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Valence Bond Theory

Earlier we saw that covalent bonding requires the sharing of electrons between two atoms, so that each atom can complete its valence shell. But how does this sharing process occur? Remember that we can only estimate the likelihood of finding an electron in a certain area as a probability. This probability is represented as a distribution in space that we call an atomic orbital (Figure 9.5 “Representations of s and p atomic orbitals”).

The valence bond theory states that atoms in a covalent bond share electron density through the overlapping of their valence atomic orbitals. This creates an area of electron pair density between the two atoms. Since these electrons are simultaneously attracted to both nuclei, the electron pair holds the two atoms together.

Let’s examine the simplest case of atomic overlap resulting in a covalent bond, the formation of H₂ from two hydrogen atoms (Figure 9.6 “A diagram showing the overlap of s orbitals of two hydrogen atoms to form H₂”). The 1s orbitals of the two hydrogens approach each other and overlap to form a bond that has cylindrical symmetry known as a sigma bond (σ bond). Repulsion forces between the two nuclei and between the two electrons are also present. The optimal distance between atoms, which maximizes the attractive forces and minimizes the repulsive forces, gives the H-H sigma bond a length of 74 pm.

For molecules that contain double or triple bonds, one of these bonds is a sigma bond, and the remaining multiple bonds are a different type of bond known as a pi bond (π bond). Pi bonds result from the sideways overlap of p orbitals, placing electron density on opposite sides of the internuclear axis (Figure 9.7 “Pi bond diagram showing sideways overlapping of p orbitals”).

Hybrid Orbitals

sp³ hybridization

A problem arises when we apply the valence bond theory method of orbital overlap to even simple molecules like methane (CH₄) (Figure 9.8 “Methane”). Carbon (1s² 2s² 2p²) only has two unpaired valence electrons that are available to be shared through orbital overlap, yet CH₄ has four C-H σ bonds!

In 1931, Linus Pauling (Figure 9.9) proposed a mathematical mixing of atomic orbitals known as hybridization. The 2s and three 2p orbitals are averaged mathematically through hybridization to produce four degenerate sp³ hybrid orbitals (Figure 9.10 “Hybridization of carbon to generate sp³ orbitals”). Note that in hybridization, the number of atomic orbitals hybridized is equal to the number of hybrid orbitals generated.

The sp³ orbitals, being a combination of a spherical s orbital and propeller- (or peanut-) shaped p orbital, give an unsymmetrical propeller shape where one lobe of the orbital is larger (fatter) than the other (Figure 9.11 “An sp³ hybridized atomic orbital”). This larger lobe is typically used for orbital overlap in covalent bonding.

According to VSEPR theory, the four degenerate orbitals will arrange as far apart from each other as possible, giving a tetrahedral geometry with each orbital 109.5^o apart (Figure 9.12 “A carbon atom’s four tetrahedral sp³ hybridized orbitals”).

sp² hybridization

Let’s examine another simple molecule, ethene (C₂H₄) (Figure 9.13 “Ethene”). Each carbon of ethene is bonded to two hydrogens and a carbon. There is also a double bond between the two carbons.

Both the unhybridized atomic orbitals of carbon and the sp³ hybridization we just examined do not explain the bonding observed in ethene. In this case, only the 2s and two of the 2p orbitals hybridize to give three new sp² hybridized orbitals capable of forming the three σ bonds of each carbon in ethene (Figure 9.14 “Hybridization of carbon to generate sp² orbitals”).

The three hybridized orbitals arrange in a trigonal planar structure with a bond angle of 120° following VSEPR (Figure 9.15 “A carbon atom’s trigonal planar  sp² hybridized orbitals”).

The unhybridized 2p orbital in both carbons are left available to form the double bond’s π bond.

sp hybridization

The final example of hybridization we will examine is the molecule ethyne (C₂H₂) (Figure 9.16 “Ethyne”).

The carbons in ethyne are each sigma bonded to a single hydrogen, but triple bonded to each other. Again, the models of hybridization we have looked at so far are insufficient to explain the bonding pattern observed. In ethyne, only the 2s and one of the 2p orbitals hybridize to give two new sp hybridized orbitals capable of forming the two σ bonds of each carbon in ethyne (Figure 9.17 “Hybridization of carbon to generate sp orbitals”).

The two hybridized sp orbitals arrange linearly with a bond angle of 180^o following VSEPR (Figure 9.18 “A carbon atom’s linear sp hybridized orbitals”).

The two remaining unhybridized 2p orbitals in both carbons are left available to form the triple bond’s two π bonds.

Other hybridizations

Other hybridizations are possible, allowing us to apply valence bond theory to explain the bonding patterns observed in most real molecules. Some additional hybridizations are summarized in Table 9.5 “Hybrid Orbitals and Geometry.”

Table 9.5 Hybrid Orbitals and Geometry^[1]

Atomic Orbitals Used	Hybrid Orbitals Formed	Geometry	Example Compound
s,p	Two sp orbitals		CO2
s,p,p	Three sp2 orbitals		SO3
s,p,p,p	Four sp3 orbitals		GeCl4
s,p,p,p,d	Five dsp3 orbitals		PCl5
s,p,p,p,d,d	Six d2sp3 orbitals		Mo(CO)6