Tetrahedral atomic orbitals

We can extend this analysis to any molecule that forms a tetrahedral set of bonds Whenever a set of equivalent, tetrahedral atomic orbitals is required by an atom, this model assumes that the atom forms a set o/"sp3 orbitals the atom is said to be sp3 hybridized. 

An answer was provided in 1931 by Linus Pauling, who showed how an s orbital and three p orbitals on an atom can combine mathematically, or hybridize, to form four equivalent atomic orbitals with tetrahedral orientation. Shown in Figure 1.10, these tetrahedrally oriented orbitals are called sp3 hybrids. Note that the superscript 3 in the name sp3 tells how many of each type of atomic orbital combine to form the hybrid, not how many electrons occupy it. 

Thus we have shown that when s and p orbitals are available and s—p quantization is broken an atom can form four (or fewer) equivalent bonds which are directed towards tetrahedron corners. To the approximation involved in these calculations the strength of a bond is independent of the nature of other bonds. This result gives us at once the justification for the tetrahedral carbon atom and other tetrahedral atoms, such as silicon, germanium, and tin in the diamond-type crystals of the elements and, in general, all atoms in tetrahedral structures. 

We cannot generate a tetrahedron by simple overlap of atomic orbitals, because atomic orbitals do not point toward the comers of a tetrahedron. In this section, we present a modification of the localized bond model that accounts for tetrahedral geometry and several other common molecular shapes. 

A carbon atom combining with four other atoms clearly does not use the one 2s and the three 2p atomic orbitals that would now be available, for this would lead to the formation of three directed bonds, mutually at right angles (with the three 2p orbitals), and one different, non-directed bond (with the spherical 2s orbital). Whereas in fact, the four C—H bonds in, for example, methane are known to be identical and symmetrically (tetrahedrally) disposed at an angle of 109° 28 to each other. This may be accounted for on the basis of redeploying the 2s and the three 2p atomic orbitals so as to yield four new (identical) orbitals, which are capable of forming stronger bonds (cf. p. 5). These new orbitals are known as sp3 hybrid atomic orbitals, and the process by which they are obtained as hybridisation ... 

Figure 11.13 Hybridization of 5- and p- atomic orbitals, (a) Linear sp hybrid, from one s- and one p-orbital. (b) sp2 hybrid, from one s- and two p-orbitals, with a plane triangular shape, (c) sp3 hybrid, from one 5-orbital and the three p-orbitals, which has a tetrahedral shape in three dimensions.

It may be argued that we have actually started from the tetrahedral array in methane to propose a tetrahedral array of atomic orbitals in carbon. 

The VSEPR theory assumes that the four electrons from the valence shell of the carbon atom plus the valency electrons from the four hydrogen atoms form four identical electron pairs which, at minimum repulsion, give the observed tetrahedral shape. To rationalize the tetrahedral disposition of four bond-pair orbitals with those of the 2s and three 2p atomic orbitals of the carbon atom, sp3 hybridization is invoked. 

Herzberg (Nobel prize for Chemistry, 1971) commented on the two distinct photoionizations from methane that this observation illustrates the rather drastic nature of the approximation made in the valence bond treatment of CH4, in which the 2s and 2p electrons of the carbon atom are considered as degenerate and where this degeneracy is used to form tetrahedral orbitals representing mixtures of 2s and 2p atomic orbitals. The molecular orbital treatment does not have this difficulty". 

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