4.1 Valence Bond Theory

Objectives

By the end of this section, you will be able to:

• Describe the formation of covalent bonds in terms of atomic orbital overlap
• Define and give examples of σ and π bonds

As we know, a scientific theory provides a strongly supported explanation for observed natural laws or large bodies of experimental data. For a theory to gain acceptance, it must explain experimental data and be able to predict behavior. For example, VSEPR theory has gained widespread acceptance because it predicts three-dimensional molecular shapes. These predictions align with experimental data collected from thousands of different molecules. However, VSEPR theory does not provide an explanation of chemical bonding.

There are successful theories that describe the electronic structure of atoms. We can use quantum mechanics to predict the specific regions around an atom where electrons are likely to be located. For instance, an s orbital has a spherical shape, while a p orbital has a dumbbell shape, and so forth. However, these predictions only describe the orbitals around free atoms. When atoms bond to form molecules, atomic orbitals are not sufficient to describe the regions where electrons will be located in the molecule. A more complete understanding of electron distributions requires a model that can account for the electronic structure of molecules. One popular theory states that a covalent bond forms when two atoms share a pair of electrons, which are simultaneously attracted to the nuclei of both atoms. In the following sections, this discuss will cover how valence bond theory and hybridization describe such bonds.

Valence Bond Theory

Valence bond theory describes a covalent bond as the overlap of half-filled atomic orbitals, each containing a single electron. This overlap yields a pair of electrons shared between the two bonded atoms. We consider orbitals on two different atoms to overlap when portions of one orbital and a portion of a second orbital occupy the same region of space.

A covalent bond forms when two conditions are met: (1) an orbital on one atom overlaps with an orbital on a second atom, and (2) the single electrons in each orbital combine to create an electron pair. The mutual attraction between this negatively charged electron pair and the positively charged nuclei of the two atoms serves to physically link the atoms. This attraction creates a force that we define as a covalent bond. The strength of a covalent bond depends on the extent of overlap of the orbitals involved, with more extensive overlap resulting in stronger bonds.

The energy of the system depends on how much the orbitals overlap. Figure 1 below illustrates how the sum of the energies of two hydrogen atoms (the colored curve) changes as they approach each other. When the atoms are far apart, there is no overlap between their orbitals. By convention, we set the sum of the energies at zero in this state. As the atoms move together, their orbitals begin to overlap, allowing each electron to feel the attraction of the nucleus in the other atom. At the same time, the electrons and nuclei begin to repel each other.

Bond Formation and Stability

While the atoms remain widely separated, the attractions slightly outweigh the repulsions. This balance causes the energy of the system to decrease as a bond begins to form. As the atoms get closer, the overlap of their orbitals increases, enhancing the nuclei’s attraction for the electrons. However, this also leads to increased repulsions among the electrons and between the nuclei.

At a specific distance between the atoms—varying depending on the atoms involved—the energy reaches its lowest (most stable) value. This optimal distance between the two bonded nuclei is the bond distance. The bond remains stable because, at this point, the attractive and repulsive forces create the lowest possible energy configuration. If the distance between the nuclei decreases further, the repulsions between them will increase. Additionally, the repulsion among electrons will also grow as they are confined closer together. As a result, there repulsive forces will outweigh the attractive forces, causing the energy of the system to rise and destabilize, as shown at the far left of Figure 1.

Bond	Length (pm)	Energy (kJ/mol)	Bond	Length (pm)	Energy (kJ/mol)
H–H	74	436	C–O	140.1	358
H–C	106.8	413	$C=O$	119.7	745
H–N	101.5	391	$C≡O$	113.7	1072
H–O	97.5	467	H–Cl	127.5	431
C–C	150.6	347	H–Br	141.4	366
$C=C$	133.5	614	H–I	160.9	298
$C≡C$	120.8	839	O–O	148	146
C–N	142.1	305	$O=O$	120.8	498
$C=N$	130.0	615	F–F	141.2	159
$C≡N$	116.1	891	Cl–Cl	198.8	243

In addition to the distance between two orbitals, the orientation of orbitals also affects their overlap (other than for two s orbitals, which are spherically symmetric). Greater overlap is possible when orbitals are oriented such that they overlap on a direct line between the two nuclei. Figure 3 below illustrates this for two p orbitals from different atoms; the overlap is greater when the orbitals overlap end to end rather than at an angle.

The overlap of two s orbitals (as in H₂), the overlap of an s orbital and a p orbital (as in HCl), and the end-to-end overlap of two p orbitals (as in Cl₂) all produce sigma bonds (σ bonds), as illustrated in Figure 4 a-c, respectively. A σ bond is a covalent bond where the electron density concentrates along the internuclear axis; in other words, a line between the nuclei passes through the center of the overlap region. In valence bond theory, single bonds in Lewis structures are described as σ bonds.

A pi bond (π bond) is a type of covalent bond that results from the side-by-side overlap of two p orbitals, as illustrated in Figure 5. In a π bond, the regions of orbital overlap lie on opposite sides of the internuclear axis. Along the axis itself, there is a node, that is, a plane with no probability of finding an electron.

While all single bonds are σ bonds, multiple bonds consist of both σ and π bonds. As the Lewis structures below suggest, O₂ contains a double bond, and N₂ contains a triple bond. A double bond consists of one σ bond and one π bond. In contrast, a triple bond consists of one σ bond and two π bonds. Between any two atoms, the first bond that forms will always be a σ bond. However, there can only be one σ bond in any given location. In any multiple bond, there will be one σ bond, while the remaining bonds will be π bonds. This chapter provides a more detailed description of these bonds later on.

As seen in the table above, an average carbon-carbon single bond is 347 kJ/mol, while in a carbon-carbon double bond, the π bond increases the bond strength by 267 kJ/mol. Adding an additional π bond causes a further increase of 225 kJ/mol. We can see a similar pattern when we compare other σ and π bonds. Thus, each individual π bond is generally weaker than a corresponding σ bond between the same two atoms. In a σ bond, there is a greater degree of orbital overlap than in a π bond.