The Concept of Valence

The view that each different chemical substance may be associated with a fixed molecular structure, and that this structure could be elucidated by chemical means, was of central importance in the development of modem chemical thinking. Indeed, as Hmn [26] has commented, this construct may be the most ffoitful conceptual scheme in all of the history of sdence . The scheme is usually designated nowadays as structure 

By 1865, the six membered zing formula for benzene had been postulated by various workers [28,29] including Kekuld [47]. The new formulas became widely disseminated in 1866 when FVankland [48] published his celebrated Lecture Notes for Chemico/ StssdentSj in which he made use of the notation advocated by Crum Brown [46]. Within a year or so, the drawing of circles around the individual atoms was discontinued, and, in virtually all respects, modern structural formulas were launched and rapidly came into general use. 

Fi re 9. Reproductions of the graphical formulas employed by Crum Brown (1864) to represent the topological positions of atoms in a variety of motecutes. 

The concept of the cyclomatic number has also played an important part in the description of chemical structure. This number is defined in terms of the equation  

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Much of quantum chemistry attempts to make more quantitative these aspects of chemists view of the periodic table and of atomic valence and structure. By starting from first principles and treating atomic and molecular states as solutions of a so-called Schrodinger equation, quantum chemistry seeks to determine what underlies the empirical quantum numbers, orbitals, the aufbau principle and the concept of valence used by spectroscopists and chemists, in some cases, even prior to the advent of quantum mechanics. 

Several methods of quantitative description of molecular structure based on the concepts of valence bond theory have been developed. These methods employ orbitals similar to localized valence bond orbitals, but permitting modest delocalization. These orbitals allow many fewer structures to be considered and remove the need for incorporating many ionic structures, in agreement with chemical intuition. To date, these methods have not been as widely applied in organic chemistry as MO calculations. They have, however, been successfully applied to fundamental structural issues. For example, successful quantitative treatments of the structure and energy of benzene and its heterocyclic analogs have been developed. It remains to be seen whether computations based on DFT and modem valence bond theory will come to rival the widely used MO programs in analysis and interpretation of stmcture and reactivity. 

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. 

The seminal studies on these complex compounds were conducted by Alfred Werner in an intensive period of work at the turn of the century. A typical example of the problems that Werner addressed lies in the various compounds which can be obtained containing cobalt, ammonia and chlorine. Stable and chemically distinct materials with formulations Co(NH3) Cl3 (n = 4,5 or 6) can be isolated. The concepts of valency and three-dimensional structure in carbon chemistry were being developed at that time, but it was apparent that the same rules could not apply to... 

The concept of valence has been subject to revision over the years. Initially, valence was regarded as the combining power of an element and was derived from the composition of compounds. At the end of the period before the age of quantum chemistry, valence was generally formulated in relation to the octet rule [1—3), a simple relation which still finds useful application in modem chemistry. 

The concept of valence-shell expansion originated as a striking... 

The concept of valence developed in the preceding section is the basis of the first correlations aiming at a global theory of the actinide metallic bond. These correlations were established between the atomic volumes of actinide elemental metals, and the electronic configuration of the actinide atoms Their aim was to provide a general theory of actinides (i.e. to give an answer to the questions i. and ii. of Sect. A.I.l.) within the framework of a simple model of the metallic bond. 

In many cases it is only by forcing an explanation for the particular case that the valency theory can be adhered to, but the formula obtained in such circumstances do not indicate the behaviour of the substance chemically. These difficulties in correlating the compounds of higher order with the older valency theory rendered it necessary either to extend the conception of valency still further or to adopt some other theory. 

At about the time that Claus proposed his ammonia theory, the concept of valence was being formulated and developed by a number of chemists — in particular, Kekule, Frankland, Williamson, Odling, Kolbe and Couper. During the late 19th and early 20th centuries the principal difficulty in the field of valence was its application to all types of chemical compound, and one of the main controversies involved whether or not a given element could possess more than one valence. Since coordination compounds pose a number of basic constitutional problems, it is not surprising that they became involved in the question of variable vs. constant valence. 

A molecular compound is formed by the union of two or more already saturated molecules apparently in defiance of the ordinary rules of valence. The class includes double salts, sails with water of crystallization, and metal ammonium derivatives. These salts are usually formed by Van der Waals attraction between (he constituent molecules. They do nol differ in any characteristic manner from compounds formed in strict accordance with the concept of valence They are also called addition compounds. 

For the theoretical approach to inorganic chemistry, see the books listed in Section A.7 of the Appendix. See also the books listed in Section 4.8, especially Chapter 1 of Johnson (1982). The historical development of bonding theory is thoroughly treated by Palmer, W. G. (1965). A History of the Concept of Valency to 1930. Cambridge University Press. 

W. G. Palmer, A History of the Concept of Valency to 1930, Cambridge University Press, Cambridge, 1965. 

An understanding of the three-dimensional structures of molecules has played an important part in the development of organic chemistry. The first experiments of importance to this area were reported in 1815 by the French physicist J. B. Biot, who discovered that certain organic compounds, such as turpentine, sugar, camphor, and tartaric acid, were optically active that is, solutions of these compounds rotated the plane of polarisation of plane-polarized light. Of course, the chemists of this period had no idea of what caused a compound to be optically active because atomic theory was just being developed and the concepts of valence and stereochemistry would not be discovered until far in the future. 

STRUCTURAL FORMULAE Using the concept of valency the composition of compounds can be expressed with structural formulae. Each valency of an element can be regarded as an arm or hook, through which chemical bonds are formed. Each valency can be represented by a single line drawn outwards from the symbol of the element, like... 

The notion of isomerism for synthons was defined in [18,21,16], in the present communication we shall study the synthons that are constructed over the same vertex set A. Therefore, they are automatically isomeric. The set of all synthons (nonisomorphic) constructed over the set A is called the family of isomeric synthons, and is denoted by 3F A). The synthons from a family will be advantageously classified in our forthcoming considerations as stable, unstable, and forbidden. This will be done by making use of the concept of valence states of vertices. 

In his 1965 book History of the Concept of Valency to 1930, W. G. Palmer stated that it is yet too early to assess the very rapid developments since 1930 in a jnst historical perspective . The same can be said abont coordination chemistry. For this reason and because of space limitations, this historical account of coordination chemistry mnst close at this point. In general, research, discoveries, and innovations in the field since the 1930s have taken place at an ever-accelerating rate. 

At this point it is useful to introduce the concept of valence electrons, the electrons in the outermost principal quantum level of an atom. The valence electrons of the nitrogen atom, for example, are the 2s and 2p electrons. For the sodium atom the valence electron is the electron in the 3s orbital, and so on. Valence electrons are the most important electrons to chemists, because they are involved in bonding, as we will see in the next two chapters. The inner electrons are known as core electrons. 

More Precise Concepts. The concept of valence as discussed above is not rigorously defined, and many puzzling questions may present themselves. Thus elementary hydrogen may be considered to have either the valence 0, since it is not combined with any other element, or the valence 1, since the molecule may be assigned the structural formula H—H. Similarly oxygen in hydrogen peroxide, H Oo, may be taken As univalent, since.it is combined with an equal number of... 

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