Directed valences

The concepts of directed valence and orbital hybridization were developed by Linus Pauling soon after the description of the hydrogen molecule by the valence bond theory. These concepts were applied to an issue of specific concern to organic chemistry, the tetrahedral orientation of the bonds to tetracoordinate carbon. Pauling reasoned that because covalent bonds require mutual overlap of orbitals, stronger bonds would result from better overlap. Orbitals that possess directional properties, such as p orbitals, should therefore be more effective than spherically symmetric 5 orbitals. 

The spherical harmonics in real form therefore exhibit a directional dependence and behave like simple functions of Cartesian coordinates. Orbitals using real spherical harmonics for their angular part are therefore particularly convenient to discuss properties such as the directed valencies of chemical bonds. The linear combinations still have the quantum numbers n and l, but they are no longer eigenfunctions for the z component of the angular momentum, so that this quantum number is lost. 

Due to the simplicity and the ability to explain the spectroscopic and excited state properties, the MO theory in addition to easy adaptability for modern computers has gained tremendous popularity among chemists. The concept of directed valence, based on the principle of maximum overlap and valence shell electron pair repulsion theory (VSEPR), has successfully explained the molecular geometries and bonding in polyatomic molecules. 

Independently of each other, Pauling and Slater worked out a quantum mechanical explanation of the directional valences characteristic of chemical molecules. They did this by proposing directional properties for the p wave functions and for the sp3 wave functions resulting from "hybridization" of electron wave functions, or orbitals.73... 

JACS 53 (1931) 32253237 John C. Slater, "Directed Valence in Polyatomic Molecules," Physical Review 37 (1931) 481489. Also see Linus Pauling, The Nature of the Chemical Bond (1939) and Schweber, "Young John Clarke Slater," 386387. 

Slater, John Clarke. "Directed Valence in Polyatomic Molecules." Physical Review 37 (1931) 481489. 

In addition to chemical reactions which result in direct valency coupling, other reactions, for example, those that lead to the formation of charge-transfer complexes are rather generally characteristic of the [2.2]para-cyclophane system. 

Slater, J.C. Directed Valence in Polyatomic Molecules. Physic. Rev. 37,... 

A rigorous quantum-mechanical treatment of directed valence bonds has not been given, for the reason that the Schrodinger wave equation has not been rigorously solved for any complicated molecule. Several approximate treatments have, however, been carried out, leading in a... 

The foregoing discussion of valence is. of course, a simplified one. From ihe development of the quantum theory and its application to the structure of the atom, there has ensued a quantum theory of valence and of the structure of the molecule, discussed in this hook under Molecule. Topics thal are basically important to modem views of molecular structure include, in addition to those already indicated the Schroedinger wave equation the molecular orbital method (introduced in the article on Molecule) as well as directed valence bonds bond energies, hybrid orbitals, the effect of Van der Waals forces and electron-dcticiem molecules. Some of these subjects are clearly beyond the space available in this book and its scope of treatment. Even more so is their use in interpretation of molecular structure. [However, sec Crystal Field Theory and Ligand.)... 

The problem of directed valence is treated from a group theory point of view. A method is developed by which the possibility of formation of covalent bonds in any spatial arrangement from a given electron configuration can be tested. The same method also determines the possibilities of double and triple bond formation. Previous results in the field of directed valence are extended to cover all possible configurations from two to eight s, p, or d electrons, and the possibilities of double bond formation in each case. A number of examples are discussed. 

In the previous papers no attempt has been made to discover all the possible stable electron groups which lead to directed valence bonds, nor have the possibilities of double bond formation been completely explored. In the present paper both of these deficiencies in the theory have been removed. 

In otder to construct such sets of orbitals, it is most convenient to make use of group theory. Each set of equivalent directed valence orbitals has a characteristic symmetry group. If the operations of this group are performed on the orbitals, a representation, which is usually reducible, is generated. By means of the character table of the group7 this representation, which we shall call the a representation, can be reduced to its component irreducible representations. The s, p, and d orbitals of the atom also form representations of the group, and can also be divided into sets which form irreducible representations.8... 

In addition to cobalt and iron (discussed above), other metals frequently function as cofactors in enzyme-catalyzed reactions. Like coenzymes, they are useful because they offer something not available in amino acid side chains. The most important of such features of metals are their high concentration of positive charge, their directed valences for interacting with two or more ligands, and their ability to exist in two or more valence states. 

G.E. Kimball, Directed valence, Journal of Chemical Physics 8 (1940) 188-198. 

Grabner et al. have shown that in titanium dioxide sols containing chloride (which is either introduced into the solution as HC1 to adjust the pH or is present on the particle surface when TiCU is used as starting compound to prepare Ti02) Cl2 " radical anions are formed. Their formation was postulated to occur by direct valence-band hole oxidation of surface adsorbed Cl" (reactions (7.18), (7.19)) [4f]. 

Intramolecular rearrangements provide dramatic evidence to the inadequacy of the theories of directed valence bonds. The Beckmann rearrangement of ketoximes into acid amides, represented by the scheme ... 

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