Methane hybrid orbital description

We are now ready to account for the bonding in methane. In the promoted, hybridized atom each of the electrons in the four sp3 hybrid orbitals can pair with an electron in a hydrogen ls-orbital. Their overlapping orbitals form four o-bonds that point toward the corners of a tetrahedron (Fig. 3.14). The valence-bond description is now consistent with experimental data on molecular geometry. 

Such a transformation can be used for relocalizing a given set of delocalized molecular orbitals in conformity with the chemical formula. For instance, the occupied orbitals of methane can be transformed into orbitals very close to simple two-center MO s constructed from tetrahedral sp3 hybrid orbitals and Is hydrogen orbitals 24,25,26) a. unitary transformation can hardly modify the wave function, except for an immaterial phase factor therefore, it leads to a description which is as valid as that in terms of the canonical delocalized Hartree-Fock orbitals. Of course, the localization obtained in this way is not perfect, but it is usually much better than is often believed. In the case of methane, the best localized orbitals are uniquely determined by symmetry 27> for less symmetric molecules one needs a criterion for best localization 28 29>, a problem on which we shall not insist here. A careful inspection reveals that there are three classes of compounds ... 

The valence bond description of methane, ammonia, and water predicts tetrahedral geometry. In methane, where the carbon valence is four, all the hybrid orbitals are involved in bonds to hydrogen. In ammonia and water, respectively, one and two nonbonding (unshared) pairs of electrons occupy the remaining orbitals. While methane... 

Conceptual, mathematical, and physical models are essential tools in organic chemistry because they help rationalize the results of experiments (observables) with theory (nonobservables). Yet the paradox is that these models may be most useful to us when they are oversimplified to the point of being incorrect in some way. Without a straight line or pair of dots to represent a chemical bond, we would find it difficult to describe chemistry in a practical way. Yet in some cases we find it advantageous to draw those lines curved instead of straight, and sp hybrid orbitals cannot be relied on even to predict all of the properties of methane. A more detailed description of that line and of those orbitals can be made only with the help of computers and high level mathematics. 

The s and p orbitals used in the quantum mechanical description of the carbon atom, given in Section 1.10, were based on calculations for hydrogen atoms. These simple s and p orbitals do not, when taken alone, provide a satisfactory model for the tetravalent— tetrahedral carbon of methane (CH4, see Practice Problem 1.22). However, a satisfactory model of methane s structure that is based on quantum mechanics can be obtained through an approach called orbital hybridization. Orbital hybridization, in its simplest terms, is nothing more than a mathematical approach that involves the combining of individual wave functions for r and p orbitals to obtain wave functions for new orbitals. The new orbitals have, in varying proportions, the properties of the original orbitals taken separately. These new orbitals are called hybrid atomic orbitals. 

The strong bonds are classified as covalent, ionic, or metallic. Figure 1.5 illustrates the covalent bonds for fluorine, Fj, and methane, CH4. The bonds involve sharing of electrons between the bonding partners. Important in the description of a covalent bond is its directiveness, governed by the molecular oibital that contains the electron pair. Most of the bonds of interest in polymer science involve hybrid bonds of s and p orbitals (molecular orbitals are described by combinations of atomic orbitals, see also Fig. 1.3). Because of the close approach of the atoms in a covalent bond and the frequent involvement of only s and p orbitals in bonding, coordination numbers, CN, of one to four are most frequent. 

The descriptive valence bond approach to the bonding in ethylene and acetylene and their congeners is analogous to that of methane. In ethylene (Fig. 1.3), each carbon bears three ligands and sp hybridization, wherein three sp orbitals are... 

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