Homopolar bonds

Heitler, W., London, F. (1927). Wechselwirkung neutraler Atome und hombopolare Bindung nach der Quantenmechanik [Interactions Between Neutral Atoms and Homopolar Bonding According to the Quantum Theory]. ZeitschriftfurPhysik, 44, 455 72. 

While this definition of electron-pair covalency neglects the effective charges on the bonded atoms, the designation "homopolar bond appears to be reserved for the special case of an electron-pair bond... 

However, is intrinsically restricted to homopolar bonding. In order to... 

On the homopolar line between the A(P and the C(P regions, for example, the usual anionic chemisorption of the last section and the unusual cationic chemisorption of this section coalesce, and a homopolar bond is formed between the foreign atom and the lattice. One electron is lost from an impurity level for each foreign atom adsorbed, and this homopolar chemisorption is depletive. 

Figures 2c and 2b depict, respectively, a strong donor and a strong acceptor bond of a Cl atom formed from a weak bond (see Fig. 2a ), when a free hole or, respectively, a free electron, is drawn into the bond. In the first case (Fig. 2c ) we have a quasi-molecule CI2 with typical homopolar bond, in the second case (Fig. 2b ) a quasi-molecule NaCl with its characteristic ionic bond.

In both cases we may consider that the free valence of the Na atom is saturated by the (positive or, respectively, negative) valence of the surface. The mutual saturation of two valencies of the same sign (positive valence of Na atom + free positive valence of the surface) leads to the formation of a homopolar bond (Fig. 2b) the mutual saturation of two valencies of opposite sign (positive valence of Na atom -f- free negative valence of the surface) leads to the formation of an ionic bond (Fig. 2c). In the given case, the strong i-bond and the strong p-bond thus represent valence-saturated forms of chemisorption. They are symbolically depicted in Fig. 4b and, respectively. Fig. 4c. 

Contents Formal Oxidation Numbers. Configurations in Atomic Spectroscopy. Characteristics of Transition Group Ions. Internal Transitions in Partly Filled Shells. Inter-Shell Transitions. Electron Transfer Spectra and Collectively Oxidized Ligands. Oxidation States in Metals and Black Semi-Conductors. Closed-Shell Systems, Hydrides and Back-Bonding. Homopolar Bonds and Catenation. Quanticule Oxidation States. Taxological Quantum Chemistry. 

Raman studies, 23 287, 294 residue compounds, 23 283, 314-315 staging, 23 282-283 with xenon fluorides, 23 296-300 comparative survey of, 1 263-264 mode of reaction of, 1 224-226 oxide, homopolar bonding and, 1 226-230 polar bonding... 

Bipolarons are mobile electron pairs. They have been identified in a small temperature interval above the semiconductor-metal transition in Ti407 In this case, they represent mobile electron-pair bonds in a mixed-valence compound, the electrons condensing into metal-metal homopolar bonds that are ordered at low temperatures, but become disordered and mobile at somewhat higher temperatures. 

In M0O2 and WO2, R < R and one d electron per metal atom is involved in cation-cation homopolar bonding through fn orbitals. The extra d electron partly fills the n band, rendering the oxides metallic (Fig. 6.16(d)). This simplified picture does... 

The simple theory of the heteropolar bond was developed rapidly in contrast to the theory of the homopolar bond where great difficulties were encountered. Nevertheless, in the last decades important advances have been made, but the enormous mathematical difficulties encountered have resulted in the strict theory being applied only to the simplest examples of chemical combination. The theory of the ionic bond has no difficulties of a mathematical kind and in consequence can be used for more complicated compounds. In the following pages this theory will be treated first, and later a very elementary, schematic presentation of the theory of the homopolar bond will be given. 

Polarization is one of the reasons for the asymmetrical form of the water molecule, and also may be partially responsible for the non-linearity of H2S molecules. Polarization would lead to the pyramidal shape observed for the molecules NH3 and PH3, but it is very doubtful whether it can be held responsible for the asymmetrical form of molecules such as PC13 and SOa. In these molecules, the central ion is positive, if it is assumed that the bonds in these compounds are ionic, and since positive ions have not a large polarizability, the distortion of the molecule can scarcely be due to polarization effects. Indeed, we cannot continue to consider these compounds as purely ionic in character, but will find it necessary to explain their asymmetry on the basis of the homopolar bond (see Section 53). Even in hydrogen compounds such as H20 and NH3 we shall find we have to take into account their partial homopolar structure in order to arrive at a really satisfactory explanation of their structures. 

Some metals crystallize in more than one structural type, which means that there are two alio tropic modifications. The metals marked do not conform precisely to the closest-packed structure, but deviate slightly from it. Uranium, manganese, gallium and indium have very abnormal structures, and the last two are transitional between metallic and non-metallic elements of the carbon group. The picture presented by the metallic structures is utterly different from that of elements of the four last groups of the periodic system. The homopolar bonds of these latter strive to produce a state in which the number of neighbours of each atom is determined by its valency. In the other elements, however, forces appear to be acting that tend to surround each atom with as many other atoms as possible. 

Occasionally, some residual homopolar bonds remain in metals, for example a small per cent of the molecules Li—Li, Na—Na, etc. are found in the vapours of these metals, analogous to the hydrogen molecule, but there is no trace of them in the solid state. The most characteristic property of metals, in which the smallest potential difference produces an electric current, is their electrical conductivity. Since no transport of mass takes place in a metallic conductor, a metal must contain free electrons, from which it follows that positive ions must also be present. The picture of a metal is thei efore one in which the lattice is composed of positive ions held together by electrons which move freely in the space between. It is as though the ions were cemented together by an electronic gas. 

In the homopolar bond, a pair of atoms are coupled together by two electrons while, in a metal, all the electrons hold all the ions together in the crystal. The theory of the metallic bond is even more complicated than that of the homopolar bond, as the subsequent discussion will show. In this section we shall only discuss how metallic properties are distributed in the periodic system. 

The covalent energy, Ec, arising from electron sharing. It is a maximum in a homopolar bond and decreases with ionicity. 

While the H—H bond in H2 was considered as purely covalent in Heitler and London s paper (1) (Eq. 3.2 and Structure 1), as we saw in Chapter 2, the exact description of H2 or any homopolar bond OPvB-fuii) involves a small contribution of the ionic structures 3 and 4, which mix by configuration interaction (Cl) in the VB framework. Typically, for homopolar and weakly polar bonds, the weight of the purely covalent structure is 75%, while the ionic structures share the remaining 25%. By symmetry, the wave function maintains an average neutrality of the two bonded atoms (Eq. 3.4). 

A homopolar bond is non-polar where as a heteropolar bond is polar. The polar nature is described as polarity of the bond. 

Actually, the eigenvalues of eq. (37) are even functions of S12. In the particular case of homopolar bonds with Hu = H22, approximate eigenvalues are... 

When secondary complications are surely eliminated, it is worth while to examine the possibilities of solvation in comparing reaction rates in various solvents and in the gas phase. An important classification of different types of solvation has been made recently by Moelwyn-Hughes and Sherman8 emphasizing the different kinds of electrostatic attractions. Quantum mechanical calculations are satisfactory in explaining strictly homopolar bonds but electrostatic forces are important not only in electrolytic solutions but also in many reactions which are not considered to be ionic. 

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