1.5 Resonance Forms and the Curved Arrow Formalism
Often, more than one Lewis structure is possible for a molecule. This statement is especially true for charged molecules, but it applies to many neutral species as well. (You may already have encountered this phenomenon in comparing your answers with ours.) How do we decide which Lewis structure is the correct one? The answer almost always is that none of the alternative Lewis structures is complete all by itself. Instead, the molecule is best described as a combination of all reasonable Lewis structures, that is, as a combination of resonance forms, which are different electronic representations of the same molecule. Whether or not a Lewis structure is reasonable or whether it is an important contributor will be addressed in this section. The word electronic is emphasized to remind you that the only differences allowed in a set of resonance forms are differences in electron distribution. There can be no change in the position of the atoms in resonance forms.
Let’s use nitromethane, H3C―NO2, as an example. The nitro group, ―NO2, is a functional group, which is a collection of atoms that behave more or less the same way wherever they appear in a molecule. In Chapter 2, we will introduce the most common functional groups, but for now, you can go to the inside front cover of the book to find the structures. The problem with the nitro functional group is that the condensed formula NO2 doesn’t contain structural information about how the atoms are connected to one another. For that matter, neither does CH3. Over time, you will become familiar with most functional groups and will be able to write the appropriate structures without even thinking about it.
Even though nitromethane is a neutral molecule, there is no good way to draw it without separated charges. Figure 1.26 shows a Lewis structure for nitromethane in which the nitrogen is positive and one of the oxygens is negative. But this is not the only Lewis structure possible! We can draw the molecule so the other oxygen bears the negative charge. The two renderings of nitromethane in Figure 1.27 are resonance forms of the molecule. Note that the arrangement of the atoms is identical in the two forms. Resonance forms are different electronic representations of the same molecule, not pictures of different molecules. The real molecule is the combination of all its resonance forms and is often called a resonance hybrid.
FIGURE 1.26 One electronic representation of nitromethane.
FIGURE 1.27 Two equivalent resonance forms for nitromethane.
PROBLEM 1.12 Draw a Lewis structure for nitric acid (HO―NO2), and verify that the nitrogen is positive and one of the oxygens is negative (see Fig. 1.26).
Neither Lewis structure in Figure 1.27 is completely accurate because in the real nitromethane molecule, the two oxygens share the negative charge equally. Thus, the two resonance forms in Figure 1.27 are equivalent electronic representations for nitromethane. Notice the special, double-headed arrow between the two forms. This symbol is a resonance arrow and in the notation of chemistry is used exclusively to indicate resonance forms. Also notice the red, curved arrows in Figure 1.27. These arrows are a notation used to show how we move a pair of electrons from one point to another. In this case, such movement converts one resonance form into the other. Using curved arrows to show how electrons move from one point to another is called the curved arrow formalism. Other terms you might encounter that are used to describe this type of analysis are arrow formalism or electron pushing. This formalism is so important and is used so often that it deserves its own section.
The curved arrow formalism not only tracks the movement of electrons in converting one resonance form into another but also is used to follow electron flow in all chemical reactions. We will use it countless times in the rest of the book. We haven’t yet studied any reactions (that state of affairs will change very soon), so here we work through the rules for the curved arrow formalism using for the most part examples of resonance. Exactly the same set of rules applies to reactions, and we will show more examples as reactions appear.
PROBLEM 1.13 Use the curved arrow formalism to convert your Lewis structure for nitric acid (HO—NO2,Problem 1.12) into a resonance form.
WORKED PROBLEM 1.14 Draw another structure for nitromethane in which every atom is neutral. Hint: There are only single bonds in this structure.
ANSWER You can arrive at the answer by using arrows to push electron pairs in the following way:
Note that as a new bond is formed between the two oxygen atoms, the two charges originally on oxygen and nitrogen are canceled. Notice also the long oxygen–oxygen bond. Remember: In drawing resonance forms, you move only electrons, not atoms. The oxygen–oxygen distance must be the same in each resonance form.
Is this cyclic form an important resonance form? Is it a good representation of the molecule? The problem is the long bond between the oxygens. This bond must be weak just because it is so long. In the language of organic chemistry, we would say that the cyclic resonance form contributes little to the structure of nitromethane.
Is the cyclic structure that follows a resonance form? Resonance involves different electronic structures that do not differ in the positions of atoms. If atoms have been moved, as in the figure below in which there is a normal oxygen–oxygen bond, the two structures are not resonance forms.
CONVENTION ALERT The Use of Curved Arrows
We must stress that although the curved arrows in this section have no physical significance, they do constitute an extraordinarily important bookkeeping device. They map out the motions of electrons. But be careful—these arrows, useful as they are, do not represent more than a bookkeeping process. We will use curved arrows throughout this book, and all organic chemists use them to keep track of electron movement, not only in drawing resonance forms but also in writing of chemical reactions. Being able to draw resonance forms quickly and accurately is an essential skill for anyone wishing to master organic chemistry.
The bookkeeping represented by curved arrows in resonance forms is accomplished by moving or “pushing” pairs of electrons. Be careful when doing this sort of thing not to violate the rules of valence—not to make more bonds than are possible—for this mistake is easy to make. Figure 1.30 gives more examples of this kind of electron-pair pushing in molecules best represented as combinations of resonance forms.
FIGURE 1.30 Resonance forms.
It is important to be extremely clear on the following point about resonance structures. Nitromethane does not spend half its time as one resonance form and half as the other. There is no equilibration between the resonance forms. Nitromethane is best described as a combination of the two electronic structures shown in Figure 1.27. In nitromethane, the two resonance forms are equivalent because there is no difference between having the negative charge on one oxygen or the other, and thus nitromethane can be reasonably described as a 50:50 combination (average) of the two forms.
Here’s an analogy that might help: Frankenstein’s monster was always a monster. You might describe that poor constructed creature as part monster and part human, but he was always that combination—he did not oscillate between the two. In chemical terms, we would say that Frankenstein’s monster was a resonance hybrid of monster and human. In contrast, Dr. Jekyll and Mr. Hyde were in equilibrium. When the good Dr. Jekyll drank the potion, he became the monstrous Hyde. Later, when the potion wore off, he reverted to Jekyll. Part of the time he was Jekyll, and part of the time he was Hyde. The two were in equilibrium, not resonance.
CONVENTION ALERT Resonance Arrows versus Equilibrium Arrows
The special double-headed arrow (↔) used in Figures 1.27 and 1.30 is reserved for resonance phenomena and is never used for anything but resonance. A pair of arrows (⇆) indicates equilibrium, the interconversion of two chemically distinct species, and is never used for resonance (Fig. 1.31). This point is most important in learning the language of organic chemistry. It is difficult because it is arbitrary. There is no way to reason out the use of the different kinds of arrows; they simply must be learned.
FIGURE 1.31 The difference between equilibrium (two different species, A and B; two arrows) and resonance (different Lewis representations, C and D, for the same molecule, E; double-headed arrow).
The carbon–oxygen double bond in formaldehyde (H2CO, Fig. 1.32), gives us another opportunity to write resonance forms. In the resonance form on the left in Figure 1.32, carbon has a pair of 1s electrons and shares in four covalent bonds; therefore, it is neutral (6 − 6 = 0). Oxygen has a pair of 1s electrons, four nonbonding electrons, and a share in two covalent bonds, for a total of eight electrons (8 − 8 = 0). Oxygen is also neutral. However, we can push electrons to generate the resonance form shown on the right in Figure 1.32, in which the carbon is positive and the oxygen is negative. The real formaldehyde molecule is a combination, not a mixture, of these two resonance forms: a resonance hybrid. Because charge separation is energetically unfavorable, these two resonance forms do not contribute equally to the structure of the formaldehyde molecule. Still, neither by itself is a perfect representation of the molecule, and in order to represent formaldehyde well, both electronic descriptions must be considered. Formaldehyde is a weighted average of the two resonance forms in Figure 1.32. How we determine a weighted average is what we look at next.
FIGURE 1.32 Formaldehyde.
PROBLEM 1.15 Acetone, (CH3)2CO, is similar to formaldehyde. Draw a Lewis structure for acetone. Draw two resonance forms. Which do you suppose contributes more to the molecule? Why? Which contributes less? Why?
PROBLEM 1.16 Use the arrow formalism to convert each of the following Lewis structures into another resonance form. Notice that part (e) of this question asks you to do something new—to move electrons one at a time in writing Lewis forms.
WORKED PROBLEM 1.17 Use the arrow formalism to write resonance forms that contribute to the structures of the following molecules:
ANSWER (c) As we have seen, not only electron pairs (nonbonding electrons) can be redistributed (pushed) in writing resonance forms, but bonding electrons as well. In this case, a pair of electrons in a carbon–carbon double bond is moved.
The positive charge on the right-hand carbon disappears, but it reappears on the left-hand carbon. In the real structure, the two carbons share the positive charge equally, each bearing one-half the charge. The structure is sometimes written with dashed bonds to show this sharing:
It is important to be able to estimate the relative importance of resonance forms in order to get an idea of the best way to represent a molecule. To do so, we can assign a weighting factor, c, to each resonance form. The weighting factor is a number that indicates the percent contribution of each resonance form to the resonance hybrid. Some guidelines for assigning weighting factors are listed below. Fortunately, this is an area in which common sense does rather well.
1. The more bonds in a resonance form, the more important a contributor the form is. For example, 1,3-butadiene can be written as a resonance hybrid of several structures, four of which are shown (Fig. 1.33).
FIGURE 1.33 Four resonance forms contributing to 1,3-butadiene. Form A is by far the best.
PROBLEM 1.18 Write two more resonance forms for 1,3-butadiene.
It is reasonably well described by form A, which has a total of 11 bonds. Forms B, C, and C′ each contain 10 bonds and will contribute far less than A to the actual 1,3-butadiene structure. Forms C and C′ are equivalent (this is why they are labeled C and C′rather than C and D) and contribute equally to the hybrid. Even though A is clearly the major contributor, this does not mean that B, C, and C′ do not contribute at all. It simply means that in the equation
Butadiene = c1(A) + c2(B) + c3(C) + c3(C′)
the weighting factor c1 is much larger than the other coefficients. Therefore, 1,3-butadiene looks much more like A than B, C, or C′.
2. Separation of charge is bad. In Figure 1.33, the neutral resonance forms A and B contribute more to the resonance hybrid than do C or C′, both of which require a destabilizing separation of charge. (Form B contributes less than form A, as noted in guideline 1, because it has fewer bonds.)
3. In ions, delocalization of electrons (distributing them over as many atoms as possible) is especially important. Delocalization of electrons is a process that allows more than one atom to share electrons, and it is almost always stabilizing. Electrons are like water; if allowed to spread out, they will. The allyl cation is a good example—the two end carbons each bear one-half of the positive charge (Fig. 1.34).
FIGURE 1.34 The allyl cation is an equal combination of A and A′.
The electrons of the double bond have spread into the empty p orbital. The ion shown in Figure 1.35 is another good example. Here, the charge is shared by the carbon and the chlorine, as the two resonance forms show.
FIGURE 1.35 In this carbocation, the charge is shared by carbon and chlorine.
4. Electronegativity is important. In the allyl anion (Fig. 1.36a), for example, there are two equivalent resonance forms. As in the allyl cation, the charge resides equally on the two end carbons. Figure 1.36a shows two summary structures for the allyl anion. In one, each of the two end carbons is shown with half a negative charge; in the other, one resonance form is drawn, and any positions sharing the charge are indicated by drawing the charge in parentheses (−). The related enolate anion, in which one CH2 of allyl is replaced with an oxygen (Fig. 1.36b), also has two resonance forms, but they do not contribute equally because they are not equivalent. Each has the same number of bonds, and so we cannot choose the better representation that way. However, form A has the charge on the relatively electronegative oxygen whereas form B has it on carbon, which is considerably less electronegative than oxygen. Form A is the better representation for the enolate anion, although both forms contribute. Mathematically, we would say that the weighting factor for A, c1, is larger than that for B, c2.
FIGURE 1.36 (a) The allyl anion. (b) The enolate anion.
5. Equivalent resonance forms contribute equally to a resonance hybrid. The two forms of nitromethane in Figure 1.27 and the two forms of the allyl cation (A and A′) in Figure 1.34 are good examples. In both cases, the resonance forms are completely equal to each other (indistinguishable, same number of bonds, same number of charges, charges on same atoms).
In cases such as these, the weighting factors for the two forms, c1 and c2, must be equal. An equation to represent our allyl cation example is
Allyl = c1(form A) + c2(form A′)
where c1 is the weighting factor for resonance form A, c2 is the weighting factor for form A′, and c1 = c2.
6. All resonance forms for a given species must have the same number of paired and unpaired electrons. As we saw in Figure 1.5, two electrons occupying the same orbital must have opposite spin quantum numbers. Most organic molecules, including our example molecule 1,3-butadiene, have all-paired electrons. Therefore, resonance forms for 1,3-butadiene must also have all-paired electrons. Consider form B in Figure 1.33. It is often the convention to emphasize that all electrons are paired in this molecule by appending electron-spin arrows alongside each single electron in this form (Fig. 1.37). Opposed arrows (↓ and ↑) indicate paired spins; arrows in the same direction (↓ and ↓ or ↑ and ↑) indicate parallel (same-direction) spins.
FIGURE 1.37 In 1,3-butadiene, all electrons are paired, and all resonance forms contributing to the structure must also have all electrons paired.
WORKED PROBLEM 1.19 Add dots for the electron pairs and write resonance forms for the following structures:
ANSWER (f)
PROBLEM 1.20 Write Lewis structures and resonance forms for the following compounds. If you have problems visualizing the structures of some of these molecules, see the inside front cover of this book.
(a) NCCH2−
(b) −OSO2OH
(c) CH3COO−
WORKED PROBLEM 1.21 Which of the following pairs of structures are not resonance forms of each other? Why not? You may have to add dots to make good Lewis structures first.
ANSWER (b) These two are not resonance forms because atoms have been moved, not just electrons. These two molecules are in equilibrium.
PROBLEM 1.22 In the following pairs of resonance forms, indicate which form you think is more important and therefore contributes more to the structure. Justify your choice. You may have to add dots to make good Lewis structures first.
Summary
1. Many molecules are incompletely represented by just one Lewis structure. For these molecules, resonance structures provide a more accurate description.
2. Resonance forms are different electronic representations of the same molecule.
3. Resonance forms are not species in equilibrium: Molecules do not oscillate back and forth between resonance forms. The more accurate structure of the molecule—called the resonance hybrid—is the weighted average of all forms.
4. Some resonance forms contribute more than others to the resonance hybrid.
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