3.2: Valence Bond Theory

In introductory chemistry courses, you have learned that electrons in an atom are located in atomic orbitals with quantized energy. Depending on the quantum numbers, these orbitals may be spherical (s-orbitals), shaped like dumbbells (p-orbitals), and so forth. As a molecular bond is made by sharing electrons between atoms, it makes logical sense that the interaction of atomic orbitals must be a fundamental component of a more accurate bonding theory. Note that VSEPR theory does not utilize any aspect of atomic orbitals, and thus (1) does not always provide an accurate description of molecular geometry and (2) does not provide any useful information about how a molecule may react. All of the more advanced bonding theories that we will cover rely on a thorough understanding of atomic orbitals and how they can be used to predict reactivity and geometry.

The first of the orbital-based bonding theories that we will cover is Valence Bond theory. The basic premise of Valence Bond theory is that the atomic or hybrid orbitals on two atoms overlap to form a bond. Hybrid orbitals form when two or more atomic orbitals on the same atom combine to create the same number of hybrid orbitals. The key point to remember is the number of hybrid orbitals that need to be formed is equal to the number of σ-bonds plus the number of lone pairs. Note: we will see exceptions to this in future sections (see Part 3 Section 4.4). The most common atoms in organic molecules are found in the second row of the periodic table. The valence electrons for these atoms are in 2s and 2p atomic orbitals, so we will focus our analysis on hybrid orbitals that form from the combination of 2s and 2p orbitals.

The number of hybrid orbitals that you form must be equal to the number of atomic orbitals that you combine. If four hybrid orbitals are required for bonding, then all four atomic orbitals (all three 2p and one 2s) must be combined to form four new sp³ orbitals (sp³ designates that it is comprised of one s-orbital and three p-orbitals). These four sp³ orbitals provide a tetrahedral bonding framework, which matches the geometry predicted by VSEPR. Such a geometry would not have been possible without hybridizing the atomic orbitals.

If three hybrid orbitals are required for bonding, then three atomic orbitals must be combined. This can be achieved by combining the 2s orbital with two 2p orbitals to form three new sp² hybrid orbitals (sp² designates that it is comprised of one s-orbital and two p-orbitals). These three sp² orbitals provide a trigonal planar bonding framework (shown in purple below). The remaining 2p orbital (2p_z) is unchanged and is perpendicular to the sp² framework (shown in red below).

The final case we will consider is if only two hybrid orbitals are required for bonding. In this scenario, only two atomic orbitals must be combined. This can be achieved by combining the 2s orbital with the 2p_x orbital to form two new sp hybrid orbitals (sp designates that it is comprised of one s orbital and one p-orbital). These two sp orbitals provide a linear bonding framework (shown in purple below). The remaining 2p orbitals (2p_y and 2p_z) are unchanged and are perpendicular to the sp framework (shown in red below).

Let's examine methane using valence bond theory. The carbon in methane has 4 electrons in its valence shell, which are located in 2s and 2p atomic orbitals. To make 4 σ-bonds, the carbon must hybridize the valence shell to make 4 hybrid orbitals, which means the central carbon has to be sp³ hybridized to accommodate the bonding network. Each of the hydrogens has 1 electron in its 1s orbital (shown in blue below). Each of the orbitals overlaps to share one electron each, thus creating 4 new σ-bonds in a tetrahedral arrangement.

Let's now examine ethylene using Valence Bond theory. Each of the carbons in ethylene has 4 electrons in its valence shell, which are located in 2s and 2p atomic orbitals. To make 3 σ-bonds, the carbon must hybridize the valence shell to make 3 hybrid orbitals. The three atomic orbitals are converted to three sp² hybrid orbitals. Combination of a spherical orbital and two directional orbitals leads to the formation of three directional orbitals of equal energy in a trigonal planar shape and one remaining p-orbital, each with one electron. To complete our valence bond analysis of ethylene, it is easiest to first start with the two carbon atoms. To form a π-bond between the two carbon atoms, the p-orbitals (red orbitals) on the carbon atoms must be co-planar. Once the central σ-bond is made between the two sp² orbitals and the π-bond is made between the two p-orbitals, the rest of the hydrogen atom framework can easily be added. As you can see from the picture, if the hybrid orbitals on each carbon are trigonal planar and the p-orbitals are co-planar, then Valence Bond theory predicts that all of the carbons and hydrogens are co-planar, which is supported by experimental evidence.

Finally, let's examine acetylene (ethyne) using Valence Bond theory. The carbon in acetylene has 4 electrons in its valence shell, which are located in 2s and 2p atomic orbitals. To make 2 σ-bonds, the carbon must hybridize the valence shell to make 2 hybrid orbitals, which means the central carbon has to be sp hybridized to accommodate the bonding network. To complete our valence bond analysis of acetylene, it is easiest to first start with the two carbon atoms. To form the two π-bonds between the carbon atoms, the p-orbitals (red orbitals) must be co-planar. Once the central σ-bond is made between the two sp orbitals and the two π-bonds are made, the rest of the hydrogen atom framework can easily be added. As you can see from the picture, if the hybrid orbitals on each carbon are linear, then Valence Bond theory predicts that all of the carbons and hydrogens are linear, which is supported by experimental evidence.

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