The Valence Theory

The remarkable geometrical similarities of these hydrides is very striking and will become more so as the valence theory is developed. Superposition of the ball and stick type of molecular models on one another brings out the diborane type of geometry in the open parts of these molecules, and is very suggestive of the kinds of hybridization that may be chosen for convenience about the boron atoms. 

The theory of valence of these structures is of interest for several reasons. The hydrides themselves have an unusual set of formulas, and one might hope that a theory would correlate these and predict other members of the series. But more important, because these hydrides are electron deficient in the sense that there are more orbitals than electrons, one might hope that their electronic and geometrical structures will aid in the understanding of the large number of intermetallic compounds, and of the border line between metals and nonmetals. This interpretative problem is comparatively simpler for boron, which uses only the 2s and the three 2p orbitals, and hydrogen, which uses only the Is orbital, in the approximation discussed here. This approximation is fairly good in 

In saturated hydrocarbons, for example, C2H6, each carbon supplies four orbitals and each hydrogen supplies one. Bonds are formed by overlapping of one of the four tetrahedral sp orbitals of carbon with either the Is orbital of hydrogen to form a C-H bond, or another sp orbital of carbon to form a C-C bond. When the total number of electrons exceeds the number of available atomic orbitals, as in NHs or N2H4, excess pairs occur in hybrid orbitals. In these compounds the chemist writes chemical bonds, and unshared pairs if necessary, and regards the orbitals as filled if each element of the first row has an octet of electrons and if hydrogen has two electrons. 

The usual hybrid orbitals for boron in its better-known chemistry are tetrahedral (e.g., BH4 ) or trigonal (e.g., BF3). We shall start our description with these hybrids and with the Is orbital of hydrogen (Fig. 

(a) The spherically symmetrical Is orbital for H (b) tetrahedral hybrid orbitals for B (c) trigonal hybrid orbitals for B, showing the 7r-orbital extending above and below the plane of the sp hybrids 

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The valence theory (4) includes both types of three-center bonds shown as well as normal two-center, B—B and B—H, bonds. For example, one resonance stmcture of pentaborane(9) is given in projection in Figure 6. An octet of electrons about each boron atom is attained only if three-center bonds are used in addition to two-center bonds. In many cases involving boron hydrides the valence stmcture can be deduced. First, the total number of orbitals and valence electrons available for bonding are determined. Next, the B—H and B—H—B bonds are accounted for. Finally, the remaining orbitals and valence electrons are used in framework bonding. Alternative placements of hydrogen atoms require different valence stmctures. 

The valence theory of metals and intermetallic compounds is still in a rather unsatisfactory state. It is not yet possible to make predictions about the composition and properties of intermetallic compounds with even a small fraction of the assurance with which they can be made about organic compounds and 7— 553041. Lee brtx Nobel en /pjy. 

August Kekule ignored Frankland s work and claimed the valence theory for himself. It was 20 years before scientists recognized that Frankland had founded the theory of valency, while Kekule had contributed to it at a later date. 

In addition to atomism, the principal chemical theories of the nineteenth century included electrochemical dualism, the radical theory, the type theory, and the structure theory, the latter strongly identified with what chemists called the "law of linking" of carbon atoms. The valence theory evolved as a way of tying together the notions of chemical equivalence and chemical structure, and it carried along the old problem that some chemical elements (e.g., nitrogen) exhibit different combining values with another element in different circumstances. 

Bom frequently showed less than high respect for chemical methods and theories, referring to the "arbitrary" "speculations" of chemists about valency and contrasting their ideas with the "idea of the atom as conceived by present-day physicists [which] is, in many vital respects, free from such arbitrariness." In a letter to John Slater in 1930, he unrepentantly hailed the ability of physicists to calculate binding energy for polyatomic molecules and "to establish the cases in which the valence theory of the chemist is reliable"[ ]8... 

The basic theories of physics - classical mechanics and electromagnetism, relativity theory, quantum mechanics, statistical mechanics, quantum electrodynamics - support the theoretical apparatus which is used in molecular sciences. Quantum mechanics plays a particular role in theoretical chemistry, providing the basis for the valence theories which allow to interpret the structure of molecules and for the spectroscopic models employed in the determination of structural information from spectral patterns. Indeed, Quantum Chemistry often appears synonymous with Theoretical Chemistry it will, therefore, constitute a major part of this book series. However, the scope of the series will also include other areas of theoretical chemistry, such as mathematical chemistry (which involves the use of algebra and topology in the analysis of molecular structures and reactions) molecular mechanics, molecular dynamics and chemical thermodynamics, which play an important role in rationalizing the geometric and electronic structures of molecular assemblies and polymers, clusters and crystals surface, interface, solvent and solid-state effects excited-state dynamics, reactive collisions, and chemical reactions. 

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. 

The several sections of this review include the structures, the valence theory of known structures with emphasis on the charge distribution, the nuclear resonance studies of hydrides, derivatives and related compounds, the topological extension of the valence theory and its use in making predictions, and finally some brief remarks on the interconversions of the hydrides. 

Fia. 16. Possible BsHs" structures. Preference for structure (a) is suggested by the valence theory. 

The importance of this topological extension of the valence theory is that it yields so few predictions (15), which may be summarized as follows ... 

Actually the originator of the valence theory, Frankland, was able to visualize variable valence— just as a juggler defies the human valence of 2—so he would not have balked at compounds with varying numbers of ligands. In the hands of Kekule however, the then gum of organic chemistry, the theory of valence had come to mean absolute... 

Any attempts to prepare compounds of noble gases were put to a halt by the success of the valency theory relating to a stable octet configuration of noble gases. 

In the early twentieth century, the distinction between the physical forces and the chemical forces, at the molecular level, was superfluous imder the conjugation of the atomic theories, coming from the quantum physics, with those chemical, of the valence theory. In the modem science, it was ultimately imposed the idea that the forces which hold the atoms in molecules or in crystals are physical, but expresses the reality of the chemical bondings. 

One of the goals of the ELF approach is to provide an interpretative tool of quantum chemical calculations in terms of purely chemical concepts without the recourse to the nature of the approximate wave functions. The ELF recovers many features of the simple chemical models based on a spatial distribution of the valence electron, namely, the valence theory of G. N. Lewis, the mesomery concept of C. K. Ingold, and the VSEPR model of R. J. Gillespie and R. S. Nyholm. The partition of the electron density based on a statistical criterion provides a quantum mechanical support to the hypotheses which are explicitly or implicitly assumed in these models. Indeed, this statistical approach provides at least formally a mathematical bridge between quantum mechanics and chemistry which enables to critically think about the content and the definition of many chemical concepts related to the... 

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