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combining capacity of an atomatom
[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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 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. Atoms are called monovalent, divalent, trivalent, or tetravalent, according to whether they form one, two, three, or four bonds (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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The Relationship of Electrons and Valence

For purposes of describing chemical behavior, an atom can be considered as a positively charged nucleus surrounded by negatively charged electrons orbiting in concentric spherical shells. The number of positive charges in the nucleus determines how many electrons normally surround the nucleus; as atomic numberatomic number,
often represented by the symbol Z, the number of protons in the nucleus of an atom, as well as the number of electrons in the neutral atom. Atoms with the same atomic number make up a chemical element. Atomic numbers were first assigned to the elements c.
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 increases, the electron shells are filled, starting with those nearest the nucleus.

The valence of an atom is determined by the number of electrons in the outermost, or valence, shell. The atom exists in its most stable configuration when its outermost shell is completely filled; in combining with other atoms, it thus tends to gain or lose valence electrons in order to attain a stable configuration. If the valence shell of the atom is nearly complete, as in chlorine and other nonmetals, the atom will tend to accept electrons to complete it; if the valence shell has few electrons, as in potassium and other metals, the atom will tend to lose these electrons, so that the next shell below the valence shell becomes a completed outermost shell.

The valence of many elements is determined from their ability to combine with hydrogen or to replace it in compounds. For example, one oxygen atom combines with two hydrogen atoms to form water and the valence of oxygen is thus determined to be 2. Similarly, chlorine accepts one electron in combining with a single atom of hydrogen to form hydrogen chloride, HCl, and chlorine's valence is 1. Zinc does not combine with hydrogen but does replace it in compounds; in a typical replacement reaction, one zinc atom replaces two hydrogen atoms, as in the equation Zn+H2SO4→ZnSO4+H2, so that zinc has a valence of 2.

Valence Number

Atoms are assigned numbers, called valence numbers, oxidation numbers, or oxidation states, which range in value from −4 through 0 to +7 and describe the combining behavior of the atoms in chemical reactions, particularly oxidation-reduction reactions (see oxidation and reductionoxidation and reduction,
complementary chemical reactions characterized by the loss or gain, respectively, of one or more electrons by an atom or molecule. Originally the term oxidation
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). Metals, which commonly donate electrons and form compounds in which they exist in the positive, or cationic, state, are assigned positive oxidation numbers (see cationcation
, atom or group of atoms carrying a positive charge. The charge results because there are more protons than electrons in the cation. Cations can be formed from a metal by oxidation (see oxidation and reduction), from a neutral base (see acids and bases) by protonation, or
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). For a metal such as zinc, which donates two electrons to achieve a stable electron configuration, the oxidation number is +2. Nonmetals, which commonly accept electrons and in compounds exist in the negative, or anionic, state, are assigned negative oxidation numbers (see anionanion
, atom or group of atoms carrying a negative charge. The charge results because there are more electrons than protons in the anion. Anions can be formed from nonmetals by reduction (see oxidation and reduction) or from neutral acids (see acids and bases) or polar compounds
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). The oxidation number is −1 for chlorine and the other halogens, which accept one electron to complete their valence shell.

Some elements, like the transition metals, have electron configurations in which electrons from their inner shells can also be used as valence electrons; these elements can have several different oxidation states. For example, iron can have a valence of +2 or +3, and chromium can have a valence of +2, +3, or +6. Iron in the +3 oxidation state, Fe+3, acts as an oxidizing agent, accepting one electron to attain the Fe+2 state, while ferrous iron, Fe+2, by donating an electron in going to the +3 state, acts as a reducing agent.


(väläNs`), city (1990 pop. 65,026), capital of Drôme dept., SE France, in Dauphiné, on the Rhône River. Its many manufactures include metallurgical products, textiles, leather goods, and jewelry. It is also a processing and trade center for a fertile farm area. An old Roman town, it was taken by the Visigoths (413) and the Arabs (c.730), then changed hands many times. Although nominally under the control of various European powers, it was actually ruled by its own bishops from 1150 until the 15th cent., when its citizens put themselves under the protection of the dauphin. Its historic center, Romanesque cathedral (11th cent.; partially restored), and late Gothic palace (16th cent.) are tourist attractions. Its university was founded in 1452.



the ability of an atom to form chemical bonds. The quantitative measure of valence is usually taken to be the number of other atoms in a molecule with which a given atom forms bonds. Valence is one of the fundamental concepts in the theory of chemical structure. It was formulated together with the concept of the chemical bond, parallel with the development of synthetic chemistry and methods of investigating the structure and properties of substances. Its content was constantly broadened and varied as experimental chemistry discovered ever newer classes of compounds with previously unknown types of interactions of atoms in molecules. In the last 30-40 years its development paralleled that of quantum chemistry. At present, the accumulated experimental material of chemistry has so broadened and diversified and the pattern of chemical bonding in various compounds has become so varied, that the problem of finding a systematic, common, and universal definition of valence is extremely complex. These difficulties induced some chemists to completely renounce the search for a universal concept of valence and to replace it by a collection of narrower but more definite and precise concepts (covalence, heterovalence, coordination number, and so forth), the region of applicability of each of which is limited by compounds with some predominant type of interaction (covalent, ionic, coordination, and others). However, until the present time both in specialized literature and in textbooks, valence continues to be used as a definition of the atom’s ability to form bonds in the most general sense, as a quantitative measure of this ability, and as a synonym of the proposed narrower concepts.

A common and systematic definition of valence must be found in the framework of quantum-chemical theory of molecular orbitals.

For individual classes of compounds, where any one type of chemical interaction predominates, useful information on the ability of atoms to form bonds can be obtained from the partial concepts (particular definitions of valence) enumerated below.

(1) Definition of the concept of valence and its relation to other concepts of chemistry.

COVALENCE. Covalence is a measure of the atom’s ability to form covalent chemical bonds, arising from two electrons (one from each atom) and which have weak polarity.

The covalence is equal to the number of unpaired electrons of an atom, which participate in the formation of a bond and can often take on all the values from 1 to the maximal number, which for a large number of elements coincides with their group number in Mendeleev’s periodic system (see sections 2 and 3 for details).

HETEROVALENCE. Heterovalence (the terms “electrovalence” and “ionic valence” are also used) is a measure of an atom’s ability to form ionic chemical bonds that arise owing to electrostatic interaction of ions, formed during the complete (or almost complete) transfer of electrons from one atom to another atom. Heterovalence is equal to the number of electrons that the atom loses to or gains from another atom and coincides with the charge of the corresponding ion (see section 2).

COORDINATION NUMBER. The coordination number is equal to the number of atoms, ions, or molecules found in the immediate vicinity of a given atom in a molecule, complex compound, or crystal. In contrast to covalence and heterovalence, this concept has a purely geometric meaning and does not depend on the nature of the bond between the central atom and the ligand. Thus, for example, the coordination number of the atoms of Al, Si, and P in the complex ions [A1F6]3-, [SiF6]2-, and [PF6]- is equal to 6 and the coordination number of the atoms of B, Xe, and Ni in [BH4]-, XeO4, and Ni(CO)4 is equal to 4. In the NaCl crystal each atom of Na is surrounded by six Cl atoms, so that the Na’s coordination number is 6. The value of the coordination number can be determined by the relative dimensions of the atoms and by other, more complex, causes (see sections 2 and 3).

OXIDATION NUMBER. The oxidation number (or degree of oxidation) is a concept that has recently become widely used in inorganic chemistry. It is the electrostatic charge conventionally attributed to an atom according to the following rules. (1) In ionic compounds, the oxidation number coincides with the ion’s charge (for example, in NaCl, the oxidation number of Na is 1 and that of Cl, -1). (2) In covalent compounds, the oxidation number is taken to be equal to the charge the atom would have after all electron pairs that have formed bonds have been completely transferred to more electronegative atoms (that is, if we accept that the bond has a completely ionic character). For example, in HCl the oxidation number of H is 1 and that of Cl, -1. (3) In elementary compounds, the oxidation number is 0 (for example, in 02, Cl2, P4, S8, and in the diamond). (4) In calculating the oxidation number where there are two bound atoms of a single element, it is conventional to divide their total electronic charge in half. The concept of oxidation number is useful in setting up equations for oxidation-reduction reactions, the classification of inorganic and complex compounds, and so forth.

However, according to its definition, oxidation number, in contrast to covalence and ionic valence, which have a clear physical meaning, generally has a conventional meaning, and, except for a very limited class of compounds with purely ionic bonding, does not coincide with either the effective charges of atoms or with the actual number of bonds that the atom forms. In addition, in a number of cases, in particular when the electronegativities of two different bonded atoms are close and the bond between them has an almost purely covalent character, an uncertainty arises as to which atom should this electron pair be assigned.

(2) Evolution of the concept of valence and its role in the history of chemistry. In the beginning of the 19th century, J. Dalton formulated the law of multiple proportions, from which it followed that each atom of a single element can combine with one, two, three, and so forth atoms of another element (for example, the oxides of nitrogen: N2O, NO, N2O3, NO2, and N2O5). In the middle of the 19th century, when the relative weights of atoms were accurately determined (J. J. Berzelius and others), it became clear that the greatest number of atoms with which a given atom can combine does not exceed a definite value, which depends on the atom’s nature. For example, an F atom can combine with only one atom of H, O with two, N with three, and C with four, forming the compounds HF, H2O, NH3, and CH4, respectively. Two or four H atoms in methane CH4 can be replaced by one or two O atoms with the formation of formaldehyde CH2O and carbon dioxide CO2, respectively. Three H atoms in CH4 can be replaced by one N atom with the formation of HCN, and so on. This ability to form bonds or replace a specific number of other atoms was given the name “valence” (E. Frankland, 1853).

In such a definition, valence is, naturally, always expressed in whole numbers. Since at that time there were no known compounds of hydrogen where it was bonded with more than one atom of any other element, the H atom was selected as the standard, having a valence equal to 1. On the “hydrogen” scale, oxygen and sulfur have a valence of 2, nitrogen and phosphorus a valence of 3, and carbon and silicon a valence of 4. However, the “hydrogen” scale proved to be inadequate: in other compounds, for example in oxides, one and the same element can realize valences that are not realized in hydrides (the oxides P2O5, SO3, and Cl2O7 exist, but the hydrides PH5, SH6, and ClH7 are not found). Oxygen, with a valence of 2, was selected as the second standard.

At the end of the 1850’s, A. S. Couper and A. Kekulé postulated the principle of the constant tetravalence of carbon in organic compounds. The idea of valence played an important part in A. M. Butlerov’s theory of chemical structure (1861). The formation of a chemical bond was considered the result of the mutual saturation of two valence pairs of interacting atoms (one valence from each), multiple bonds corresponded to the saturation of several valences from each atom, and so forth. Each bond was considered to be localized between two atoms and was represented by one line connecting these atoms. Molecules came to be represented by structural formulas, which have been particularly widely used in organic chemistry.

Butlerov’s assumptions later formed the basis for a structural theory that also considered the spatial arrangement of atoms in a molecule. It was found that simple molecules of the type MXk, with an identical central atom M and different substitutes X, have a similar geometric structure. The independence of the geometric structure from the type of bond in a broad range led to the idea that the spatial arrangement of atoms in MXk molecules is determined by the valence of the central atom M and that these valences have a directed character (see section 3).

D. I. Mendeleev’s periodic law (1869) revealed the dependence of an element’s valence on its location in the periodic system. Elements of the same group have the same highest valence, in the majority of cases equal to the number of this element’s group; the highest valence is changed by 1 in the passage from one group to an adjacent group. This dependence has played an extremely important role in the development of chemistry: knowing only the position of an element (including elements that had not yet been discovered at the time) in the periodic system, it was possible to determine its valence possibilities, predict the composition of its compounds, and subsequently synthesize them. With the help of the concepts of formal (stoichiometric) valence, chemists succeeded in generalizing and systematizing a vast amount of experimental material on the structure, stoichiometric composition, and properties of many tens and hundreds of thousands of organic and inorganic compounds.

FIRST ELECTRONIC THEORIES OF COVALENCE AND HETEROVALENCE. Before the electronic formulation of the structure of matter, valence was treated in a formal manner. Only in the 20th century was it established that the chemical bond is formed by the electrons of the outer (valence) shell of atoms.

In 1916, G. Lewis postulated that the chemical bond is formed by a pair of electrons belonging simultaneously to both interacting atoms. In 1917, W. Kossel proposed the hypothesis according to which the electron pair of a bond passes over completely to one of the atoms with the formation of a ion pair (cationanion pair) held in a molecule by electrostatic forces. According to both hypotheses, the most stable compounds are those in which the valence electrons are distributed in such a way that each atom is surrounded by a shell identical to that of the nearest inert gas (the octet rule). The Lewis hypothesis marked the beginning of the electronic theory of the covalent bond and covalence and the Kossel hypothesis, the beginning of the theory of the ionic bond and heterovalence. Both represented an extreme case of the general picture of the polar bond, where the electron pair is only partially displaced toward one of the atoms and the degree of displacement can vary from 0 to 1. A valence of an atom in a compound, according to the classical electronic theory, is equal to the number of its unpaired electrons which participate in bonds, and the maximum valence is usually the total number of electrons in its valence shell—that is, the number of the group of the periodic system in which the element is found. The elements of identical groups have an identical number of valence electrons and within identical subgroups, identical or very similar electronic configurations as well (see section 3). The similarity of the structure of the valence shells of atoms determines the similarity of their compounds.

Covalence and heterovalence reflect the characteristics of the corresponding type of chemical bond. The saturability of the bonds, which determines the existence of molecules in the form of discrete particles with a specific composition and structure, is important for covalence. Covalence is prevalent in organic compounds and most simple inorganic compounds. On the other hand, in the case of heterovalence, the maximum number of ions of opposite sign, capable of being distributed around a given ion, is basically determined by the ratios of their dimensions. Ionic valence is prevalent in a comparatively limited class of compounds, primarily in various salts of alkaline, alkaline-earth, and some other metals.

VALENCE IN COMPLEX COMPOUNDS. At the end of the 19th century, A. Werner (1893) found that many compounds, both with maximum (saturated-valence) and with intermediate valences, such as BCl3, SiCl4, PCl5, and CrCl3, have a tendency to interact with other saturated-valence compounds—salts, oxides, molecules of the type H20, NH3, and others—forming rather stable complex compounds, such as K [BCl4], K2[SiCl6], and NH4[PCl6]. Investigations of their structures by X-ray methods have shown that in the complex anions MXm-k and cations MXm+k, the atoms of the ligands X are usually found at the vertices of regular polygons (octahedrons, tetrahedrons, and so forth), and that all M—X bonds are identical.

From the point of view of valence, complex compounds are unusual in the fact that their coordination numbers can be larger than the total number of valence electrons of atom M. Moreover, in paramagnetic complexes of the transition and rare-earth metals— K4[CrF6, K3[CrF6], K2[CrF6], and others—certain valence-shell electrons remain unpaired and localized near the central atom and practically do not participate in bonding. The classical valence and coordination number, as a rule, do not coincide, and the ability to form octahedral and tetrahedral complexes turned out to be extremely widespread and typical for many metals and non-metals, connected in a complex way with the position of the element in the periodic system and its valence in the starting simple compound.

Consequently, the assumption was made that, in addition to “classical” valence, which is realized in the starting simple compounds, such as BC13 and SiCl4, atoms also possess a “coordination” valence, which becomes saturated in complex compounds (see section 3 for the nature of coordination valence). Attempts were made to describe the bond in complex compounds within the framework of ionic theory, in which it is considered that anions such as [PF6]- and [MnO4]- are constructed from the ions P5+ + 6F- and Mn7++ 4O2- and that the valence of the central atom coincides with the charge of its ion. However, the energy necessary for the transfer of one atom of Mn and four atoms of O to the states Mn7+ and O2- is far from compensated by the gain in energy in the bond formation. With the development of experimental methods of determining effective charges, it became clear that the effective charges rarely exceed the values 1 or 2 for positively charged atoms and -1 for negatively charged atoms and are usually expressed in fractional parts of the charge of an electron (in the permanganate anion, the charge on Mn is only 1.5 to 2.0 in electron charge units). Consequently, for the majority of inorganic compounds, simple and complex, the ionic theory cannot be considered correct.

PROGRESS OF CHEMISTRY IN THE 20 TH CENTURY AND PROBLEMS OF THE THEORY OF VALENCE. In the 20th century, a number of new compounds have been synthesized and their structures investigated; it also proved to be impossible to fit these compounds within the framework of the classical ideas of valence. It turned out that the tendency to form coordination compounds and to saturate coordination valences was generally extremely widespread and characteristic of practically all the elements and that the consideration of valence on the basis of only one stoichiometric composition very often proved to be inconclusive without exact data on the structure of the compounds and the geometric arrangement of the nearest coordination sphere of the atom under consideration. As structural methods developed, it became known that many compounds with simple empirical compositions (A1C13, PdCl2, Mo03, and others), previously considered simple in the vapor phase have dimer and polymer structures, that is, Al2Cl6, (PdCl2)x (see Figure 1, a, b), and (MoO3)2-5. In them “bridging” ligands, connected by identical bonds from two atoms of the metals (denoted by 2 in Figure 1), have a coordination number of 2. In compounds in the solid state, which are often constructed still more complexly, the coordination number of halogens and oxygen, previously selected as the standard bivalent element, can be 3 or even 4. In boron hydrides, each “bridging” atom of hydrogen, which was formerly considered to be the standard univalent element, is connected by identical bonds with two boron atoms (see Figure 1, c). Alkyl groups are also able to form bridging bonds in organometallic compounds like A12(CH3)6.

Figure 1. Bridging ligands (Cl, H, CH3) in dimer and polymer compounds: (a) AI2CI6, (b) (PdCI2)(X)(c) B 2H6) and (d) AI 2(CH3)6.

In compounds of the transition and a number of nontransition elements, it became characteristic to make use of an additional valence due to the formation of metal—metal bond (cluster compounds), in which the distance between metal atoms proved to be considerably less than in individual metals. For example, in molybdenum (see Figure 2) and tungsten dihalides, the stable group Me6Hal4+8 (see Figure 2), in which the metal atoms (Me) form a regular octahedron, is preserved in many chemical reactions; each Me atom is bonded to four other Me atoms and to four halogen (Hal) atoms, and each Hal atom is bonded to three Me atoms. The Me—Me bonds in clusters can be multiple (as, for example, in Re2CI2-8, where the Re—Re distance is 0.5 À less than in metallic Re, and in their formation, the atoms can expend not one but several valences).

Figure 2. Cluster structure of Mo6Cl84+ (•- Mo atom; • -Cl atom).

The inadequacy of the classical conception of valence is clear also for the example of the so-called zero-valence compounds, in which the atom of the metal is bonded exclusively to neutral molecules: examples are the metal carbonyls, such as Ti(CO)7, Cr(CO)6, and Fe(CO)5, and the ammines, such as Pt(NH3)4, among others. In them, there is absolutely no classical valence interaction (in the C and N atoms in the CO and NH3 molecules, there are no unpaired electrons), and the bond is realized only through the coordination valences of the metal’s atom and ligand molecules. Neutral ligands often turn out to be bridged and bonds form in twos—for example, in Co4(CO)12—and even in threes—for example, in Rh6(CO)16.

In the theory of valence, there is special interest in so-called π -complexes of the transition metals with aromatic molecules or molecules with conjugate bonds as ligands (ethylene, cyclopentadienyl, benzol, and others), such as ferrocene Fe(C5H5)2, dibenzenechromium Cr(C6H6)2 (see Figure 3, a, b), tetracyclopentadienyl titanium Ti(C5H5)4, and other compounds. In contrast to such complexes as [Cr(NH3)6]3+, [Cr(H20)6]2+, or Cr(CO)6, where the central atom forms the bond with a ligand via one atom of each ligand (by way of N in ammines O in hydrates, and so forth), in π -complexes the Fe, Cr, and Ti atoms interact identically with all the C atoms of each aromatic ring. The unfitness of classical valence or coordination numbers is obvious here; one has to consider all carbon atoms to be pentavalent and the Fe, Cr, and Ti atoms to be 10-, 12-, and 20-valent respectively. The only unpaired electron that exists in the -C5H5 radical (just as in many other aromatic radicals, such as tropyl C7H7, among others) belongs to an equal extent to all the carbon atoms of the ring. For this class of compounds, an understanding of a delocalized (“group”) valence, which characterizes a whole collection of C atoms in an aromatic ring, became necessary.

Figure 3. π-complexes of transition metals (• — metal atom; • —C atom): (a) ferrocene, Fe(C5H5)2 and (b) dibenzenechromium, Cr(C 6H6)2.

Now it became clear that the coordination number in complexes, like valence in simple compounds, is not a a rigidly specific characteristic of an element; for a large number of metals, complexes with all the intermediate values of coordination number from 3 to 7, 8, and 9 were found. Here, difficulties arose with the definition of coordination number itself; in low-symmetry, high-coordination complexes, the M—X distances, even for identical ligands X, often proved to be different; at the same time their distances can be longer than those sufficiently short distances for which the presence of a strong interaction is indisputable but their distances are not long enough to confidently exclude the atoms from the coordination sphere of the complex.

New problems in valence arose in other branches of chemistry as well. There was great development in the study of free radicals [for example, methyl CH3, triphenylmethyl … C(C6H5)3, and others], in which there are trivalent carbon atoms. In the last decade, such compounds of inert gases as XeF2, XeF4, XeF6, and XeO3 have been synthesized—that is, compounds of elements that were previously considered incapable of chemical interaction. It also became clear that the valence of elements can vary greatly with changing external conditions, in particular temperature. For example, PCl5, which exists at moderate temperatures in the gaseous phase in the form of monomeric molecules, upon condensation disproportionates, yielding a cation-anion pair: cation— PCI4+ (coordination number = 4)—and anion— PCI6- (coordination number =6). On the other hand, at higher temperatures, the molecules PCl3, PCL2, PCl and ions PCI4+, PCI3+, PCI2+, PCI+ and so forth are found. Owing to the success of the chemistry of gaseous molecules, in the past 20 years a large number of compounds (often of complex composition) have been found with intermediate and unusual valences, which are not found in compounds under ordinary conditions. For example, besides the long known anions of the type CO3 and SO4, the anions CO3- and SO4- and the neutral molecules CO3 and SO4 have now been found; in addition to the saturated molecules such as CH4 and C2H6, ions like CH5+ and C2H7+ have been found; in addition to the H2 molecule, the H3+ ion has been found; and so forth.

It has now been established that the overwhelming majority of elements can exhibit a variable valence, forming a whole series of “valence-unsaturated” compounds with all the values from 1 to the maximum, varying by 1 (for example, the known molecules include BF, BF2, and BF3; CF, CF2, CF3, and CF4). Valence cannot be considered a rigidly specific characteristic of an element; one can speak only of the relative typicalness or relative stability of various valence values. In the nontransition elements of even and odd groups, the most stable valences are the even and odd, respectively—for example, in molecules of the type PF3, PF5, SF2, SF4, SF6, IF, IF3, IF5, IF7, and so on, where the typical valence of the P, S, and I atoms changes by two units.

Radicals of the type · PF4, · SF3, · SF5, · IF2, · IF4, and so on of tetravalent phosphorus, odd-valent analogs of sulfur, and inert gases and even-valent halogens are considerably less stable and have a clearly expressed tendency to split off one electron (with the formation of more stable cations, such as PF4+,SF3+,SF5+,IF2+, IF4+) or one of the substitute atoms and are characterized by a considerably shorter lifetime. In elements of the side groups, the relations between typical and less typical valences are of a more complex nature.

The study of electronic spectra has shown that diatomic molecules such as 02, S2, and OS have two unpaired electrons; within the framework of the classical conceptions this must be interpreted as meaning that in similar molecules, each atom keeps one of its valences unused, although there are no visible obstacles to their use.

Until now, the problem of the valence in intermetallic compounds has remained unsolved; these compounds usually have a complex composition such as Cu5Zn8, Cu31Sn8, and Zn21Fe5; nonstoichiometric oxides; nitrides; carbides; suicides; and other compounds of metals in which the composition can vary continuously in a comparatively broad range.

Thus, the search for a general definition of valence that would encompass all the known types of compounds, and that would also predict the possibility or impossibility in principle of the existence of yet unknown classes of compounds, constitutes a complex problem. Of course, parallel with “nonclassical” compounds, chemists synthesized many hundreds of thousands of compounds that can be interpreted within the framework of ordinary classical conceptions of valence. However, it is clear that all the existing individual definitions of valence (see section 1) are limited by the specific classes and types of compounds in which any one type of chemical interaction predominates. In the general case, however, the bonds have an intermediate character between purely ionic and purely covalent, and all types of interactions take place simultaneously, but in different quantitative ratios. These change sharply from class to class and more smoothly from compound to compound within a single class. In the absence of a general definition of valence, the difficulty consists of defining the boundaries where a particular definition of valence ceases to hold true and another definition replaces it. To solve this problem only on the basis of experimental facts and the classical conceptions is impossible. The quantum theory of the chemical bond and valence can be of considerable help in doing this.

(3) Modern quantum-chemical formulation of valance. Beginning in the 1930’s, the formulation of the nature and character of valence constantly broadened and deepened, parallel with the broadening and deepening of the concept of the chemical bond. Substantial progress was made in 1927 when W. Heitler and F. London performed the first quantitative quantum-chemical calculation for the H2 molecule. In corroborating Lewis’s hypothesis, it was shown that the chemical bond in H2 is actually realized by a pair of electrons and is the result of electrostatic (coulombic) interactions of electrons and nuclei. The formation of a molecule from atoms is energetically favored, if the electron spins are directed in opposite directions when the attraction of the electrons for the nucleus (core) of foreign atoms is greater than the energy of repulsion between electrons and nuclei. The parallel orientation of spins leads to repulsion of the atoms from each other.

Later, the ideas of Heitler and London were extended to polyatomic molecules, which led to the creation of the theory of localized pairs. According to this theory, the general pattern of electron density distribution in MXk-type molecules is formed from k independent M—X fragments, the bond in each being formed by a pair of electrons (one electron from the central atom M and one from the substitute X), localized between the atoms M and X. According to this theory, valence is not simply connected with the presence of an unpaired electron but is also characterized by the state in which this electron is found to be or, in terms of the theory of the chemical bond, the atomic orbital it occupies. Atomic orbitals of different types have different orientations in space: the s orbital is spherically symmetric; the px , py and pz orbitals are elongated along three mutually perpendicular axes; and so forth. The electrons of the atoms in a molecule are in general described by “hybrid” (mixed) orbitals, which, in principle, can include any valence atomic orbitals in various quantitative ratios and in which the electron clouds are concentrated along the directions of the M—X bonds considerably more so than they are in simple atomic orbitals. The state of the valence electrons, and consequently the properties of the valence of atom M, to a considerable extent determine the regularities in the properties of MXk molecules for a wide range of substitutes X. The most fruitful conceptions turned out to be those of directed valences and valence states of atoms, permitting the explanation and generalization of a number of regularities in the geometric structure and energies of chemical bonds of organic and inorganic molecules.

THEORY OF DIRECTED VALENCES. In the theory of directed valences, it is assumed that the M—X bonds in MXk molecules are stronger the greater the overlap of the electron clouds of the hybrid orbitals of the M and X atoms—that is, the more heavily these clouds are concentrated along the M—X directions. Consequently, the MXk, molecules must have a geometric structure such that the density of the hybrid atomic orbitals along the bond directions is maximal and the valence angles X—M—X coincide with the angles between the directions of the hybrid atomic orbitals of the central atom. For example, in molecules such as PH3 and SH2 the bonds are formed by almost pure 3p orbitals of the central atoms, and consequently PH3 and SH2 have a pyramidal and angular structure with the H—M—H angles approximately equal to 90°. In the dihalogens of Zn, Cd, and Hg, dioxides, disulfides, and other compounds of carbon and its analogs, the bonds are formed with sp-hybrid atomic orbitals with valence angles of 180°, so that all molecules like CdCl2, Hg(CH3)2, Hgl2, CS2, and Si02 in the vapor phase have a linear structure. In the case of Ca, Sr, Ba, Ra, and the transition metals of groups III-VI, the mixed hybridization of sp + sd orbitals leads to an angular structure for molecules like CaF2, SrF2, BaHal2, TiO2, HfO2, TaO2, ThO2, and UO2.

VALENCE STATE OF AN ATOM. Closely connected with the problem of valence is the approximate concept of the valence state of an atom—the hypothetical state in which an atom exists in a molecule. It is characterized by a valence configuration, that is, by the type and number of filled and empty atomic-orbital valences; their hybridization, which reproduces the geometric structure of the innermost sphere of the atom under consideration; by the number of electrons (in the theory of the localized pair, this is a whole number: 2, 1, or 0), which populate each of the hybrid atomic orbitals; and by the relative orientation of the electron spins. For example, in the methane molecule CH4 (see Figure 4), the C atom has a valence configuration of 2s 2p3 with four tetragonal sp3-hybrid orbitals (te), directed toward the vertices of a tetrahedron, each of which is populated by one electron with an indefinitely oriented spin that forms a single Heitler-London bond with the corresponding H atom. As a rule, the valence state of an atom in a molecule does not coincide with the principal state of an isolated atom. Thus, in carbon and its analogs the principal state (Figure 4, a) can only be bivalent. In all group II atoms the principal state s2 cannot generally be valence states, and in the formation of molecules such as ZnCl and ZnCl2 it is necessary to excite the s electron to the nearest empty p level. The energy of excitation to a valence state from the principal state differs from element to element and can attain several hundreds of kcal/mole, making a substantial contribution to the total energy balance of formation of molecules from atoms. In the case of Zn, Cd, and Hg, the excitation sp occurs upon the addition of the first halogen atom and requires considerable energy expenditures (90-120 kcal/mole). Consequently, the energy of breaking the M—Hal bond in diatomic MHal molecules is considerably less than for the HalM—Hal bond in triatomic MHal2 molecules. In Ca, Sr, Ba, and Ra the energy expenditures for the sp or sd excitation is considerably less (30-50 kcal/mole), and here the energies of breaking the bonds in halide molecules are much closer to each other.

Figure 4. Diagram of the excitation of the valence state (d) of the carbon atom in the molecule of the type CH4 from the principal state (a), (a) Principal state of the lowest configuration 2s22p2; (b) lower state of the valence configuration 2s2p3; (c) hybridization of the atomic orbital; and (d) indefinite orientation of the spins of valence electrons (valence state).

In complex compounds the coordination number of the central atom is often greater than the number of electrons in its valence shell. An important role is played here by a donor-acceptor bond and by dative bonds, which are formed by an unshared electron pair (that is, electron pairs with opposite spins occupying one atomic orbital) of one atom and the empty orbital of another. Accordingly, the formulation of valence must be broadened; the ability to form bonds, and consequently the valence of an atom as well, is due not only to unpaired electrons but also to unshared pairs and empty orbitals of the valence shell. The greatest total valence must be equal to the number of all the atomic orbitals making up the atom’s valence shell, since each valence atomic orbital, independently of how many electrons fill it for an atom in a valence state, is potentially capable of forming one bond (Heitler-London, donor-acceptor, or dative). Within the framework of this formulation, the maximum valence of all the elements of the second period from Li to F is equal to 4 (one s orbital + three p orbitals), and, for the elements of the following periods, 9 (owing to an additional five d orbitals), and so on. The answer to the question which of the four or nine valences are saturated and which remain unused is determined in the compounds of each concrete type not only by the properties of the atom itself and its location in the periodic system but also by the special features of the compound as a whole. The complete answer to it can be obtained by means of quantum-chemical calculations. Owing to donor-acceptor interaction, the actual number of bonds of an atom (and consequently its valence as well) in complex and even in simple compounds can in general be larger than the number of its unpaired electrons and the number of neighboring atoms bonded to it.

Let us recall that the subdivision of the bonds in compounds into Heitler-London, donor-acceptor, and dative types has, in general, only genetic meaning, since, after the compound is formed, a redistribution of the electron density and the equalization of the bonds takes place in it: for example in each of the complex anions such as [BF4]-, [BeF4]2-, [SiF6]2-, [A1F6]3-, and [ZnF6]4-, all the M—F bonds are completely identical.

It has also been established that in salts, the NO3- ion has a regular triangular structure and the SO42 and PO43 ions, a regular tetrahedral structure. Consequently, the structure of the molecules of the corresponding salts is more accurately described by the structural formulas given in Figure 5, d-f, and not by the traditional formulas of Figure 5, a-c, which do not take into account the actual structure of the ions.

Figure 5. Structural formula of molecules NaNO3 (a and d), Na 3SO4(b and e), and Na3PO4(c and e).

The theory of localized pairs is limited mainly to nonconjugated organic and simple inorganic compounds. Thus, in the case of “electron-excessive” molecules such as PF5, SF6, IF7, and XeF6, this theory cannot explain the formation of higher valences in the atoms P, S, I, and Xe without invoking valence states from higher integer-valued populations of the outer d orbitals (sp3d for P, sp3d3 for I, s2p 3d 3 for Xe, and so forth). However, the excitation energies of the latter atoms P, S, I, and Xe are so great (200-400 kcal/mole and greater) that the energy expenditures for their excitation can probably not be made up for by the energy gain in bond formation. Similar difficulties arise in the consideration of complex compounds, coordination crystals, and others. In “electron-deficient” molecules such as B2H6 (Figure l,c), the number of bonds formed by the H atom is greater than the number found in its valence atomic orbitals, so that the bonds of the bridged H’s with the two B atoms can be described only by tricentered molecular orbitals that encompass the B—H—B fragments. In the case of aromatic and conjugated molecules such as C5H5, C6H6, and C7H7, their complexes with metals (Figure 3) and other derived valence 2 -electrons belong to an equal extent to all the C atoms and can be described only by means of delocalized molecular orbitals encompassing the whole ring or carbon core as a whole. In other words, the formulation of localized valences and bonds has turned out to be too narrow to accommodate all known types of compounds.

Consequently, the natural next step in the development of the general theory of valence was the molecular orbital method, which deals with the molecule as a collection of nuclei and electrons, where each electron moves in the field of the remaining electrons and all the nuclei. The molecular orbitals that describe the state of electrons in general encompass all the atoms of the molecule, so that each atom is capable in principle of forming bonds with all the remaining atoms of the molecule. The molecular orbital method is considerably more general and systematic, which makes it in principle suitable for the description of any class of compounds.


Syrkin, la. K. Periodicheskaia sistema i problema valentnosti. Moscow, 1971.
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.)
Shustorovich, E. M. Novoe v uchenii o valentnosti. Moscow, 1968.
Coulson, C. Valentnost’. Moscow, 1965. (Translated from English.)
Murrell, J., S. Kettle, and J. Tedder. Teoriia valentnosti. Moscow, 1968. (Translated from English.)
Astakhov, K. V. Sovremennoe sostoianie periodicheskoi sistemy D. I. Mendeleeva. Moscow, 1969.

O. P. CHARKIN (edited by Academician IA. K. SYRKIN)



in linguistics, the potential combinability of linguistic elements (phonemes, morphemes, words, and so on), which defines their ability to enter into combinations with other linguistic elements, mainly with those on the same level. Valence is categorical or individual depending on whether the combinability of whole word classes (for example, verbal predicates with noun subjects) or separate words (for example, the word znobit [to be feverish] with animate nouns in the accusative case) is meant. If the valence is necessarily realized for the functioning of an element, then it is termed obligatory. In simple valence, an element is combined with one element; in complex (multipositional) valence an element is combined with several elements at the same time—for example, a predicate is used simultaneously with a subject, an object, and an adverbial modifier. The identity of valences is one of the bases for uniting elements in one class. The determination of the valences of linguistic elements, especially on the syntactic level, is a widely used method of formal linguistic analysis.


Leikina, B. M. “Nekotorye aspekty kharakteristiki valentnostei.” In the collection Doklady na konferentsii po obrabotke informatsii, mashinnomu perevodu i avtomaticheskomu chteniiu teksta, issue 5. Moscow, 1961.

V. V. RASKIN 4-763-1


The relative ability of a biological substance to react or combine.
A positive number that characterizes the combining power of an element for other elements, as measured by the number of bonds to other atoms which one atom of the given element forms upon chemical combination; hydrogen is assigned valence 1, and the valence is the number of hydrogen atoms, or their equivalent, with which an atom of the given element combines.
The number of lines incident on a specified point of a graph.


1. another name (esp US and Canadian) for valency
2. the phenomenon of forming chemical bonds


a town in SE France, on the River Rh?ne. Pop.: 64 260 (1999)
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