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For other uses, see Resonance (disambiguation).

Resonance in chemistry is the depiction of a molecule as a hybrid of conventional Lewis structures that differ only in the placement of the valence electrons, when no single Lewis structure is adequate to describe its true structure and properties. The Lewis structures in resonance situations are inadequate and inaccurate because they do not exist as such, and do not exist as such because they are less stable than the hybrid.

Example Benzene can be drawn with one of two classic ring structures (called Kekulé structures). These are entirely equivalent Lewis structures, with no reason to choose one and not the other. However, both depict an alternation of long (single) and short (double) carbon-carbon bonds and so neither is consistent with experimental evidence, which shows the C-C bond lengths to be all equal, at a value (139 pm) intermediate between that of a typical C=C double bond (133 pm) and that of a typical C-C single bond (154 pm). The true structure is better represented as a hybrid of these two Lewis structures. Resonance is depicted using a double-headed arrow ($\leftrightarrow$) between pairs of Lewis structures and, to emphasize that only one structure is meant, the group of Lewis structures can be placed within large square brackets.

Resonance depiction of benzene as a mix of Lewis structures.

Resonance Hybrids and Resonance Contributors

Lewis structures depict molecules by placing pairs of valence electrons between atoms to represent the electron-sharing in covalent bonds, without regard to whether or not the sharing is equal, and by placing other electrons on single atoms, designating them as strictly non-bonding. However, it is often the case that some properties of a molecule can be explained with one Lewis structure but other properties are better explained by another, in which the electrons are placed differently, or that the molecular properties are best explained by an intermediate, called a resonance hybrid, between two or more Lewis structures that are then called canonical, limiting or resonance structures, resonance extremes or resonance contributors. Resonance thus approximately conveys a delocalization of the electrons, something which cannot otherwise be easily drawn, except in certain cases where the resonance structures are equivalent. A more exact description of the hybrid structure and the electron distribution is only available through quantum chemical approaches.

Example The resonance contributors for benzene (the Kekulé structures) are equivalent. To convey the fact that all carbon-carbon bonds in benzene are equal and intermediate between single and double bonds, the left-hand drawing uses dashed lines to represent half-bonds (for a total of one-and-a-half bonds between each carbon pair). The right-hand drawing uses a circle to depict the same idea and is commonly used, but was inspired by molecular orbital theory. Most cases of resonance cannot be adequately depicted with such non-conventional drawings.

Depictions of π delocalization in benzene.

Since resonance involves combining structures that differ only in the placement of electrons, all resonance contributors must have

• the same atoms, the same number of electrons and the same total charge, otherwise they would be different molecules,
• the same atom connectivity, otherwise they would be constitutional isomers, and
• the same relative disposition of the atoms in three-dimensional space, otherwise they would be conformational isomers.

But the nuclear positions can otherwise vary, since bond lengths and bond angles can differ between non-isomeric resonance contributors.

Relative Importance of Resonance Contributors

Not all possible resonance contributors to a resonance hybrid are equally relevant to the structure and properties of a molecule, since some will be less stable than others, for instance because some will have fewer bonds. Resonance contributors are qualitatively grouped into two categories, "major contributors" and "minor contributors", according to their perceived importance or "weight" in describing the true structure. The "weighting" of each is a qualitative assessment of the stability of each. "Major" resonance contributors will:

• obey as much as possible the octet rule (8 valence electrons around each atom instead of deficiencies or hypervalencies),
• carry a minimum of charged atoms (unless it serves to create additional bonds to compensate, the separation of + and - charges requires energy),
• place charges on those atoms best able to carry them (negative charge on the most electronegative atoms, positive charge on the least electronegative, unless this serves to create additional bonds).

BENZ

Resonance Stabilization

In the case of benzene, there is no difference between the two Kekulé structures. Both have the same stability, both have equal weight, and the hybrid can be considered as an average of the two in terms of atomic and electronic localization, but not in terms of energy. This averaging would not occur unless it was advantageous and, in general, resonance hybrids are truer depictions of molecules because they are more stable than their resonance contributors. Were this not so, the hybrids would have no existence, whereas it is the contributing structures that have no existence. Resonance and delocalization are therefore stabilizing.

In other molecules, the contributions of each resonance structure will be unequal, and the stabilization will draw to different extents upon each. Nevertheless, a general rule is that, all else being equal, the greater the number of resonance contributors, the greater the possible resonance-delocalization and the greater the possible stabilization.

Example The nitration of anisole is an example of a regioselective electrophilic aromatic substitution that produces mostly ortho and para products. To explain this, resonance in the cationic intermediates (the so-called σ complexes) is compared. Attack of NO2+ at either ortho and para positions gives rise to a σ complex (the para case is depicted in the upper series) in which there are four resonance contributions, one more than is available from attack at a meta position (lower series). This comparison is valid because the three meta resonance structures have equivalents in the para and ortho cases, but the fourth available in the latter cases has no equivalent in the meta case. There is a similar resonance situation in the final substitution products, showing greater stability in the ortho and para nitroanisoles.

Nitration of anisole: resonance in the σ complex from para attack.

The gain in stability of the resonance hybrid over the most stable of the (non-existent) canonical structures is called the resonance stabilization or resonance energy. This can be measured computationally by quantum chemical approaches or, in some cases, experimentally.

Example In a conjugated system, the resonance energy can be approximately measured by the heat of hydrogenation of the molecule in comparison to the heats of hydrogenation of non-conjugated analogues. For instance, the conjugated cyclohexa-1,3-diene is hydrogenated to cyclohexane with the release of 55.6 kcal/mol (232.8 kJ/mol) of heat, while the non-conjugated cyclohexa-1,4-diene releases 57.4 kcal/mol (240.3 kJ/mol) in the same process. The conjugated diene releases less energy because it is closer in energy to cyclohexane, and therefore more stable. The difference in the heats of hydrogenation, 1.8 kcal/mol (7.5 kJ/mol), approximates the resonance stabilization resulting from the conjugation of two alkene groups. From the cyclohexa-1,4-diene case and other non-conjugated alkenes, we can estimate that the heat of hydrogenation of an isolated double bond is around 28.6 kcal/mol (120 kJ/mol). The heat of hydrogenation of the Kekulé version of benzene (cyclohexa-1,3,5-triene) should be three times that much, or 85.8 kcal/mol (360 kJ/mol). However, the experimental heat of hydrogenation of benzene is around 49.8 kcal/mol (210 kJ/mol), and the difference of 36 kcal/mol (150 kJ/mol) is a measure of the resonance energy. This extraordinary degree of resonance stabilization in benzene, much stronger than expected from simple conjugation, is the property called aromaticity.

Heats of hydrogenation of cyclohexadienes and benzene.

Occurence

Resonance in organic chemistry is prevalent in arrangements where a donor group (a lone pair, an unpaired electron, a double bond or a triple bond) and an accepting group (an unpaired electron, an empty p orbital, a double bond or a triple bond) are separated by a single bond, for instance in a diene moiety, a vinyl ether grouping, in stabilized carbenes, in allylic cations, benzylic radicals and so on. All of these situations involve the mixing of p orbitals and double or triple bonds (π bonds), but resonance involving single bonds (σ bonds) has been used in some cases, as illustrated in one example below. Indeed, the unequal sharing of electrons in covalent single bonds can be viewed as a resonance between purely covalent and purely ionic bonds.

There are also many examples in main group chemistry of these same arrangements, for instance in sulfate ion and in boron-nitrogen compounds such as borazine, and several other examples given below. In transition metal chemistry, permanganate (MnO₄^-) and chromate (CrO₄^2-) ions are analogous, but metal-ligand orbital overlap involving d orbitals and electron delocalization are very common, for instance in π backbonding.

Further Examples

To generate one resonance contributor from another, one uses a curved arrow to denote the required change in position of electron pairs, or half-headed curved arrows for single electrons, or a cascade of such arrows. The examples below are illustrative.

Carboxylate ions: As with benzene, the two resonance contributors of a carboxylate ion are identical, they have the same weight and one can correctly predict that the two carbon-oxygen bonds will be of identical length, at a value intermediate between that of a typical single C-O bond and that of a typical C=O double bond (and which may be represented by a dashed bond). Resonance helps explain the increased acidity of carboxylic acids compared to alcohols. Upon deprotonation, an alcohol gives an alkoxide ion whose charge cannot be delocalised, whereas a carboxylic acid gives a carboxylate ion where resonance can distribute the charge over both oxygen atoms, which confers greater stability. In molecular orbital terms, one can state that the charged oxygen atom in either Lewis structure carries three lone pairs and can act as a π donor, while the other oxygen atom can act as a π acceptor. Other examples of this same kind of resonance are found in phosphates, sulfates, sulfonates, nitrates, carbonates, azide, ozone, amidines, guanidines, nitro groups and others.	Click to view full-size. Major resonance contributors for acetate ion, and a hybrid structure.
Allylic radicals: As with acetate ion and benzene, the two resonance contributors of allyl radical are identical. This radical is stabilized because the unpaired electron and the incomplete octet are shared. Other allylic radicals, bearing substituents at one end or the other or at both ends, will not have equal weight unless the radical is symmetrical, and the true electronic distribution may be biased toward one end or the other. Other examples of this same kind of resonance are found in propargylic and benzylic radicals, anions and cations.	Click to view full-size. Half-headed arrows are used to denote the movement of single electrons.
Enolates: These species are the conjugate bases of enols which benefit, like acetate, from resonance stabilization by distribution of the charge. However, the resonance contributors do not have equal weight, given the greater electronegativity of oxygen, and this stabilization is not large (the acidities of enols and alcohols are similar). Nevertheless, resonance explains the ambident reactivity of enolates, which react as nucleophiles at oxygen or at carbon, depending on the reagent and reaction conditions.	Click to view full-size. Enol and enolate: resonance in the conjugate base.
Cyanate ion: Resonance in this case also involves unequal resonance contributors, but also explains the ambident reactivity of cyanate ion, which can react to give cyanate or isocyanate compounds by reaction at oxygen or at nitrogen, depending on conditions. A similar dichotomy occurs with thiocyanate, cyanide, nitrite and other ions.	Click to view full-size. Cyanate resonance structures.
Amides: The nitrogen atom, with its lone pair of electrons, is a π donor, and the carbonyl group is a π acceptor. There results a partial double bond between N and C, which explains the flatness of the grouping and the relative rotational rigidity of this bond (ca. 15 kcal/mol ou 60 kJ/mol rotational barrier), and an elongated C=O double bond, which explains its infrared absorption at a lower frequency than is typical. Resonance also explains why amide nitrogens are less basic than amine nitrogens, since the lone pair in amides is not really free, and why electrophiles react at oxygen instead. Ureas, urethanes, sulfonamides and phosphorus analogues experience the same kind of resonance.	Click to view full-size. Resonance in formamide, with a π-donating nitrogen and π-accepting carbonyl group.
Carbonyl groups: Besides the neutral, doubly bonded depiction (C=O), one can draw for this group a charged species that would be classified as a 'minor' resonance contributor according to the weighting criteria given earlier. Nevertheless, this form explains the reactivity of carbonyl groups as electrophiles, because the addition of a nucleophile takes place at carbon and not at oxygen. It also explains their behaviour as nucleophiles or bases, which involves the oxygen and not the carbon. All kinds of functional groups that feature a double bond between atoms of differing electronegativity show the same kind of resonance: carbonyl (C=O) groups in aldehydes, ketones, amides, carboxylic acids, esters and carboxylic anhydrides, imino groupings (C=N) in imines and nitriles, S=O groupings in sulfoxides, sulfones and sulfonic acid derivatives, and others.	Click to view full-size. Resonance involving 'major' and 'minor' contributors.
Halonium ions: Elemental halogens (Cl2, Br2, I2) react in water with mono- or trisubstituted alkenes diastereoselectively and regioselectively, to give products called halohydrins in which the OH group is preferentially located at the more highly substituted carbon. To explain the anti selectivity of the process, a cyclic halonium ion is invoked as the reactive intermediate. To explain the regioselectivity, resonance in the halonium ion is invoked: The cyclic form can also be drawn with non-cyclic resonance contributors, which place positive charge on the carbons and, because the resonance structure placing charge on the most highly substituted carbon (the carbon best able to support a positive charge) is expected to be more stable than the other, owing to hyperconjugation and σ donation, the resonance hybrid will have a greater partial positive charge on the most highly substituted carbon, and this is the site of nucleophilic attack. The same resonance situation in protonated epoxides is used to explain the preference for ring opening at the more highly substituted carbon atom under acidic conditions, and in mercurinium ions to explain the regioselectivity of oxymercuration and alkoxymercuration.	Click to view full-size. Resonance involving σ bonds.

What resonance is not

The double-headed arrow ($\longleftrightarrow$) used to indicate resonance, the curved arrows used to show electron movement in changing one resonance structure into another, and the unfortunate name resonance itself all suggest a back-and-forth movement of electrons between limiting structures, a sort of vibration akin to the physical phenomenon of resonance, as Kekulé had imagined. However, a dynamic exchange such as this would be associated with an energy that could in principle be slowed or even stopped by lowering the temperature, but the reality is that there is no temperature-dependent electron movement from one limiting structure to another, and no equilibrium between them. There are, however, molecular vibrations which involve nuclear movement.

Relation to molecular orbital theory

Resonance is a cartoon of the delocalisation that can serve to explain what no single Lewis structure can, but it does not explain why delocalization occurs, except to say that the sharing of electrons is stabilizing. There is no means by which one can quantify that stabilization. Although one can "weigh" the contributions of each "major" or "minor" resonance contributor, one cannot quantify nor graphically depict that weighting. Resonance also does not specify the exact electronic distribution in a resonance hybrid.

Molecular orbital theory can quantify the stabilization resulting from electron delocalisation, convey the resulting electronic distribution and measure the resulting interatomic distances and angles. Molecular orbital theory explains not only π-type bonding (as well as other kinds), but also stabilization by conjugation and hyperconjugation. The mixing of atomic orbitals by overlap in space creates an equal number of hybrids called molecular orbitals (MOs), some of which will be bonding, others anti-bonding and possibly others non-bonding, depending on the number of atomic orbitals. Simply stated, the energies of the anti-bonding MOs will be higher than those of the atomic orbitals while the energies of the bonding MOs will be lower by an equal degree, such that the full population of all the molecular orbitals will be of no energetic advantage, but population of only the bonding and non-bonding orbitals will be stabilizing. The sharing of electrons that resonance depicts translates into the population of lower-energy molecular orbitals.

History

The concept of resonance was introduced by Linus Pauling in 1928. The term "resonance" came from the analogy between the quantum mechanical treatment of the H₂ molecule and a classical system consisting of two coupled oscillators. In the classical system, the coupling produces two modes, one of which is lower in frequency than either of the uncoupled vibrations; quantum-mechanically, this lower frequency is interpreted as a lower energy.

The alternative term mesomerism popular in German and French publications with the same meaning was introduced by Christopher Ingold in 1938 but did not catch on in the English literature. The current concept of mesomeric effect has taken on a related but different meaning. The double headed arrow was introduced by the German chemist Fritz Arndt who preferred the German phrase zwischenstufe or intermediate phase.

Due to confusion with the physical meaning of the word resonance, as no elements actually appear to be resonating, it has been suggested that the term resonance be abandoned in favor of delocalization. Resonance energy would become delocalization energy and a resonance structure becomes a contributing structure. The double headed arrows would be replaced by commas.

See also

• Aromaticity
• Conjugated system
• Delocalization
• Hyperconjugation
• Resonance integral

Bibliography

• R. Morrison, R. Boyd: Organic Chemistry, 5th ed. Prentice Hall, 1989; Chapter 10. (ISBN 0-87692-560-3)
• L. Pauling: The Nature of the Chemical Bond, Cornell University Press (1939) (ISBN 0801403332)
• L. G. Wade, Jr.: Organic Chemistry, 6th ed. Prentice-Hall, 2006 (ISBN 0-13-169957-1) <