1.10 Resonance Theory

Some species are not described well by Lewis structures. In , for example, both of the C—O bonds are identical experimentally; they have the same bond length and bond strength, intermediate between those of a single and a double bond (Fig. 1-21a). However, the Lewis structure of (Fig. 1-21b) shows one C—O single bond and one C═O double bond, suggesting that the two bonds are different. Furthermore, experiments show that both oxygen atoms carry an identical partial negative charge (δ–), whereas the Lewis structure suggests that one oxygen atom bears a full negative charge and the other is uncharged. In other words, the Lewis structure suggests that the C═O double bond and the –1 charge are both confined to a specific region in space, or localized, whereas in the real species, they are spread out, or delocalized.

An electrostatic potential map and a Lewis structure of the formate ion comparing the types of bonds and charges involved. The electrostatic potential map shows ball-and-stick model of the ion within the electron cloud. The structure shows a central carbon atom bonded to two oxygen atoms and a hydrogen atom. The color of the electron cloud toward both the oxygen atoms is of same intensity representing identical charge on each oxygen atom and the ball-and-stick model shows identical carbon-oxygen bonds. Lewis structure shows a central carbon atom single bonded to a hydrogen atom and an oxygen atom, and double bonded to an oxygen atom. The double bonded oxygen atom carries two lone pairs of electrons with formal charge, zero. The single bonded oxygen atom carries three lone pairs of electrons with formal charge, negative 1. The caption reads, Limitations of Lewis structures: The actual features of formate ion with negative charge (a) disagree with those suggested by the Lewis structure (b) In the actual structure, both carbon-oxygen bonds are identical and the charge on each oxygen atom is the same. The Lewis structure indicates a carbon-oxygen single bond and a carbon-oxygen double bond, as well as different charges on each oxygen atom.
FIGURE 1-21 Limitations of Lewis structures The actual features of HCO2- (a) disagree with those suggested by the Lewis structure (b). In the actual structure, both carbon–oxygen bonds are identical and the charge on each O atom is the same. The Lewis structure indicates a C—O single bond and a C═O double bond, as well as different charges on each O atom.

How, then, do we reconcile the differences between the Lewis structures of species like and their observed characteristics? The answer is through resonance theory, the key points of which can be summarized by the following rules:

Rule 1

Resonance exists in species for which there are two or more valid Lewis structures.

For such species, each valid Lewis structure is called a resonance structure or a resonance contributor. In , there are two possible resonance contributors. As we can see on the next page, they differ in how we apply Step 5 for drawing Lewis structures—that is, which neighboring lone pair is used to construct the C═O double bond.

Lewis structures show how to obtain the two resonance structures of the HCO2 anion. The two different Lewis structures for the HCO2 anion are drawn according to steps 1 to 4. Each has a central carbon atom that is bonded to a hydrogen atom and two oxygen atoms, one above and one on the right, by single bonds. Each oxygen atom has three lone pairs. In the first structure, the oxygen atom above the carbon has a lone pair highlighted, while in the second, the oxygen atom on the right has a lone pair highlighted. An arrow labeled �step 5� leads from each Lewis structure to two resonance structures with a double-headed arrow between them. Each resonance structure has a central carbon atom bonded to a hydrogen atom and an oxygen atom by single bonds, and to another oxygen atom by a double bond. The highlighted lone pairs have been converted into double bonds. In the first resonance structure, the oxygen atom above the carbon is connected to it by a double bond, while in the second, the oxygen atom on the right is bonded by a double bond. In each resonance structure, the oxygen atom bonded to the carbon by a single bond carries a negative charge.

As a result:

Resonance structures differ only in the placement of their valence electrons, not their atoms.

Rule 2

Resonance structures are imaginary; the one, true species is represented by the resonance hybrid.

A resonance hybrid is a weighted average of all resonance structures. In the case of , the hybrid is an average of two resonance structures:

Lewis structures show how to obtain the resonance hybrid from the two resonance structures of the HCO2 anion. Each resonance structure has a central carbon atom bonded to a hydrogen atom and an oxygen atom with three lone pairs by single bonds, and to another oxygen atom with two lone pairs by a double bond. In the first resonance structure, the oxygen atom above the carbon is connected to it by a double bond, while in the second, the oxygen atom on the right is bonded by a double bond. In each resonance structure, the oxygen atom bonded to the carbon by a single bond carries a negative charge. An arrow labeled �take the average� leads from the two resonance structures to the resonance hybrid, which has a central carbon atom that is bonded to a hydrogen atom by a single bond and to two oxygen atoms each by a single bond combined with a partial double bond. This is represented by a single solid line and a dashed line. The two oxygen atoms each carry a partial negative charge.

Averaging the two C—O bonds (a single and a double bond) makes each one an identical 1.5 bond—more than a single bond, but less than a double bond. (A partial bond is represented in a resonance hybrid by a dashed line connecting the two atoms.) Averaging the charge on each oxygen atom gives each an identical –0.5 charge. This resonance hybrid is now consistent with experimental results.

Three photos show an analogical representation of how a resonance hybrid is obtained. The first photo shows a duck and the second shows an otter. An arrow from these two photos leads to a third, which shows a duck-billed platypus. The caption reads, �An analogy of resonance: A duck-billed platypus has characteristics of a duck and an otter, just as a resonance hybrid has characteristics from its resonance contributors.�
FIGURE 1-22 An analogy of resonance A duck-billed platypus has characteristics of a duck and an otter, just as a resonance hybrid has characteristics from its resonance contributors.
Lewis structures show the two resonance structures of a HCO2 anion, separated by a double-headed arrow. Each resonance structure has a central carbon atom bonded to a hydrogen atom and an oxygen atom with three lone pairs by single bonds, and to another oxygen atom with two lone pairs by a double bond. In the first resonance structure, the oxygen atom above the carbon is connected to it by a double bond, while in the second, the oxygen atom on the right is bonded by a double bond. In each resonance structure, the oxygen atom bonded to the carbon by a single bond carries a negative charge.

To help us remember that resonance structures are imaginary, we draw square brackets, [ ], around the group of resonance structures and we place double-headed single arrows (↔) between them, as shown at the right. These are not equilibrium arrows (⇌), which indicate a chemical reaction, because a compound does not rapidly interconvert between its resonance structures. Rather, think of a resonance hybrid in the same way as you might think of a duck-billed platypus (Fig. 1-22). That is, a platypus has characteristics of both a duck and an otter, but it is a unique species that does not rapidly interconvert between those two animals!

Rule 3

The resonance hybrid looks most like the lowest energy (most stable) resonance structure.

The two resonance contributors of are equivalent. Each is composed of one H—C bond, one C═O double bond, and one C—O single bond, and each has a –1 formal charge on the singly bonded O. As a result, each structure contributes equally to the resonance hybrid.

In cases in which resonance structures are inequivalent, we must be able to determine their relative energies to determine their relative contributions to the hybrid. In general:

A resonance structure is lower in energy (i.e., more stable) with:

●  a greater number of atoms having an octet

●  more covalent bonds

●  fewer atoms having a nonzero formal charge

The issues surrounding formal charge and resonance structures are covered in greater detail in Chapter 6.

Connections Cationic species like this are reactive intermediates in various organic reactions, including substitution (Chapter 8), elimination (Chapter 8), and addition reactions (Chapter 11).

Solved Problem 1.18

Which of these resonance structures makes a greater contribution to the resonance hybrid?

Lewis structures show two resonance structures separated by a double-headed arrow. Each resonance structure shows a carbon atom bonded to another, which is further bonded to an oxygen atom. The oxygen is bonded to a third carbon atom. In the first structure, which consists of only single bonds, the oxygen atom has two lone pairs and the second carbon carries a positive charge. In the second structure, the second carbon atom is connected to the oxygen atom by a double bond. The oxygen atom has one lone pair and carries a positive charge.

Think
SHOW SECTION

Are both resonance structures equivalent? If not, which has more atoms with an octet? Which structure has more bonding pairs of electrons? Which structure has fewer atoms with a nonzero formal charge?

Solve
SHOW SECTION

The resonance structures are inequivalent. In the structure on the right, all nonhydrogen atoms have an octet, whereas in the structure on the left, the central carbon atom has less than an octet. Additionally, there is one additional bond in the structure on the right, between the C and O. For both of these reasons, the structure on the right makes a much greater contribution to the overall resonance hybrid.

problem 1.19 Which of these resonance structures makes a greater contribution to the resonance hybrid? Note: Formal charges are not shown.

Lewis structures show two resonance structures separated by a double-headed arrow. Each resonance structure shows a central carbon atom bonded to a methyl group, an oxygen atom, and a chlorine atom. In the first structure, the oxygen atom has two lone pairs and is bonded to the carbon by a double bond, while the chlorine atom has three lone pairs and is bonded to the carbon by a single bond. In the second structure, the oxygen atom has three lone pairs and is bonded to the carbon by a single bond, while the chlorine atom has two lone pairs and is bonded to the carbon by a double bond.

Rule 4

Resonance provides stabilization.

The stabilization due to resonance results from the delocalization of electrons; that is, electrons have lower energy when they are less confined. In , four electrons are delocalized over three atoms (Fig. 1-23). In a single resonance structure, on the other hand, those electrons are localized. The extent by which a species is stabilized in this fashion is called its resonance energy or its delocalization energy.

Rule 5

Resonance stabilization is usually large when resonance structures are equivalent.

An energy diagram shows the difference in energy levels of the resonance structures of a HCO2 anion and its resonance hybrid. An upward arrow indicates increasing energy levels. Each resonance structure has a central carbon atom bonded to a hydrogen atom and an oxygen atom with three lone pairs by single bonds, and to another oxygen atom with two lone pairs by a double bond. In the first resonance structure, the oxygen atom above the carbon is connected to it by a double bond, while in the second, the oxygen atom on the right is bonded by a double bond. In each resonance structure, the oxygen atom bonded to the carbon by a single bond carries a negative charge. The resonance structures have localized electrons, and are located higher on the energy scale than the resonance hybrid, which has a central carbon atom that is bonded to a hydrogen atom by a single bond and to two oxygen atoms each by a single bond combined with a partial double bond. This is represented by a single solid line and a dashed line. The two oxygen atoms each carry a partial negative charge. Here, the four electrons are delocalized over three atoms. The caption reads, Resonance stabilization: In each resonance structure of HCO2 minus, the four electrons in red are localized. In the resonance hybrid, those four electrons are delocalized over three atoms. Delocalization results in lower energy and greater stability.
FIGURE 1-23 Resonance stabilization In each resonance structure of HCO2-, the four electrons in red are localized. In the resonance hybrid, those four electrons are delocalized over three atoms. Delocalization results in lower energy and greater stability.
Condensed structural formulas show the two resonance structures and the resonance hybrid of benzene. The two resonance structures of benzene are separated by a double headed arrow, and each shows a six-carbon ring with alternating single and double bonds. An arrow from these resonance structures leads to the resonance hybrid, which shows a ring of six carbon atoms connected by single bonds and partial double bonds. These bonds are each represented by a single solid line and a dashed line. The six electrons in the resonance hybrid are delocalized over the six carbon atoms. The caption reads, Equivalent resonance structures: The two resonance structures of benzene on the left are equivalent, so they contribute equally to the resonance hybrid on the right.
FIGURE 1-24 Equivalent resonance structures The two resonance structures of benzene (left) are equivalent, so they contribute equally to the resonance hybrid (right).

Connections Benzene (Fig. 1-24) is an aromatic hydrocarbon that is naturally found in crude oil and, because of its high octane number, is an important component of gasoline.

Rule 5 is an outcome of Rules 3 and 4. If resonance structures are equivalent, then they will contribute equally to the hybrid, allowing electrons the greatest possible delocalization. The two resonance structures of are equivalent, so its resonance energy is quite substantial. Another example is benzene, whose resonance structures and hybrid are shown in Figure 1-24. Benzene’s resonance energy is estimated to be about 150 kJ/mol (36 kcal/mol), which is nearly half the energy of a C—C bond! We discuss benzene in much greater depth in Chapter 14, where we explain that much of benzene’s resonance energy is due to a phenomenon called aromaticity.

Acetic acid (CH3CO2H) is not stabilized greatly by resonance. Although it has two resonance structures, only the one on the left in Figure 1-25 contributes significantly. The one on the right is much higher in energy because of the presence of the two charges. Therefore, the electrons involved in resonance are not very highly delocalized.

Lewis structures show the two resonance structures of acetic acid with a double-headed arrow between them. Each structure shows a carbon atom bonded to three hydrogen atoms and a carboxyl group, which basically consists of a carbonyl group bonded to a hydroxyl group. In the first structure, the carbon atom in the carboxyl group is bonded by a double bond to one of the oxygen atoms, and by a single bond to the other oxygen, which is further bonded to a hydrogen atom. Both the oxygen atoms have two lone pairs each. In the second structure, the oxygen atom bonded to the hydrogen atom has one lone pair, carries a positive charge, and is bonded to the carbon atom by a double bond. The other oxygen atom has three lone pairs, carries a negative charge, and is bonded to the carbon atom by a single bond. The caption reads, �Nonequivalent resonance structures: The two resonance structures of acetic acid are nonequivalent, so they contribute unequally to the resonance hybrid. The one on the left is lower in energy, so it has the greater contribution.�
FIGURE 1-25 Nonequivalent resonance structures The two resonance structures of acetic acid are nonequivalent, so they contribute unequally to the resonance hybrid. The one on the left is lower in energy, so it has the greater contribution.

Connections Acetic acid, when it is diluted to about 5% by volume, is familiar to us as vinegar. In organic chemistry, acetic acid is used as a reagent in a wide variety of organic reactions. It can also be used as a solvent.

Photo of a bottle of white distilled vinegar. The label on the bottle shows the name of the brand �Supreme Star,� and reads, �White Distilled Vinegar: Vinagre Blanco Destilado.�

Rule 6

All else being equal, the greater the number of resonance structures, the greater is the resonance stabilization.

Rule 6 is an outcome of Rule 4, because additional resonance structures mean electrons are more widely delocalized, which lowers the energy even more.