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molecule (mŏlˈəkyo͞ol) [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. Unlike ions, molecules carry no electrical charge.

Nature of Molecules

Molecules are made up of two or more atoms, either of the same element or of two or more different elements, joined by one or more covalent chemical bonds. According to the kinetic-molecular theory, the molecules of a substance are in constant motion. The state (solid, liquid, or gaseous) in which matter appears depends on the speed and separation of the molecules in the matter. Substances differ according to the structure and composition of their molecules. A molecular compound is represented by its molecular formula; for example, water is represented by the formula H2O. A more complex structural formula is sometimes used to show the arrangement of atoms in the molecule.

Molecules differ in size and molecular weight as well as in structure. In a chemical reaction between molecular substances, the molecules are often broken apart into atoms or radicals that recombine to form other molecules, i.e., other substances. In other cases two or more molecules will combine to form a single larger molecule, or a large molecule will be broken up into several smaller molecules.

Molecules can assume many shapes and sizes. Molecules of hydrogen gas, H2, are very small; each consists of two atoms of hydrogen. Water molecules, H2O, are much larger, containing an atom of oxygen as well as two of hydrogen. The atoms in a water molecule are arranged at the corners of an isosceles triangle; the oxygen atom is located where the two equal sides meet and the angle between these sides is about 105°. A carbon dioxide molecule, CO2, is linear, with the two oxygen atoms an equal distance on either side of the carbon atom. In methane, CH4, the hydrogen atoms are arranged at the corners of a tetrahedron with the carbon atom in the center. In benzene, C6H6, the carbon atoms form a hexagonal ring with a hydrogen atom joined to each carbon atom. More complex molecules resemble rings, chains, helices, or other forms. Many molecules occurring in living organisms are very complex. RNA and DNA molecules resemble giant helices. By polymerization a large number of small molecules may be joined to form a single large polymer molecule. Typical polymers include synthetic resins, rubbers, and plastics.

Evolution of Molecular Theory

The terms atom and molecule were used interchangeably until the early 19th cent. Initial experimental work with gases led to what is essentially the modern distinction. J. A. C. Charles and R. Boyle had shown that all gases exhibit the same relationship between a change in temperature or pressure and the corresponding change in volume. J. L. Gay-Lussac had shown that gases always combine in simple whole-number volume proportions and had rediscovered the earlier findings of Charles, which had not been published.

Dalton's Theory

One early theorist was John Dalton, best known for his atomic theory. Dalton believed that gases were made up of tiny particles, which he thought were atoms. He thought that these atoms were stationary and in contact with one another and that heat was a material substance, called caloric, that was contained in shells around the atom (these shells of caloric were actually what was in contact). When a gas was heated, the amount of caloric was increased, the shells became larger, and the gas expanded. Dalton did not accept Gay-Lussac's findings about combining volumes of gases, perhaps because it could not be explained by his theory.

Avogadro's Hypothesis

A different theory from Dalton's that could explain the combining volumes of gases was proposed by the Italian physicist Amadeo Avogadro in 1811. According to his theory, under given conditions of temperature and pressure, a given volume of any gas contains a definite number of particles. From the earlier observation that one volume of hydrogen gas and one volume of chlorine gas react to form two volumes of hydrogen chloride gas he deduced that the particles in gaseous hydrogen or chlorine could not be single atoms, but must be some combination of atoms. He called this combination a molecule. He reasoned that the two volumes of hydrogen chloride that are formed must contain twice as many particles as either single volume of hydrogen or chlorine. Thus, if there were 100 particles each of hydrogen and chlorine, there would be 200 particles of hydrogen chloride produced; but there could be only 100 particles produced if the original particles of hydrogen and chlorine were indivisible atoms, since each particle of hydrogen chloride contains both hydrogen and chlorine. An assumption that there are two atoms in a molecule of gaseous hydrogen or chlorine and one atom each of hydrogen and chlorine in a molecule of hydrogen chloride preserves both the hypothesis of indivisible atoms and the hypothesis of equal numbers of particles in equal volumes of gases. Similar reasoning would allow a larger even number of atoms in the molecules of hydrogen or chlorine, but Avogadro favored a rule of simplicity, using the smallest possible number. In the model of gases proposed by Avogadro, the particles were not in contact and much of the volume of the gas was empty space.

Cannizaro's Compromise

Avogadro's theory was not well accepted; most responses were very critical. Meanwhile, Dalton's theory prompted extensive experimentation and especially the determination of combining weights of the elements. Many shortcomings of Dalton's theory were uncovered, and although a number of modifications were suggested, none were very successful. It was not until 1858 that the Italian chemist Stanislao Cannizaro suggested a merging of Avogadro's and Dalton's theories. The acceptance of this revised theory was assisted by the acceptance by physicists at about the same time of the kinetic-molecular theory of gases that was first proposed in 1738 by Daniel Bernoulli.
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A molecule may be thought of either as a structure built of atoms bound together by chemical forces or as a structure in which two or more nuclei are maintained in some definite geometrical configuration by attractive forces from a surrounding swarm of negative electrons. Besides chemically stable molecules, short-lived molecular fragments called free radicals can be observed under special circumstances. See Molecular structure and spectra

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.



the smallest particle of a substance that can exhibit all the chemical properties of the substance. A molecule is composed of atoms (more precisely, of atomic nuclei, their surrounding inner electrons, and their outer valence electrons, which form a chemical bond). The inner electrons of atoms usually do not participate in the formation of such bonds. The molecular composition and structure of a given substance do not depend on the method of preparation used. In the case of monatomic molecules (for example, inert gases), the concepts of the molecule and the atom are congruent.

The concept of the molecule was first introduced into chemistry because of the necessity of distinguishing between the molecule, as the smallest quantity of a substance that takes part in a chemical reaction, and the atom, as the smallest quantity of a given element contained in a molecule (Karlsruhe Congress, 1860). The basic laws governing molecular structure were established through the study of chemical reactions, the analysis and synthesis of chemical compounds, and the application of various physical methods.

In most cases, the atoms of a molecule are joined by chemical bonds. This type of bonding is formed by one, two, or three electron pairs that are shared by two atoms. A molecule can contain positively and negatively charged atoms, or ions; in this case electrostatic interaction is achieved. In addition, weaker atomic interactions also take place in molecules. Repulsive forces exist between atoms that are not connected by valence bonding.

Molecular composition is expressed by chemical formulas. The empirical formula (for example, C2HeO for ethanol) is determined from the atomic ratio of the elements making up the substance, as determined by chemical analysis, and from the molecular weight.

The development of the theory of molecular structure is closely associated, above all, with advances in organic chemistry. The theory of the structure of organic compounds, formulated in the 1860’s in the works of A. M. Butlerov, F. A. Kekule, and A. S. Couper, made possible the representation of molecular structures by structural formulas, which express the ordering of valence chemical bonds in the molecule. Molecules with various structures and properties can be represented by the same empirical formula (isomerism)—for example, ethanol, C2H5OH, and dimethyl ether, (CH3)2O. The structural formulas for these compounds differ as follows:

In certain cases isomeric molecules are rapidly converted from one form to another, thus establishing a dynamic equilibrium between the two. Subsequently, J. H. van’t Hoff and the French chemist J. A. Le Bel independently arrived at an understanding of the spatial arrangement of atoms in a molecule and an explanation of the phenomenon of stereoisomerism. In 1893, A. Werner extended the general concepts of the structure theory to include inorganic complex compounds. By the beginning of the 20th century, chemistry had a detailed theory of molecular structure based only on the study of the chemical properties of molecules. It is remarkable that, in the vast majority of cases, direct physical methods of analysis developed in later years fully confirmed the structural chemical formulas that had been established by the study of macroscopic quantities of a given substance rather than individual molecules.

In physics, the concept of the molecule proved essential in explaining the properties of gases, liquids, and solids. Direct experimental evidence of the existence of molecules was first obtained during the study of Brownian movement by the French physicist J. Perrin in 1906.

In a solid, molecules may or may not retain their individuality. For example, most of the molecules in organic compounds form molecular crystals whose lattice points contain molecules that are bonded to each other by relatively weak intermolecular forces. On the other hand, no individual molecules are present in ionic crystals (for example, NaCl) and atomic crystals (diamond), and the entire crystal resembles a single molecule. Molecular structure may be altered during the transition of a crystal into a gas. Thus, in the gaseous state N2O5 is composed of single molecules, whereas its crystal form is made up of NO2+ and NO3- ions. Gaseous PCls contains molecules of trigonal bipyramidal configuration, and its solid form is made up of the octahedral PCI6- and tetrahedral PC16+ ions.

Figure 1. Potential energy U of a diatomic molecule (or an individual chemical bond) as a function of internuclear distance r: (r0) equilibrium distance, (D) dissociation energy, (0, 1, 2, . . .) oscillatory energy levels

Structure. The geometric structure of a molecule is determined by the equilibrium distribution of atomic nuclei. The energy of atomic interaction depends on the internuclear distance and is equal to zero in the case of very great distances. If a chemical bond is formed as the atoms converge, then the atoms become strongly attracted to one another (weak attraction is observed without the formation of a chemical bond); electrostatic repulsive forces act on the atomic nuclei as the atoms continue to approach one another. Close approach of atoms is also hampered by the impossibility of superposition of the inner electron shells. Figure 1 shows the relationship between the potential energy of a diatomic molecule and the internuclear distance r. This energy is at a minimum at an equilibrium distance ro, approaches zero as r → ∞ , and increases to ∞ as r →, 0. The energy difference at r = r0 and r → ∞ determines the bonding energy and the dissociation energy D (see Table 1). In diatomic and polyatomic molecules the equilibrium distances ro—and, consequently, the distribution of atomic nuclei in molecules—are determined by spectroscopy, X-ray diffraction analysis, and electron diffraction, as well as by neutron-diffraction studies, which also yield information on electron distribution (density) in molecules. The use of X-ray analysis in studying molecular crystals makes it possible to establish the geometric structure of highly complex molecules (even protein molecules).

Table 1. Equilibrium internuclear distances r0 and dissociation energies D (at 25°C) for some diatomic molecules
H2 ........................0.74426.5 (104.18)
Li2 .......................2.67104.7 (25)
N2 ........................1.0994.3 (22.5)
O2 ........................1 214957 (1183)
F2.......................1.481 55 (37)
Na2 .......................3.0878.5 (17.3)
CI2 .......................1.99242.6 (57.9)
Br2 .......................2 141 92 7 (46)
I2 ........................2.67147 1 (35 1)
LiH .......................1 .59243 (58)
NaH .......................1.89196.9 (47)
HF ........................0.92565.6(135)
HCI .......................1 27431 6 (103)
HI ........................1.60264 (63)

Indirect but highly detailed information on complex molecular structures is obtained by means of various spectroscopic methods, particularly using spectra of nuclear magnetic resonance (NMR); spectroscopy has also proved to be an efficient means of studying the geometry of simple molecules, which contain a small number of atoms. The distances (in angstroms [Å]) between two given atoms joined by a valence bond are approximately constant in the molecules of various compounds and decrease with an increase in bond frequency (see Table 2).

A specific atomic, or covalent, radius (in the case of an ionic bond, an ionic radius) that defines the dimensions of the electron shell of the atom or ion forming the chemical bond may be assigned to each atom in a particular valence state. The approximate constancy of these radii is useful in estimatinginteratomic distances and, consequently, in determining molecular structures. The length of the bond is the sum of the corresponding atomic radii.

Table 2. Distances between atoms joined by a valence bond (Å)
C—C ........................1.54
C═C ........................1.34
C===C (in bonzene) ........................1.39
C≡C ........................1.20
C—H ........................1.09
C—O ........................1.42
C═0 ........................1.21
C—N ........................1.46
C—F ........................1.39
C—Cl ........................1.77
C—Br ........................1.92
C—1 ........................2.10
C—S ........................1.82
O—H ........................0.96
N—H ........................1.01
S—H ........................1.35

The size of a molecule as a whole—that is, the size of its electron shell—is to some extent an arbitrary value; there exists a nonzero, although very small, probability of finding electrons in a molecule located at a great distance from the atomic nuclei. In practical terms, the size of a molecule is determined by the equilibrium distance to which molecules may be brought in close packing in a molecular crystal and in a liquid. At greater distances, molecules attract one another; at smaller distances they are mutually repelled. Therefore, the size of a molecule can be found by X-ray structural analysis of molecular crystals; the order of magnitude of the dimensions may be determined from the coefficients of diffusion, thermal conductivity, or gas viscosity, as well as from the density of the substance in the condensed state. The average values of van der Waals’ radii (in A) may be used to represent the distance at which atoms (of the same molecule or different molecules) that are not connected by valence bonding may converge (see Table 3).

Table 3. Average van der Waals’ radii (Å)
H ........................1.0-1.2
C ........................1.75-2.0
N ........................1.5
P ........................1.9
As ........................2.0
Sb ........................2.2
O ........................1.4
S ........................1.9
Se ........................1.0
Te ........................2.2
F ........................1.4
Cl ........................1.8
Br ........................2.0
I ........................2.2

Van der Waals’ radii are considerably greater than covalent radii. Given the values of the van der Waals’ covalent, and ionic radii, visual models of molecules may be constructed that illustrate the shape and size of the electron shells (Figure 2).

Covalent chemical bonds are situated at specific angles in the molecule, depending on the state of hybridization of the atomic orbitals. For example, a tetrahedral bond arrangement formed by a carbon atom is characteristic of the molecules of saturated organic compounds, whereas molecules with a double bond (C—C) have a planar bond arrangement. Molecules of compounds

Figure 2. Structural models of some simple molecules (the radii of the spheres are van der Waals radii)

containing a triple bond (C=C) have linear bond distribution:

Thus, a polyatomic molecule has a specific spatial configuration — that is, a specific geometric bond arrangement — that cannot be altered without scission of the bonds. A molecule is characterized by a particular symmetry of atomic distribution. If there is no plane or center of symmetry, then the molecule can exist in two configurations, which are mirror images of one another (optical antipodes, or stereoisomers). All the most important biologically functional substances in the living world occur in a single, specific stereoisomeric form.

Molecules containing single bonds, or sigma bonds, can exist in various conformations, which are formed by the rotation of atomic groups about single bonds. The conformational properties determine the important characteristics of macromolecules in synthetic polymers and biopolymers.

Atomic interaction in the molecule. The nature of chemical bonds in molecules remained a mystery until the founding of quantum mechanics, since classical physics was unable to explain the saturation and orientation of valence bonds. The principles of the theory of chemical bonds were formulated in 1927 by W. Heitler and the German scientist F. London, using as an example the simplest molecule, H2 Substantial improvements were made in the theory and methods of calculation over the years, particularly through the widespread application of the molecular orbital method, and quantum chemistry made possible the calculation of interatomic distances, molecular energy, chemical bond energy, and the distribution of electron density for complex molecules. The data from computations correlate well with experimental findings.

The chemical bonds in molecules of most organic compounds are covalent. On the other hand, a number of inorganic compounds have both ionic and donor-acceptor bonds, which are formed by the collectivization of an unshared electron pair in the atom. The energy of formation of molecules from atoms is approximately additive in many series of related compounds. In other words, in these cases the energy of a molecule may be considered to be equal to the sum of bond energies, which have constant values in the particular series. This suggests the practicality of assigning approximately autonomous electron shells to chemical bonds.

The additivity of molecular energy does not always hold. The planar molecules of organic compounds with conjugate bonds (that is, alternating multiple and single bonds) are a clear example of the disturbance of additivity. In these cases the valence electrons determining bond multiplicity, called π-electrons, become delocalized — that is, common to the entire system of conjugate bonds. Such electron delocalization results in additional stability of the molecule. For example, the molecular energy of formation of 1,3-butadiene, H2C=CH— CH=CH2, exceeds the energy expected from additivity by 16.8 kilojoules per mole (kJ/mol), or 4 kcal/mol. The equalization of electron density as a result of collectivization of π-electrons along the bonds is expressed by the elongation of double bonds and the shortening of single bonds. All the intercarbon bonds in a regular benzene ring (see formula) are identical and are intermediate in length between single and double bonds. The conjugation of bonds is clearly shown in molecular spectra(see below).

Modern quantum-mechanical theory of chemical bonding takes into account the partial delocalization not only of π-electrons but also of σ-electrons that is observed in every molecule. Generally speaking, this does not disturb the additivity of molecular energy.

In most cases, the total spin of valence electrons in a molecule is equal to zero—that is, the spins of electrons are saturated in pairs. Molecules containing unpaired electrons, or free radicals (for example, atomic hydrogen, H, or methyl, CH3), are usually unstable, since their combination is accompanied by a marked reduction of energy because of the formation of valence bonds. The most efficient method of studying the structure of free radicals is electron paramagnetic resonance (EPR).

Electrical and optical properties. The behavior of a substance in an electric field is determined by the basic electric properties of its molecules—that is, the permanent dipole moment and polarizability. The dipole moment denotes misalignment of the centers of gravity of positive and negative charges in the molecule, or the electric asymmetry of the molecule. Accordingly, molecules that have centers of symmetry, such as H2, have no permanent dipole moment; however, the electrons in HC1 are displaced toward the Cl atom, and the dipole moment is equal to 1.03 D (1.03 X 10−18 cgs unit). Polarizability is defined as the ability of an electron shell in any molecule to shift under the influence of an electric field, resulting in the creation of an induced dipole moment. Values of the dipole moment and polariz-ability are obtained experimentally by measuring the dielectric constant. In the case of additivity of molecular properties, the dipole moment of a molecule may be represented as the sum of the dipole moments of the bonds (taking into account their orientation); the same is true for molecular polarizability.

The optical properties of a substance determine its behavior in the variable electric field of a light wave, as well as the molecular polarizability of the substance. A direct relationship exists between polarizability and refraction, scattering of light, optical activity, and other phenomena examined in molecular optics, the branch of physical optics devoted to studying the optical proper-ties of substances.

Magnetic properties. The molecules and macromolecules of most chemical compounds are diamagnetic. The magnetic susceptibility x of a molecule may be expressed as the sum of values of x for individual bonds in a number of organic compounds; however, the additivity of x is realized less fully than that of polarizability α. Both x and a are determined by the properties of the outer electrons in the molecule and are interrelated.

Molecules that have a permanent magnetic moment are para-magnetic. Examples of such molecules are those containing an odd number of electrons in their outer shell (NO and all free radicals) and those composed of atoms with open (unfilled) inner shells (for example, the transition metals). The magnetic susceptibility of paramagnets is governed by temperature, since heat flow hinders the orientation of magnetic moments in a magnetic field. The structure of paramagnetic molecules may be efficiently studied using the EPR method.

The atomic nuclei of elements with odd atomic numbers or mass numbers have nuclear spin paramagnetism. Such nuclei have nuclear magnetic resonance, whose spectrum is governed by the electron encirclement of the nuclei in the molecule. Therefore, the NMR spectra provide highly detailed information on molecular structures, including such very complex formations as protein molecules.

Molecular spectra and structure. The electric, optical, magnetic, and other properties of molecules are ultimately related to the wave functions and energies of various molecular states, which also express the electric dipole moment, magnetic moment, polarizability, and magnetic susceptibility. Molecular spectra yield direct information on the molecular states and on the probability of transition from one state to another.

The frequencies observed in spectra corresponding to rotational transitions depend on the moments of inertia of the molecules, determination of which from spectroscopic data makes it possible to find the most accurate values of interatomic distances in molecules.

The total number of lines or bands in an oscillatory molecular spectrum depends on the molecule’s symmetry. The oscillation frequencies observed in the spectra are determined by the atomic masses and their arrangement, on the one hand, and by the dynamics of atomic interactions, on the other. Correspondingly, the theory of vibrations of polyatomic molecules is based on the theory of chemical structure and the classical mechanics of coupled vibrations. The study of vibrational spectra makes it possible to draw a number of conclusions regarding molecular structure and atomic and molecular interactions, and also to study tautomerism and rotational isomerism.

Electron transfers in molecules characterize the structure of their electron shells and the state of their chemical bonds. The spectra of molecules containing a large number of conjugate bonds are characterized by long-wave absorption bands in the visible region. Substances composed of such molecules have the property of chromaticity; this group includes all organic dyes. The study of electron-oscillatory molecular spectra is necessary for an understanding of natural and magnetic optical activity.

Molecules in chemistry, physics, and biology. The concept of the molecule is fundamental to chemistry. Most of the information on molecular structure and function currently available to scientists comes from chemical research. Chemical reactions are accompanied by the transformation of one type of molecule into another; this usually requires a certain quantity of excess molecular energy, or activation energy. During chemical interaction the molecules pass through the configuration of the activated complex, or the transient molecular state. The nature and rate of a chemical reaction are determined by this state, which in turn depends on the structure of the reacting molecules. Chemistry deals with two main problems relating to molecules: it establishes the structure of molecules on the basis of chemical reactions and, conversely, determines the course of chemical reactions from the molecular structure. The vast array of major problems confronted by modern chemistry, including those still unsolved, reduces to the theory of chemical reactivity. The study of these problems requires the use not only of theoretical methods of quantum chemistry but also of experimental data obtained by chemical and physical methods.

Physical phenomena that are determined by the structure and properties of molecules are studied in molecular physics. The thermodynamic properties of any substance made up of molecules are ultimately expressed as the energy values of all possible molecular states, which are found from spectroscopic data. Molecular structure and molecular interactions characterize the equilibrium, nonequilibrium, and kinetic properties of a substance. A certain period of time, called the relaxation time, is required for the establishment of equilibrium; this may not be possible during rapid changes in the state of a substance. For example, such phenomena are observed during the passage of ultrasound through a substance, and they affect the absorption and dispersion of sound waves. Equilibrium is established by molecular interaction upon collisions in gases and liquids and by the absorption and emission of light. The relaxation time of molecules in a condensed medium essentially depends on temperature; an increase in temperature increases molecular mobility. In many cases, molecules in a liquid medium virtually lose their mobility even before crystallization (that is, vitrification takes place). The diffusivity, viscosity, and thermal conductivity of a substance are determined by molecular mobility. The absorption and dispersion of electromagnetic waves, NMR, and EPR are among the methods used for direct study of molecular mobility and determination of relaxation time.

Large chain molecules, which form polymers, have specific equilibrium and kinetic properties. The behavioral characteristics of macromolecules are primarily determined by their flexibility—that is, the ability to exist in many different conformations, formed by rotation about single bonds.

The development of biology, chemistry, and molecular physics led to the founding of molecular biology, which studies the basic phenomena of life on the basis of the structure and properties of biologically functional molecules. Organisms exist on the basis of intricately balanced chemical and nonchemical molecular interactions. Thus, the study of the structure and properties of molecules is of fundamental importance for natural science in general.


Syrkin, la. K., and M. E. Diatkina. Khimicheskaia sviaz’ i stroenie molekul. Moscow-Leningrad, 1946.
Pauling, L. Priroda khimicheskoi sviazi. Moscow-Leningrad, 1947. (Translated from English.)
Vol’kenshtein, M. V. Stroenie i fizicheskie svoistva molekul. Moscow-Leningrad, 1955.
Vol’kenshtein, M. V. Perekrestki nauki. Moscow, 1972.
Kondrat’ev, V. N. Struktura atomov i molekul, 2nd ed. Moscow, 1959.
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The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.


A group of atoms held together by chemical forces; the atoms in the molecule may be identical as in H2, S2, and S8, or different as in H2 O and CO2; a molecule is the smallest unit of matter which can exist by itself and retain all its chemical properties.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.


the simplest unit of a chemical compound that can exist, consisting of two or more atoms held together by chemical bonds
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005