Resonance Structures and Electron Delocalization

Resonance structures are two or more valid Lewis structures for the same molecule or ion that differ only in the placement of electrons, and the real structure, called the resonance hybrid, is an average of them with delocalized electrons spread over several atoms. In brief: ozone (O₃) can be drawn as O=O–O or O–O=O, but in reality both O–O bonds are identical, with a bond order of 1.5 and a length of 128 pm, between that of a single bond (148 pm) and a double bond (121 pm).

Some molecules cannot be described accurately by a single Lewis structure. Their properties, such as bond lengths and stability, show that electrons are spread over more than two atoms. This article explains the idea of resonance, how to recognize the need for it, how to calculate bond order and charge distribution, shows examples such as ozone, nitrate and benzene, compares resonance structures with real isomers, includes a table of bond lengths, and gives the history of the concept.

What is resonance?

When you draw the Lewis structure of ozone, O₃, you find that you can put the double bond on either side. The two structures are O=O–O and O–O=O. If either structure were correct, the molecule would have one short and one long bond. Experiments show two bonds of equal length. The true electron distribution is an average (a hybrid) of the two structures. The two structures are connected by a double-headed arrow (↔), which does not mean that the molecule switches back and forth between them. The molecule has only one structure, which is intermediate and cannot be drawn by a single Lewis diagram.

The electrons that are involved are mostly the pi electrons, which are spread over three or more atoms and are said to be delocalized.

What are some examples of resonance?

• Ozone, O₃: two resonance structures, each bond has bond order 1.5.
• Nitrate ion, NO₃⁻: three structures, with the double bond on each of the three oxygen atoms. Each N–O bond has bond order 4 ÷ 3 = 1.33, and each oxygen carries a charge of about −⅔.
• Carbonate ion, CO₃²⁻: three structures, each C–O bond has bond order 1.33.
• Benzene, C₆H₆: two Kekulé structures with alternating double and single bonds in a ring. All six C–C bonds are equal (bond order 1.5, 140 pm).
• Acetate ion, CH₃COO⁻: two structures. Both C–O bonds are identical, with bond order 1.5.
• Nitrite ion, NO₂⁻ and sulfur dioxide, SO₂: two structures each, similar to ozone.

What are the rules for drawing resonance structures?

1. All resonance structures must have the same arrangement of atoms. Only electrons (lone pairs and pi bonds) are moved.
2. All structures must have the same total number of electrons and the same overall charge.
3. Each structure must be a valid Lewis structure, with correct octets for the second-period elements.
4. The most stable (major) contributors have complete octets, minimal formal charges and negative charges on the most electronegative atoms.
5. Structures that are equivalent contribute equally to the hybrid. The more stable a structure is, the more it contributes.

Bond lengths in resonance hybrids

In every case the observed length lies between the single-bond and double-bond values, and it is closer to the double-bond value when the bond order is closer to 2.

Worked examples

1. Draw the resonance structures of NO₃⁻. The skeleton has nitrogen in the center, with three oxygen atoms. The total is 5 + 18 + 1 = 24 electrons. One structure has one N=O and two N–O⁻. Moving a lone pair from one of the singly bonded O atoms to form a new N=O (and the double bond back to a lone pair) gives two more equivalent structures. There are three structures in all.
2. Bond order in nitrate. In each structure there are 4 bonds shared among 3 positions (1 double + 2 single = 4). The average is 4 ÷ 3 = 1.33.
3. Bond order in ozone. Each structure has 3 bonds in 2 positions (1 double + 1 single). The average is 3 ÷ 2 = 1.5.
4. Bond order in benzene. A Kekulé structure has 3 double and 3 single bonds, a total of 9 bond units over 6 positions, so the average is 9 ÷ 6 = 1.5.
5. Charge on each oxygen in carbonate. The total charge is 2−, and there are three equivalent oxygen atoms. The formal charge in each structure is −1 on two oxygen atoms and 0 on the double-bonded one. The average per oxygen is −2 ÷ 3 = −0.67.
6. Resonance energy of benzene. The heat of hydrogenation of cyclohexene (one C=C bond) is about −120 kJ/mol. A hypothetical “cyclohexatriene” with three isolated double bonds would release 3 × 120 = 360 kJ/mol. Benzene releases only 208 kJ/mol. The difference, 360 − 208 = 152 kJ/mol, is the resonance (stabilization) energy of benzene, which shows that delocalization makes it more stable.

Why does delocalization stabilize a molecule?

When electrons are spread over more atoms, they are less confined and the energy decreases. In quantum mechanical terms, the hybrid wave function that mixes several structures has lower energy than any single structure. This explains the unusual stability of benzene, which does not react like an alkene, and the strong acidity of carboxylic acids: the carboxylate ion is stabilized by delocalization of the negative charge over two oxygen atoms. Resonance also explains the color of many dyes and the properties of conducting polymers.

What does resonance not mean?

• The molecule does not oscillate between structures. There is one structure.
• Resonance structures are not isomers. Isomers have different arrangements of atoms and can be separated.
• Resonance structures are not equilibrium forms (which use two arrows ⇌). Resonance uses a double-headed arrow (↔).
• An analogy: a mule is a real animal with features of both a horse and a donkey. It is not a horse at one moment and a donkey at the next. In the same way, a resonance hybrid is a single, real species whose properties are a blend of those suggested by the individual structures.

How did the concept develop?

August Kekulé proposed in 1865 that benzene is a ring with alternating double and single bonds, and later suggested that the bonds oscillate between two arrangements to explain why benzene has only one isomer of 1,2-disubstituted derivatives. In the 1930s, Linus Pauling and George Wheland developed the theory of resonance, based on the quantum mechanics of Heitler and London, and Pauling’s 1939 book The Nature of the Chemical Bond made it widely known. Today, the idea is known as the delocalization of electrons, described more precisely by molecular orbital theory.

Which mistakes are common?

Mistake 1: Thinking that the molecule flips between structures

The hybrid is a single, static structure. The individual drawings are just a way of showing it.

Mistake 2: Moving atoms between resonance structures

Only electrons move. If an atom moves, the structures are isomers.

Mistake 3: Using resonance arrows for equilibria

Use ↔ for resonance and ⇌ for a chemical equilibrium.

Mistake 4: Forgetting to check the electron count

All resonance structures must have the same number of electrons and the same net charge.