- Describe valence bond theory as it pertains to the formation of a covalent bond between atoms.
- Describe the process of electron promotion and hybridization during the formation of hybrid orbitals.
- Explain the relationship between electron domain geometry and the various types of hybrid orbitals.
- Distinguish between sigma and pi bonding.
- hybrid orbitals
- pi bond (π)
- sigma bond (σ)
- valence bond theory
Check Your Understanding
Recalling Prior Knowledge
- How are electrons arranged in atomic orbitals?
- What is the difference between the electron domain geometry of a molecule and its molecular geometry?
Earlier in this chapter, you learned how to draw Lewis electron-dot structures for molecules and predict their shapes using VSEPR theory. In this lesson, we will see how these concepts relate to the way in which electrons behave in their atomic orbitals when a covalent bond forms.
Valence Bond Theory
You have learned that a covalent bond forms when the electron clouds of two atoms overlap with each other. In a simple H2 molecule, the single electron in each atom becomes attracted to the nucleus of the other atom in the molecule as the atoms come closer together. An optimum distance between the two nuclei, equal to the bond length, is eventually attained, and the potential energy reaches a minimum. At this point, a stable single covalent bond has formed between the two hydrogen atoms. Other covalent bonds form in the same way as unpaired electrons from two atoms “match up” to form the bond. In a fluorine atom, there is an unpaired electron in one of the 2p orbitals. When a F2 molecule forms, the 2p orbitals from each of the two atoms overlap to produce the F−F covalent bond. The overlapping orbitals do not have to be of the same type. For example, in a molecule of HF, the 1s orbital of the hydrogen atom overlaps with the 2p orbital of the fluorine atom (Figure below).
In a molecule of hydrogen fluoride (HF), the covalent bond occurs due to an overlap between the 1s orbital of the hydrogen atom and the 2p orbital of the fluorine atom.
In essence, any covalent bond results from the overlap of atomic orbitals. This idea forms the basis for a quantum mechanical theory called valence bond (VB) theory. In valence bond theory, the electrons in a molecule are assumed to occupy atomic orbitals of the individual atoms and a bond results from overlap of those orbitals.
The bonding scheme described by valence bond theory must account for molecular geometries as predicted by VSEPR theory. To do that, we must introduce a concept called hybrid orbitals.
Unfortunately, overlap of existing atomic orbitals (s, p, etc.) is not sufficient to explain some of the bonding and molecular geometries that are observed. Consider the carbon atom in the methane (CH4) molecule. An isolated carbon atom has an electron configuration of 1s22s22p2, meaning that it has two unpaired electrons in its 2p orbitals, as shown below.
According to the description of valence bond theory so far, carbon would be expected to form only two bonds, corresponding to its two unpaired electrons. However, methane is a common and stable molecule that contains four equivalent C−H bonds. One way to account for this might be to promote one of the 2s electrons to the empty 2p orbital.
Now, four bonds are possible. The promotion of the electron “costs” a small amount of energy, but recall that the process of bond formation is accompanied by a decrease in energy. The two extra bonds that can now be formed result in a lower overall energy, and thus a greater stability, for the CH4 molecule. Carbon normally forms four bonds in most of its compounds.
The number of bonds is now correct, but the geometry is wrong. The three p orbitals (px, py, pz) are oriented at 90° angles relative to one another. However, as we saw in our discussion of VSEPR theory, the observed H−C−H bond angle in the tetrahedral CH4 molecule is actually 109.5°. Therefore, the methane molecule cannot be adequately represented by simple overlap of the 2s and 2p orbitals of carbon with the 1s orbitals of each hydrogen atom.
To explain the bonding in methane, it is necessary to introduce the concept of hybridization and hybrid atomic orbitals. Hybridization is the mixing of the atomic orbitals in an atom to produce a set of hybrid orbitals. When hybridization occurs, it must do so as a result of the mixing of nonequivalent orbitals. For example, s and p orbitals can hybridize but p orbitals cannot hybridize with other p orbitals. Hybrid orbitals are the atomic orbitals obtained when two or more nonequivalent orbitals from the same atom combine in preparation for bond formation. In the current case of carbon, the single 2s orbital hybridizes with the three 2p orbitals to form a set of four hybrid orbitals, called sp3 hybrids.
The sp3 hybrids are all equivalent to one another. Spatially, the hybrid orbitals point towards the four corners of a tetrahedron (Figure below).
The process of sp3 hybridization is the mixing of an s orbital with a set of three p orbitals to form a set of four sp3 hybrid orbitals. Each large lobe of the hybrid orbitals points to one corner of a tetrahedron.
The large lobe from each of the sp3 hybrid orbitals then overlaps with normal unhybridized 1s orbitals on each hydrogen atom to form the tetrahedral methane molecule.
Another example of sp3 hybridization occurs in the ammonia (NH3) molecule. The electron domain geometry of ammonia is also tetrahedral, meaning that there are four groups of electrons around the central nitrogen atom. Unlike methane, however, one of those electron groups is a lone pair. The resulting molecular geometry is trigonal pyramidal. Just as in the carbon atom, the hybridization process starts as a promotion of a 2s electron to a 2p orbital, followed by hybridization to form a set of four sp3 hybrids. In this case, one of the hybrid orbitals already contains a pair of electrons, leaving only three half-filled orbitals available to form covalent bonds with three hydrogen atoms.
The trigonal pyramidal ammonia molecule also results from sp3 hybridization of the central (nitrogen) atom. Of the four groups of electrons surrounding the nitrogen atom, three form single covalent bonds to hydrogen atoms, while one group is a lone pair.
The methane and ammonia examples illustrate the connection between orbital hybridization and the VSEPR model. The electron domain geometry predicted by VSEPR leads directly to the type of hybrid orbitals that must be formed to accommodate that geometry. Both methane and ammonia have tetrahedral electron domain geometries and thus both undergo sp3 hybridization.
Likewise, the bent-shaped water molecule (H2O) also involves the formation of sp3 hybrids on the oxygen atom. In this case, however, there are two hybrid orbitals which have lone pairs and two which bond to the hydrogen atoms. Because the electron domain geometry for H2O is tetrahedral, the hybridization is sp3.
Boron trifluoride (BF3) is predicted to have a trigonal planar geometry by VSEPR. First, a paired 2s electron is promoted to an empty 2p orbital.
This is followed by hybridization of the three occupied orbitals to form a set of three sp2 hybrids, leaving the 2pz orbital unhybridized. The choice of which p orbital to leave unhybridized is arbitrary, but 2pz is conventionally chosen in the case of sp2 hybrids.
The geometry of the sp2 hybrid orbitals is trigonal planar, with the large lobe of each orbital pointing towards one corner of an equilateral triangle (Figure below). The angle between any two of the hybrid orbital lobes is 120°. Each can bond with a 2p orbital from a fluorine atom to form the trigonal planar BF3 molecule.
The process of sp2 hybridization involves the mixing of one s orbital with a set of two p orbitals (px and py) to form a set of three sp2 hybrid orbitals. Each large lobe of the hybrid orbitals points to one corner of a triangle.
Other molecules with a trigonal planar electron domain geometry also form sp2 hybrid orbitals. For example, the electron domain geometry of ozone (O3) is trigonal planar, although the presence of a lone pair on the central oxygen atom makes the molecular geometry bent. The hybridization of the central O atom of ozone is sp2.
A beryllium hydride (BeH2) molecule is predicted to be linear by VSEPR. The beryllium atom contains only paired electrons, so it must also undergo hybridization. One of the 2s electrons is first promoted to an empty 2p orbital.
The occupied orbitals are then hybridized, and the result is a pair of sp hybrid orbitals. The two remaining p orbitals (arbitrarily chosen to be py and pz) do not hybridize and remain unoccupied.
The geometry of the sp hybrid orbitals is linear, with the large lobes of the two orbitals pointing in opposite directions along one axis, arbitrarily defined as the x-axis (Figure below). Each can bond with a 1s orbital from a hydrogen atom to form the linear BeH2 molecule.
The process of sp hybridization involves the mixing of an s orbital with a single p orbital (conventionally the px orbital), to form a set of two sp hybrids. The two lobes of the sp hybrids point in opposite directions to produce a linear molecule.
Other molecules whose electron domain geometry is linear and for whom hybridization is necessary also form sp hybrid orbitals. Examples include CO2 and C2H2, which will be discussed further in the section on hybridization and multiple bonds.
Hybridization of s, p, and d orbitals
Elements in the third period and beyond are capable of expanding their octet to form molecules with either trigonal bipyramidal or octahedral electron domain geometries. In order to accomplish this, the previously unoccupied orbitals in the d sublevel of the central atom are involved in the hybridization process.
For phosphorus pentachloride (PCl5), the electron domain and molecular geometries are trigonal bipyramidal. The electron promotion is from the 3s orbital to an empty 3d orbital.
The hybridization then occurs with a single s orbital, three p orbitals, and a single d orbital. The set of five hybrid orbitals are called sp3d hybrids.
The overlap of the five hybrid sp3d orbitals with the 3p orbital of each chlorine atom results in the five covalent bonds of PCl5. Other molecular geometries derived from trigonal bipyramidal electron domain geometry (seesaw, T-shaped, linear) also display the same hybridization.
Sulfur hexafluoride (SF6) has an octahedral electron domain and molecular geometry. In this case, a 3s and a 3p electron are each promoted to two empty 3d orbitals.
The hybridization now occurs with one s orbital, three p orbitals, and two d orbitals. The resulting set of six equivalent orbitals are called sp3d2 hybrids.
The overlap of the six hybrid sp3d2 orbitals with the 2p orbital of each fluorine atom results in the six covalent bonds of SF6. Other molecular geometries derived from an octahedral electron domain geometry (square pyramidal, square planar) also exhibit this type of hybridization. Figure below shows the shape and orientation of the sp3d and sp3d2 hybrid orbital sets.
The expanded octet trigonal bipyramidal and octahedral geometries are a result of sp3d and sp3d2 hybridization, respectively.
The process of hybridization can be summarized by the following steps:
- Draw the Lewis electron-dot structure of the molecule.
- Use VSEPR theory to predict both the electron domain geometry and the molecular geometry of the molecule.
- Match the electron domain geometry to the appropriate hybridization of the central atom.
Table below summarizes all of the possibilities along with examples of each.
Summary of Hybrid Orbitals
Electron Domain Geometry
Hybridization of the Central Atom
Number of Hybrid Orbitals
Possible Molecular Geometries
trigonal planar, bent
BF3, CO32−, O3
tetrahedral, trigonal pyramidal, bent
CH4, NH3, H2O
trigonal bipyramidal, seesaw, T-shaped, linear
PCl5, SF4, ClF3, I3−
octahedral, square pyramidal, square planar
SF6, BrF5, XeF4
Hybridization in Molecules with Double or Triple Bonds
The hybridization model helps explain molecules with double or triple bonds. Consider the ethene molecule (C2H4). In the lesson “Lewis Electron Dot Structures,” we saw that C2H4 contains a double covalent bond between the two carbon atoms and single bonds between the carbon atoms and the hydrogen atoms. The entire molecule is planar.
As can be seen in Figure above, the electron domain geometry around each carbon atom is trigonal planar, which corresponds to sp2 hybridization. Previously, we saw carbon undergo sp3 hybridization in a CH4 molecule, so how does it work in this case? As seen below, the electron promotion is the same, but the hybridization occurs only between the single s orbital and two of the three p orbitals. Thus generates a set of three sp2 hybrids along with an unhybridized 2pz orbital. Each orbital contains one electron and is capable of forming a covalent bond.
The three sp2 hybrid orbitals lie in one plane, while the unhybridized 2pz orbital is oriented perpendicular to that plane. The bonding in C2H4 is explained as follows. One of the three sp2 hybrids forms a bond by overlapping with the identical hybrid orbital on the other carbon atom. The remaining two hybrid orbitals from bonds by overlapping with the 1s orbital of a hydrogen atom. Finally, the 2pz orbitals on each carbon atom form another bond by overlapping with one another sideways.
It is necessary to distinguish between the two types of covalent bonds in a C2H4 molecule. A sigma bond (σ bond) is a bond formed by the overlap of orbitals in an end-to-end fashion, with the electron density concentrated between the nuclei of the bonding atoms. A pi bond (π bond) is a bond formed by the overlap of orbitals in a side-by-side fashion, with the electron density concentrated above and below the plane of the nuclei of the bonding atoms. Figure below shows the two types of bonding in C2H4. The sp2 hybrid orbitals are orange and the pz orbital is green. Three sigma bonds are formed by each carbon atom with its hybrid orbitals. The pi bond is the “second” bond of the double bond between the carbon atoms and is shown as an elongated blue lobe that extends both above and below the plane of the molecule, which contains the six atoms and all of the sigma bonds.
The C2H4 molecule contains five sigma bonds and one pi bond. Sigma bonds are formed by a direct overlap of bonding orbitals, while a pi bond is formed by a side-to-side overlap of unhybridized p orbitals.
In a conventional Lewis electron-dot structure, a double bond is shown as two lines between the atoms, as in C=C. It is important to realize, however, that the two bonds are different; one is a sigma bond, while the other is a pi bond.
Ethyne (C2H2) is a linear molecule with a triple bond between the two carbon atoms. Since each carbon atom is bonded to two other atoms and has no lone pairs, the hybridization of each carbon is sp.
Again, the promotion of an electron in the carbon atom occurs in the same way. However, the hybridization now involves only the 2s orbital and the 2px orbital, leaving the 2py and the 2pz orbitals unhybridized.
The sigma bond between the two carbon atoms is formed from sp hybrid orbitals, and the remaining hybrid orbitals form sigma bonds to the two hydrogen atoms. Both the py and the pz orbitals on each carbon atom form pi bonds with each other. As with ethene, these side-to-side overlaps are not directly on the line between the two bonded atoms. Additionally, these two pi bonds are perpendicular to one another; one pi bond is above and below the line of the molecule, while the other is in front of and behind the page.
In general, single bonds between atoms are always sigma bonds. Double bonds are comprised of one sigma and one pi bond. Triple bonds are comprised of one sigma bond and two pi bonds.
- Valence bond theory describes the formation of covalent bonds in terms of the overlap of singly occupied atomic orbitals.
- The hybridization of nonequivalent atomic orbitals is necessary to correctly predict the bonding and molecular geometries of many molecules. Hybrid orbitals form on the central atom and can either be sp, sp2, sp3, sp3d, or sp3d2. The type of hybrid orbitals that are used is dictated by the electron domain geometry.
- Sigma bonds are formed by the end-to-end overlap of bonding orbitals. Pi bonds are formed by the side-to-side overlap of p orbitals. Single bonds are normally sigma bonds. A double or triple bond consists of one sigma bond and either one or two pi bonds.
Lesson Review Questions
- How does valence bond theory describe covalent bonding?
- What is meant by hybridization of atomic orbitals?
- Indicate the hybridizations associated with each of the following electron domain geometries:
- trigonal planar
- trigonal bipyramidal
- Can two 2p orbitals of an atom hybridize to give two hybridized orbitals? Explain.
- What are the bond angles between two orbitals of each hybrid?
- What is the difference between a sigma bond and a pi bond?
- Describe the bonding that occurs in each of the following diatomic molecules according to valence bond theory, including which atomic orbitals overlap.
- Given the following structure:
- Indicate the hybridization of each of the five carbon atoms.
- How many total sigma bonds and pi bonds are there in the molecule?
- State the electron domain geometry and hybridization of the central atom in each of the following molecules. Then, give the molecular geometry of each.
Further Reading / Supplemental Links
Points to Consider
In future chapters, we move away from the microscopic world of chemistry and back to a macroscopic view, focusing on the mathematics involved in the analysis of chemical reactions.
- What are different ways to measure the amount of something?
- Since atoms and molecules are so small, how do chemists keep track of the number of them that are taking part in a given reaction?