The Modern Theory of Valency

The Liversidge Lecture, delivered before the Chemical Society in the Royal Institution on June 3rd, 1948. 

The modem theory of valency is not simple—it is not possible to assign in an unambiguous way definite valencies to the various atoms in a molecule or crystal. It is instead necessary to dissociate the concept of valency into several new concepts—ionic valency, covalency, metallic valency, oxidation number—that are capable of more precise treatment and even these more precise concepts in general involve an approximation, the complete description of the bonds between the atoms in a molecule or crystal being given only by a detailed discussion of its electronic structure. Nevertheless, these concepts, of ionic valency, covalency, etc., have been found to be so useful as to justify our considering them as constituting the modern theory of valency. 

This description would assign to the caesium atom in the caesium fluoride crystal a resultant charge + and to the fluorine atom a charge — It has seemed to me likely that in general all of the atoms in the complexes that constitute stable chemical substances have resultant electrical charges smaller than those shown by these most electropositive and electronegative atoms in their compounds with one another, and I have accordingly formulated the postulate of the essential electrical neutrality of atoms namely, that the electronic structure of substances is 

A covalent bond between two atoms requires two electrons and two orbitals, one for each atom.f The factors determining the properties of the covalent bonds formed by an atom are primarily the number and nature of the orbitals (hybridised bond orbitals) available to the atom, and the number of electrons that it can use in bond formation without losing its electrical neutrality. The opportunities for stabilisation through resonance of covalent bonds among alternative positions are also important. 

For elements adjacent to the noble gases the principal orbitals used in bond formation are those formed by hybridisation of the s and p orbitals. For the transition elements there are nine stable orbitals to be taken into consideration, which in general are hybrids of five d orbitals, one s orbital, and three p orbitals. An especially important set of six bond orbitals, directed toward the comers of a regular octahedron, are the d2sps orbitals, which are involved in most of the Werner octahedral complexes formed by the transition elements. 

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Speakman, J. C. " An Introduction to the Modern Theory of Valency. Arnold. 1943. 

Pauling L (1948) The modern theory of valency. J Chem Soc 1461-1467 Sanderson RT (1954) Electronegativities in inorganic chemistry. J Chem Educat 31 238-245 Reed JL (2003) Electronegativity coordination compounds. J Phys Chem A 107 8714—8722 Suchet JP (1965) Chemical physics of semiconductors. Van Nostrand, London Suchet JP (1977) Electronegativity, ionicity, and effective atomic charge. J Electrochem Soc 124 30C-35C... 

Ibid. See J. H. Van Vleck and J. Albert Sherman, "The Quantum Theory of Valence," Reviews of Modern Physics 7 (1935) 167228. 

Modern theories of valency are electrochemical in character, arc concerned with the nature of the atom, and assume union between elements to take place by exchange or sharing of electrons, although theories of how this exchange or sharing takes place differ considerably. 

The periodic system developed from Bohr s atomic theory is of the greatest importance in chemical science because it demonstrates that the properties of the elements depend on their positions in the system. It is immediately apparent that chemical valency depends on the number of loosely-bound electrons in the atom. Thus, the alkali metals have one such electron while the divalent alkaline-earth metals have two, etc. Valency is therefore closely connected with electronic structure and provides the foundation for the modern theory of the chemical bond, the basis of which is to be found in the coupling or transfer of the valency electrons. 

Ever since the discovery by Gomberg in 1900 of the dissociation of hexaphenylethane into triphenylmethyl radicals the search for a theoretical explanation of the phenomenon has been carried on. The modern theory of the stability of the aromatic free radicals attributes it in the main to the resonance of the free valence among many atoms.28... 

Yield.—66% theoretical (10 gms.). Colourless crystals insoluble in water M.P. 61° gives a deep violet coloration with ferric chloride and a bluish-green crystalline precipitate of copper benzoyl acetone with alcoholic copper acetate. This shows the compound to be tautomeric, a little of the enol form being present at ordinary temperatures. The acidity of the hydroxyl group in the enol form is not so marked as it is in the case of the hydroxymethylene compounds nevertheless, the metallic salts of benzoyl acetone and such di-ketones are remarkably stable, and on account of their great crystallising power have been used for the determination of the valency and atomic weight of the rare elements. They are also of importance in the modern theory of co-ordination. (C., 1900,1., 588 B., 34, 2584.)... 

N.V. Sidgwick, Coordination compounds and the Bhor atom, J. Chem. Soc. CXIII, 725 (1923) The Electronic Theory of Valency, Oxford (1927) W.G. Palmer, Valency, Classical and Modern, Cambridge (1944) also cited in J.R. Partington, A Short History of Chemistry, 3rd ed., p. 373, Dover Publications, New York (1989). 

The reagents are strong bases and poorly soluble metal hydroxides. In the above equations, the metal hydroxides function as acids, in agreement with the modern theory of their amphoteric behavior. As far as is presently known, the following metals (arranged in order of increasing valence) form hydroxo salts ... 

The full explanation of these facts is based on wave mechanics and the modern theories of electron distribution in chemical bonds. A simplified explanation is that the carbon atoms in benzene are held together by valencies (3 electrons). Two valency electrons are firmly located in a bond directly between each pair of carbon atoms, but the remaining electrons are pooled between all six atoms and are free to move to particular atoms when the molecule is influenced by some outside reagent... 

Kekule s remarkable hypothesis, if the motion of the carbon atoms is replaced vby the motion of their valency electrons, is equivalent to the modern theory of resonance (see p. 962). 

The structure for benzene which rvill be assumed in this chapter is one in which all atoms are coplanar with the carbon atoms and the hydrogen atoms at the corners of concentric, regular hexagons (Fig. 10-1). The Kekul6 structure, in which alternate carbon-carbon bonds, but not adjacent ones, are equivalent, would be somewhat less symmetrical, but modern theories of valence regard all six such bonds as equivalent. Moreover, there is good experimental evidence (aside from the vibrational spectrum) for the most symmetrical planar structure for example, it is supported by electron diffraction experiments. ... 

Dots stand for the terms obtained by permutation of the couple of indices (ij) and (kl). The strain derivatives appearing in Eqs. (4-5) must be evaluated at r = 0. The strain derivatives of the wavefunctions can be deduced by perturbing the Schrodinger-type Eq. (2) (see Appendix). Eqs. (3-5) constitute a link between the phenomenological elastic theory and the modern theory of the cohesion of the solid. The correspondence between the elastic theory and the valence-force-field model is shown in Ref. 1. 

Werner literally dreamed up the modern theory of coordination compounds in 1892. He envisioned that metals had two types of valence, which we refer to today as oxidation state and coordination number. Some ligands satisfy only the coordination number, whereas others simultaneously satisfy the oxidation state. These ideas explain why some chlorides in the cobalt ammonate chlorides are ionizable and some are not. By comparing the actual number of known isomers with the number that should exist for various geometries, Werner concluded that the six ligands in the cobalt ammonates were in an octahedral arrangement. 

The acetylene molecule with its unique six-electron chemical bond, strength, high energy, and at the same time its vulnerability to diverse transformation hardly fits the Procrustean bed of modern theories of valency and reactivity. Being a steady challenge to theorists [121,122], it stimulates the development of fundamental works in the field of structure of matter and energy transformation. 

Of course we cannot consider here, not even in a modest way, the quantum mechanical treatment of the problem of semiconduction. The modern theory of solids makes use of the band theory permitting us to modify the classical concept of bound electrons in valence crystals. Impurities may play a very important part in semiconduction. If one adds foreign atoms (impurities) we introduce new electronic levels in the forbidden regions. This substance will have semiconduction properties if the electron is thermally lifted to the empty band. Lattice defects may induce similar properties. The conductance depends on the number of electrons filling the band. 

The theory of valency is equivalent to the theory of structural chemistry. This theory has now passed through the first stage of its modern development, that of the formal assignment of structures to chemical substances, and is entering upon its second stage, the development of a system permitting the prediction of the approximate thermodynamic stabilities corresponding... 

G. N. Lewis, J. Am. Chem. Soc. 38 (1916), 762 G. N. Lewis, Valence and the Structure of Atoms and Molecules (New York, The Chemical Catalog Co., 1923). As observed by Pauling (in note 51, p. 5), this remarkable work forms the basis of the modern electronic theory of valence. ... 

G. N. Lewis (1876-1946), the renowned U.S. chemist, was the first to grasp the significance of the electron-pair in molecular structure. He laid the foundation for modern theory of structure and bonding in his treatise on Valence and the Structure of Atoms and Molecules (1923). 

To systematize the structural problems of the so-called compounds of higher order he reconsidered valency. Thus, he advanced the idea of Hauptvalenz and Nebenvalenz, which could be said to contain the image of modern ionic and covalent bonding theory. Furthermore, he visualized the valence bond not as small sticks existing around atoms in a plane, as conceived by Kekul6, but as positions taken by bond arms on the surfaces of spherical atoms in three dimensions. Could this idea not be a precursor to the modern conception of bond orbitals ... 

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