment, instantaneous dipoles are formed when most of the electrons happen to be on one side of an atom. Of course, this only happens for an infinitesimal fraction of time, but it serves to create a weak attraction. Only at very low temperatures do London dispersion forces become strong enough to result in the formation of a solid. (Thus, for instance, oil and rubbing alcohol freeze only at low temperatures.)

Molecular Structure

The Couper system and Lewis structures, discussed in the Chemical Bonding essay, provide a means of representing the atoms that make up a molecule. Though Lewis structures show the distribution of valence electrons, they do not represent the three-dimensional structure of the molecule. As noted earlier in this essay, the structure is highly important, because two compounds may be isomers, meaning that they have the same proportions of the same elements, yet are different substances.

Stereochemistry is the realm of chemistry devoted to the three-dimensional arrangement of atoms in a molecule. One of the most important methods used is known as the VSEPR model (valence shell electron pair repulsion). In bonding, elements always share at least one pair of electrons, and the VSEPR model begins with the assumption that the electron pairs must be as far apart as possible to minimize their repulsion, since like charges repel.

VSEPR structures can be very complex, and the rules governing them will not be discussed here, but a few examples can be given. If there are just two electron pairs in a bond between three atoms, the structure of a VSEPR model is like that of a stick speared through a ball, with two other balls attached at each end. The "ball" is an atom, and the "stick" represents the electron pairs. In water, there are four electron pairs, but still only three atoms and two bonds. In order to keep the electron pairs as far apart as possible, the angle between the two hydrogen atoms attached to the oxygen is 109.5°.

WHERE TO LEARN MORE

Basmajian, Ronald; Thomas Rodella; and Allen E. Breed. Through the Molecular Maze: A Helpful Guide to the Elements of Chemistry for Beginning Life Science Students. Merced, CA: Bioventure Associates, 1990.

Burnie, David. Microlife. New York: DK Publishing, 1997.

"Common Molecules" (Web site). <http://www.recipnet.indiana.edu/common/common.html> (June 2, 2001).

Cooper, Christopher. Matter. New York: DK Publishing, 2000.

Mebane, Robert C. and Thomas R. Rybolt. Adventures with Atoms and Molecules, Book V: Chemistry Experiments for Young People. Springfield, NJ: Enslow Publishers, 1995.

"The Molecules of Life" (Web site). <http://biop.ox.ac.uk/www/mol_of_life/Molecules_of_Life.html> (June 2, 2001).

"Molecules of the Month." University of Oxford (Web site). <http://www.chem.ox.ac.uk/mom/> (June 2, 2001).

"Molecules with Silly or Unusual Names" (Web site). <http://www.bris.ac.uk/Depts/Chemistry/MOTM/silly/sillymols.htm> (June 2, 2001).

"Theory of Atoms in Molecules" (Web site). <http://www.chemistry.mcmaster.ca/faculty/bader/aim/> (June 2, 2001).

Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.

KEY TERMS

AVOGADRO'S NUMBER:

A figure, named after Italian physicist Amedeo Avogadro (1776-1856), equal to 6.022137 × 10²³. Avogadro's number indicates the number of molecules in a mole.

BOND ENERGY:

The energy required to pull apart the atoms in a chemical bond.

CHEMICAL BONDING:

The joining, through electromagnetic force, of atoms representing different elements.

COMPOUND:

A substance made up of atoms of more than one element. These atoms are usually joined in molecules.

COVALENT BONDING:

A type of chemical bonding in which two atoms share valence electrons.

DIATOMIC:

A term describing an element that exists as molecules composed of two atoms.

DIPOLE-DIPOLE ATTRACTION:

A form of intermolecular bonding between molecules formed by a polar covalentbond.

ELECTRON:

A negatively charged particle in an atom.

ELECTRONEGATIVITY:

The relative ability of an atom to attract valence electrons.

EMPIRICAL FORMULA:

A chemical formula that shows the smallest possible whole-number ratio of the atoms involved. Compare with molecular formula and structural formula.

HYDROGEN BONDING:

A kind of dipole-dipole attraction between molecules formed of hydrogen along with an element having a high electronegativity.

INTERMOLECULAR BONDING:

The bonding that exists between molecules. This is not to be confused with chemical bonding, the bonding of atoms within a molecule.

ION:

An atom or group of atoms that has lost or gained one or more electrons, and thus has a net electric charge.

IONIC BONDING:

A form of chemical bonding resulting from attractions between ions with opposite electric charges.

ISOMERS:

Substances having the same chemical formula, but which are chemically dissimilar due to differences in the arrangement of atoms.

LONDON DISPERSION FORCES:

A term describing the weak intermolecular bond between molecules that are not formed by a polar covalent bond.

MOLE:

The SI fundamental unit for "amount of substance." A mole is, generally speaking, Avogadro's number of molecules; however, in the more precise SI definition, a mole is equal to the number of carbon atoms in 12.01 g of carbon.

MOLECULAR FORMULA:

A chemical formula that indicates the types and numbers of atoms involved, showing the actual proportions of atoms in a molecule. Compare with empirical formula and structural formula.

MOLECULAR SOLID:

A form of crystalline solid—a solid in which the constituent parts have a simple and definite geometric arrangement repeated in all directions—in which the molecules have a neutral electric charge. Table sugar (sucrose) is an example.

MOLECULE:

A group of atoms, usually but not always representing more than one element, joined in a structure. Compounds are typically made up of molecules.

OCTET RULE:

A term describing the distribution of valence electrons that takes place in chemical bonding for most elements, which end up with eight valence electrons.

POLAR COVALENT BONDING:

The type of chemical bonding between atoms that have differing values of electronegativity. Water molecules are an example of a polar covalent bond.

SHELL:

The orbital pattern of the valence electrons at the outside of an atom.

STEREOCHEMISTRY:

The area of chemistry devoted to the three-dimensional arrangement of atoms in a molecule.

STRUCTURAL FORMULA:

A diagram that shows how the atoms are bondedtogether, complete with lines representing covalent bonds. Compare with empirical formula and molecular formula.

VALENCE ELECTRONS:

Electrons that occupy the highest energy levels in anatom. These are the only electrons involved in chemical bonding.

VALENCY:

The property of the atom of one element that determines its ability to bond with atoms of other elements.

VSEPR (VALENCE SHELL ELECTRON PAIR REPULSION) MODEL:

A means of representing the three-dimensional structure of atoms in a molecule.

Molecules

A molecule is the smallest entity of a pure compound that retains its characteristic chemical properties, and consequently has constant mass and atomic composition. It is an assembly of nonmetallic atoms held together into specific shapes by covalent bonds . As much as a car is a single unit made up of many parts, a molecule is a unit made up of atoms bonded around each other in certain fixed geometries. Shapes influence the physical and chemical properties and consequently much of the chemistry of a molecule.

While molecules may be monoatomic (such as the inert gases helium, neon, or krypton), most molecules are diatomic, triatomic, or polyatomic, consisting of two or more atoms (some molecules may be a collection of thousands of atoms). A diatomic molecule may be homonuclear (e.g., O₂ or N₂) or heteronuclear (e.g., CO or NO). Similarly, a triatomic molecule may be homonuclear (e.g., O₃) or heteronuclear (e.g., HCN).

The modern concept of the covalent bond has resulted in the ability to predict the geometry and hence the properties of matter such as reactivity, toxicity, and solubility. A fundamental challenge in chemistry is to determine the arrangement of atoms in a molecule in order to elucidate its bonding, geometry, and properties.

Historical Development

Since Roman times matter had been viewed by some as discrete particles somehow linked together. Early in the eighteenth century the behavior of gases was viewed as a function of kinetic theory . Kinetic theory is a group of assumptions to explain the behavior of gases. Among these assumptions are that gases are individual molecules moving in straight lines, that they do not react chemically and occupy essentially no volume compared to the volume between molecules. In 1805 English chemist and physicist John Dalton (1766–1844) proposed that atoms form compounds by joining together in simple, whole numbers. In 1811 Italian chemist Amedeo Avogadro (1776–1856) solidified the distinction between molecules and atoms by proposing that, at constant temperature and pressure, equal volumes of all

gases contain equal numbers of molecules. While Avogadro's theory was published, it was ignored by the scientific community until 1858, when it was revived by Italian chemist Stanislao Cannizzaro (1826–1910), thereby reconciling many inconsistencies chemists were observing. During this same time, valency (the combining capacity of an atom) was defined as the number of hydrogens an atom can combine with.

Initially the structure of molecules was studied using chemical methods, thereby identifying composition, chemical reactions, and the existence of isomers . It was understood that bonds had direction, rigidity, and a certain degree of independence from molecule to molecule. The discovery of the electron in 1897 by English physicist Joseph John Thomson (1856–1940) immediately linked electrons with covalent bonding. Though attacked vigorously for his views, Dutch physical chemist Jacobus Hendricus van't Hoff (1852–1911) discarded the flat-molecule model in favor of geometric relations within each molecule. His brilliant postulate of the tetrahedral arrangement of carbon (proposed simultaneously, but independently, by French chemist Joseph-Achille Le Bel [1847–1930]) was a major breakthrough for chemistry. Later in the nineteenth century the advent of physical methods of investigation led to a great deal of additional information regarding atomic configuration.

Danish physicist Niels Bohr (1885–1962) proposed a quantum theory of the hydrogen atom by suggesting that the electron moves about its nucleus in discrete quanta (the energies of electrons are restricted to having only certain values, quanta, much as stairs do as opposed to a ramp), establishing a balance between the electron's centrifugal force and its attraction for the nucleus. It was not until 1927 that covalent bonding was properly understood, thanks to the contributions of American physical chemist Gilbert N. Lewis (1875–1946), American physicist Edward Uhler Condon (1902–1974), German physicist Walter Heitler (1904–1981), and German physicist Fritz London (1900–1954).

In his 1916 paper The Atom and the Molecule, Lewis proposed that a chemical (covalent) bond between two atoms involves the sharing of electrons between the nuclei. Thus a single bond (for hydrogen, H-H) results when an electron from each atom forms an electron pair that is shared between the two nuclei (H:H); a double bond involves two electrons from each atom (e.g., the carbon-carbon bond in (H:)₂C::C(:H)₂); and a triple bond involves three electrons from each atom (e.g., the carbon-carbon bond in H:C:::C:H). Such representations are referred to as Lewis dot structures. Lewis further postulated that an electron octet (and in a few cases an electron pair) forms a complete shell of electrons with spatial rigidity and chemical inertness—hence a stable arrangement.

American chemist Irving Langmuir (1881–1957) proposed that many chemical facts could be coordinated by applying these new ideas. Others followed by suggesting that a bond is a balance between nucleus-nucleus and electron-electron repulsions and electron-nuclei attractions. American chemist Linus Pauling (1901–1994) assembled these ideas in his seminal book, The Nature of the Chemical Bond.

Valence Shell Electron Pair Repulsion Theory

Molecular geometries are determined by the number and locations of valence electrons around the atoms. Both bonded and lone pair electrons repel each other, staying as far apart as possible, thereby causing the molecule to occupy specific shapes (much as balloons assume fixed arrangements when tied together). These geometries are important in determining chemical properties. One method for determining the structure of covalent molecules is the valence shell electron pair repulsion (VSEPR) method, proposed in 1957 by Canadian chemist Ronald Gillespie and Australian chemist Ronald Nyholm in a classic paper titled "Inorganic Stereochemistry." The theory states that the geometry around a given atom is a function primarily of minimizing the electron pair repulsions. The key postulates of the VSEPR theory are:

• All electrons are negatively charged.
• Bonds are electron groups.
• Lone pair and bonded electrons (and therefore bonds) repel each other.

Geometries of most covalent molecules may be determined by following these steps:

• Determine the central atom. This may be the atom present singly (e.g., B in BF₃), the larger atom (e.g., P in POCl₃), the atom written in the center (e.g., C in HCN), or the atom with the largest number of bonds (e.g., C in Cl₂CO).
• Determine the number of bonds needed for each atom to be bonded to the central atom and write the corresponding Lewis dot structure. Thus, for Cl₂CO, each chlorine needs a single bond and oxygen needs two bonds; the Lewis dot structure would be (Cl:)₂C::O. Note that a single bond needs a pair of electrons (one group), a double bond needs two pairs (also one group), and a triple bond needs three pairs (still just one group, since it points in one direction only).

• Count the total number of bonded and lone pair electron groups about the central atom. For Cl₂CO it would be three (all bonded) groups. In the case of :NH₃ it would be one lone pair group and three bonded groups for a total of four groups.
• Establish the best electronic (counting all electron groups) and molecular (counting only bonded groups) geometries. Table 1 summarizes this information for bonded groups.

The trigonal bipyramidal shape merits a special note. Contrary to the other shapes, it possesses two types of bonds: the two axial bonds located at 180° from each other, and the three equatorial bonds located perpendicularly to the axis and at 120° from each other.

Each of the examples given in Table 1 has only bonded electrons around its central atom. The existence of lone pair electrons has an effect on the geometry, as seen in Table 2.

For example, water (H₂O) has two bonded and two lone pair valence electrons about the central atom, oxygen. Its electronic geometry, determined by four total groups, is tetrahedral, and its molecular geometry (meaning the H-O-H shape) is bent. Similarly, the :NH₃ molecule has three

bonded and one lone pair electron groups about nitrogen, giving an electronic geometry that is nearly tetrahedral, and a molecular geometry that is pyramidal . Because two bonded pairs repulse less than a bonded pair and a lone pair, which in turn repulse less than two lone pairs, the H-O-H bond angle in water is not 109.5° as expected for a tetrahedron, but 104.5°, with the H-O bonds having been pushed by the lone pairs toward each other. For the trigonal bipyramidal shape, lone pairs always occupy equatorial planar positions. Thus, the molecular geometry of BrF₃ is T-shaped, rather than trigonal planar.

Properties

Both physical and chemical properties are affected by the geometry of a molecule. For instance, the polarity of a molecule is determined by the electronegativity differences of its atoms (electronegativity is the ability of an atom in a molecule to draw electrons toward itself), and the relative geometries of the atoms within the molecule. The molecule BCl₃, for example, displays a flat triangle (120°) with each Cl atom pulling electrons symmetrically, making the molecule nonpolar . In the pyramidal molecule PCl₃, however, all chlorines are pulling electrons more or less to one side, making the molecule polar. Since polarity goes hand in hand with solubility, CF₄ is a nonpolar tetrahedral molecule not soluble in water, whereas SF₄, a distorted tetrahedron, is instantly hydrolyzed by water.

Chemical properties are also very dependent on geometries. For example, in the square planar molecule Pt(NH₃)₂Cl₂, the chloro (and hence the ammonia) ligands may be placed adjacent to each other (cis isomer), or they may be opposite each other (trans isomer). In addition to having different physical properties, their chemical reactivities are also quite remarkable. The cis isomer is an effective treatment of testicular, ovarian, and certain other cancers, whereas the trans isomer is ineffective. Similarly, the linear, nonpolar CO₂ molecule is inert, whereas the polar CO molecule is a poison.

Other Theories

The VSEPR theory allows chemists to successfully predict the approximate shapes of molecules; it does not, however, say why bonds exist. The quantum mechanical valence bond theory, with its overlap of atomic orbitals , overcomes this difficulty. The resulting hybrid orbitals predict the geometries of molecules. A quantum mechanical graph of radial electron density (the fraction of electron distribution found in each successive thin spherical shell from the nucleus out) versus the distance from the nucleus shows maxima at certain distances from the nucleus—distances at which there are higher probabilities of finding electrons. These maxima correspond to Lewis's idea of shells of electrons.

This theory, however, treats electrons as localized, does not account for unpaired electrons, and does not give information on bond energies. The molecular orbital theory attempts to solve these shortcomings by considering nuclei arranged as in a molecule and determining the resulting molecular orbitals when electrons are fed in one by one.

The electronic and molecular geometries of covalent molecules, and hence their resulting polarities, can thus be predicted fairly accurately. Armed with these tools, one can predict whether or not a molecule should be soluble, reactive, or even toxic.

see also Bonding; Avogadro, Amedeo; Bohr, Niels; Cannizzaro, Stanislao; Dalton, John; Le Bel, Joseph-Achille; Lewis, Gilbert N.; Lewis Structures; Pauling, Linus; Thomson, Joseph John; van't Hoff, Jacobus.

Erwin Boschmann

Bibliography

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