Free valence definition

The definition of free valence was originally given in terms of bond orders defined by resonance theory for a general account see ref. 7. 

Figure 3.4 Dispersion (Ns/Nt) and free-valence dispersion (Dfv) for cubo-octahedra dependence on number of atoms m per side (see text for definition of Dfv).

The synthon S(A) over an atomic set A is defined as one or several molecules (or their parts) composed of atoms from the set A. In contrast to the definition of the Ensemble of Molecules, EM (A) [13], S(A) is more general because it may also involve free valences, i.e. bonds which do not connect two atoms but only start from an atom. The set of all synthons constructed over the atomic set A is called the Family of Isomeric Synthons and is denoted FIS(A). Implicitly, it means... 

Definition. A chemical group is a substructure having all its free valences equivalent, whereas a fragment is a substructure having two or more nonequivalent free valences. 

A free valence in a group of atoms—an unsaturated molecule or radical—is really the property of a definite atom rather than resulting from the total group of atoms. This follows immediately from hypothesis V, which focused attention on the dependency of the connection possibilities on the order in which the atoms are connected. With this we have obtained the possibility of representing molecules by structure formulas with valence lines , as is usual in chemistry, so that the formal equivalence of the concept of valence to chemistry is evident. 

In 1923. Lewis published a classic book (later reprinted by Dover Publications) titled Valence and the Structure of Atoms and Molecules. Here, in Lewis s characteristically lucid style, we find many of the basic principles of covalent bonding discussed in this chapter. Included are electron-dot structures, the octet rule, and the concept of electronegativity. Here too is the Lewis definition of acids and bases (Chapter 15). That same year, Lewis published with Merle Randall a text called Thermodynamics and the Free Energy of Chemical Substances. Today, a revised edition of that text is still used in graduate courses in chemistry. 

According to the electronic theory, a particle chemisorbed on the surface of a semiconductor has a definite affinity for a free electron or, depending on its nature, for a free hole in the lattice. In the first case the chemisorbed particle is presented in the energy spectrum of the lattice as an acceptor and in the second as a donor surface local level situated in the forbidden zone between the valency band and the conduction band. In the general case, one and the same particle may possess an affinity both for an electron and a hole. In this case two alternative local levels, an acceptor and a donor, will correspond to it. 

The first satisfactory definition of crystal radius was given by Tosi (1964) In an ideal ionic crystal where every valence electron is supposed to remain localised on its parent ion, to each ion it can be associated a limit at which the wave function vanishes. The radial extension of the ion along the connection with its first neighbour can be considered as a measure of its dimension in the crystal (crystal radius). This concept is clearly displayed in figure 1.7A, in which the radial electron density distribution curves are shown for Na and Cl ions in NaCl. The nucleus of Cl is located at the origin on the abscissa axis and the nucleus of Na is positioned at the interionic distance experimentally observed for neighboring ions in NaCl. The superimposed radial density functions define an electron density minimum that limits the dimensions or crystal radii of the two ions. We also note that the radial distribution functions for the two ions in the crystal (continuous lines) are not identical to the radial distribution functions for the free ions (dashed lines). 

Table III shows the abundance of various elements in the earth s crust and the oxidation states they frequently occupy. The table indicates that of the 14 most abundant elements, only six participate in redox reactions in the surface layers of the earth. [PH3 seems to be extremely rare (42) and will not be discussed.] Because by definition free oxygen as 02 is absent in the anoxic zone, it is evident that oxides of Fe(III) are the most important oxidizers in anoxic environment and that S042 and higher oxides of manganese are of importance only locally. Reducing compounds of importance are organic matter and sulfides, the latter frequently from volcanic emanations. Hydrogen is commonly combined with other elements, as in H20, CH4, and NH3 but may locally occur free as H2. Since iron is the most widespread element that can serve as an oxidizer in the anoxic environment the distribution of the valence states of iron in various rocks is of interest (see Table IV). Sandstones frequently have a high Fe203/Fe0 ratio, but shales and clays may also be highly oxidized as shown in Tables IV and V. Since approximately 75% of the earth s surface is covered with sediments and since the sediments...

The most definite and indisputable evidence for the existence of free radicals is obtained from spectroscopy. Physicists are able to interpret band spectra without ambiguity on the basis of such units as OH, CN, BeCl, SiO, CH2, C2 and others. There is a whole host of radicals of this type which can explain quantitatively all the lines of a complex band spectrum and there is no other way to explain them. Moreover calculations based on quantum mechanics show that many of these free radicals, which violate all rules of the classical theories of valence, are stable and do not necessarily decompose at ordinary or even at moderately high temperatures. The difficulty in finding them is not that they are too unstable but rather that they are so very reactive that they combine immedi-... 

Secondary atomic properties as those, which require, in addition to the experimentally determined quantities for the free atoms, theoretical concepts of the quantum mechanical characerisation of the electronic structure of the atoms. These are orbitals, the shell structure of atoms with emphasis of the valence shell as well as concepts like hybridisation, the definition of the valence state and the valence state promotion energy in its relation to the spectroscopic term values of the free atoms. 

Pantclides (1975c) also discussed the valence bands for the inert-gas solids, indicating that they consist of a narrow p band and an s band, which may be taken as completely sharp. He gave a universal width for the p band, of fi / md), with f/v = 4.2. (Again, his numerical value was different because of a different definition of d.) Presumably the conduction bands, corresponding to electrons added to the crystal, would be quite like free-electron bands. 

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