Hybrid Bond Orbitals

From what has been said so far, one might expect carbon with the configuration to form only com- 

Pauling and Slater have resolved this discrepancy between theory and experiment by introducing the concept 

By way of illustration let us suppose that we have a s and a p orbital available to form two bonds  

For atoms forming three covalent bonds we expect sp hybridization  

The sp orbitals have their axes in a common plane because the p orbitals are thereby utilized most effectively. The predicted overlapping power of these orbitals is 1. 99. 

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One-bond CH coupling constants Jqh ( Jch) proportional to the s character of the hybrid bonding orbitals of the coupling carbon atom, (Table 2.6, from left to right)according to... 

The energy of the one-electron bond in the lithium molecule ion is calculated with consideration of the s-p separation to be 1.19 e. v and the hybrid bond orbital involved is shown to involve about equal contributions from the 25 and 2p orbitals of the lithium atom. 

Bond angles in transition-metal tricarbonyl compounds A test of the theory of hybrid bond orbitals ... 

Some 50 years have now passed since the publication of a series of papers bearing the title The Nature of the Chemical Bond. 1 7 These papers have provided chemists, physicists, biologists, and mineralogists with the conceptual framework, based on simple valence bond theory and the theory of hybrid bond orbitals, required to investigate a myriad of problems involving the nature of the bonding exhibited in molecules and solids. The ideas contained in these papers were subsequently elaborated on in The Nature of the Chemical Bond which is probably the most often-cited book in the scientific literature.9... 

Second, the theory of hybrid bond orbitals was utilized recently to discover a new type of chemical bond involving the resonating unshared electron pair.30 31 For example, bis(bistrimethylsilylmethyl) tin(II), (CH3)3 Si 2HCSnCH Si(CH3)3 2, forms dimers in the solid state having a tin-tin bond characterized by resonance of an unshared electron pair or... 

Pauling, L. Correlation of Nonorthogonality of Best Hybrid Bond Orbitals with Bond Strength of Orthogonal Orbitals Proc. Natl. Acad. Sci. (USA) 1976, 73, 274-275. 

Herman, Z.S. Recent Advances in Simple Valence-Bond Theory and the Theory of Hybrid Bond Orbitals Int. J. Quantum Chem. 1983, 23, 921-943. 

Herman, Z.S. Pauling, L. Hybrid Bond Orbitals and Bond Strengths for Pentacovalent Bonding Croat. Chem. Acta 1984, 57, 765-778. 

Our knowledge of the properties of orbitals indicates that some of the 3d orbitals might be combined with the 45 and 4p orbitals to form bond orbitals in metals, the other 3d orbitals being unsuited to bond formation, but does not suffice to give a theoretical derivation of the number of d orbitals in each of these classes. Empirical evidence, outlined below, indicates that about 2.44 d orbitals (on the average) show only weak interatomic interactions, and that the remaining 2.56 d orbitals combine with the 5 orbital and the p orbitals to form hybrid bond orbitals. 

This system is based on the observations (Pauling 1947) that a linear relation between single-bond radius and atomic number holds for bonds of constant hybrid character, and that for an element the single-bond radius is (at least approximately) linearly dependent on the d character of the dsp hybrid bond orbitals. 

At that time I was handicapped by my remembering a misinterpretation that I had made of some results obtained in 1932 by one of my students, Ralph Hultgren (6). He had begun to make a thorough study of sets of equivalent spd hybrid bond orbitals, and soon found that he could not handle the computational problem in those precomputer days. I pointed out that the best hybrid orbitals have cylindrical symmetry about... 

The obvious conclusion to be reached is that there are three kinds of spd orbitals hybrid bond orbitals, contracted d orbitals, and about 0.70 other orbitals. In 1938 I considered this 0.70 unstable orbital per atom to be unsuited for either bond formation or... 

In cinnabar, HgS, the sulfur atom has a normal-valence structure, in which it forms two bonds with mercury atoms. The Hg—S—Hg bond angle is 105°. The mercury atom may be described as forming two oppositely directed bonds with use of two sp hybrid bond orbitals the value of the S—Hg—S angle is 172°. The bond length, 2.36 A, leads,... 

The general qualitative agreement with experiment provides support for the theory that the potential barriers to internal rotation result from the interaction of adjacent hybrid bond orbitals with a small amount of / character. The magnitude of the potential barriers, about 4 per cent of the energy of the axial bond in case that there are three interacting bonds on each of the two atoms and proportionately less for a smaller number of bonds, is also reasonable. A detailed quantum-mechanical treatment of restricted rotation carried out along the lines sketched here should yield results that would permit a detailed test of the theory to be made in the meantime I believe that the above simple treatment and the extensive empirical support of the theory provide justification for it. 

The reaction field component along the C-H and C-F bonds ought to have the same direction. Using the contact mechanism as formulated in Eqs. (1) and (7), the field in the region of the C-H will tend to increase the s character of the C-hybrid bonding orbital and hence will lead to a more positive value for /13... 

HYBRID BOND ORBITALS THE TETRAHEDRAL CARBON ATOM... 

If the radial parts of the terms of a hybrid bond orbital of the form... 

The hybrid bond orbitals discussed in the preceding chapter have been described as having only a small amount of d and / character. The bonds in many molecules and complex ions, especially those involving atoms of the transition elements, can be discussed in a simple way in terms of hybrid orbitals with a large amount of d character (and, in a few cases, / character). These bonds and a magnetic criterion for bond type are discussed in the following sections. 

Metallic Radii and Hybrid Bond Orbitals X 1-8. METALLIC RADII AND HYBRID BOND ORBITALS... 

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