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| {{Other uses2|Resonance}}
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| [[File:Stickstoffdioxid.svg|thumb|280px|Two of the contributing structures of [[nitrogen dioxide]]]]
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| In chemistry, '''resonance''' or '''mesomerism''' <ref name='mesomerism'>IUPAC Gold Book [http://goldbook.iupac.org/M03845.html ''mesomerism''] [http://www.iupac.org/goldbook/M03845.pdf PDF]</ref> is a way of describing [[delocalized electron]]s within certain [[molecules]] or [[polyatomic ion]]s where the bonding cannot be expressed by one single [[Lewis formula]]. A molecule or ion with such delocalized electrons is represented by several '''contributing structures''' <ref name='resonance'>IUPAC Gold Book [http://goldbook.iupac.org/R05326.html ''resonance''] [http://www.iupac.org/goldbook/E02005.pdf PDF]</ref> (also called '''resonance structures''' or '''[[canonical form]]s''').
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| Each contributing structure can be represented by a Lewis structure, with only an integer number of [[covalent bond]]s between each pair of atoms within the structure.<ref name='contributing'>IUPAC Gold Book [http://goldbook.iupac.org/C01309.html ''contributing structure''] [http://www.iupac.org/goldbook/C01309.pdf PDF]</ref> Several Lewis structures are used collectively to describe the actual molecular structure. However these individual contributors cannot be observed in the actual resonance-stabilized molecule; the molecule does not oscillate back and forth between the contributing structures, as might be assumed from the word "''resonance''". The actual structure is an approximate intermediate between the canonical forms, but its overall energy is lower than each of the contributors. This intermediate form between different contributing structures is called a '''resonance hybrid'''.<ref name='Pauling'/>
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| Contributing structures differ only in the position of electrons, not in the position of nuclei.
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| Resonance is a key component of [[valence bond theory]].
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| Electron delocalization lowers the potential energy of the substance and thus makes it more stable than any of the contributing structures. The difference between the potential energy of the actual structure and that of the contributing structure with the lowest potential energy is called the '''resonance energy'''<ref name='resonance energy'>IUPAC Gold Book [http://goldbook.iupac.org/R05333.html ''resonance energy''] [http://www.iupac.org/goldbook/R05333.pdf PDF]</ref> or delocalization energy.
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| Resonance is distinguished from [[tautomerism]] and [[conformational isomerism]], which involve the formation of isomers, thus the rearrangement of the nuclear positions.
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| == History ==
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| The concept of resonance was introduced into [[quantum mechanics]] by [[Werner Heisenberg]] in 1926 in a discussion of the quantum states of the helium atom. He compared the structure of the helium atom with the classical system of resonating coupled [[harmonic oscillator]]s.
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| <ref name='Pauling'/><ref>Linus Pauling: [http://osulibrary.oregonstate.edu/specialcollections/coll/pauling/bond/notes/1946a.3-ts-01-large.html ''Resonance''] p.1</ref>
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| [[Linus Pauling]] used this analogy to introduce his resonance theory in 1928.
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| <ref>[http://cabierta.uchile.cl/revista/6/linus.htm The Science and Humanism of Linus Pauling.] See last paragraph of section 1.</ref>
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| 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 stage''.
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| In the Soviet Union, resonance theory — especially as developed by Linus Pauling — was attacked in the early 1950s as being contrary to the Marxist principles of [[dialectical materialism]], and in June 1951 the Soviet Academy of Sciences under the leadership of [[Alexander Nesmeyanov]] convened a conference on the chemical structure of organic compounds, attended by 400 physicists, chemists, and philosophers, where "the pseudo-scientific essence of the theory of resonance was exposed and unmasked".<ref>''Terror and Progress USSR: Some Sources of Change and Stability in the Soviet Dictatorship'' by [[Barrington Moore, Jr.]] (1954), pp. 142-143.</ref>
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| 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''.<ref>''If It's Resonance, What Is Resonating?'' Kerber, Robert C. . J. Chem. Educ. '''2006''' 83 223. [http://www.jce.divched.org/Journal/Issues/2006/Feb/abs223.html Abstract]</ref> Resonance energy would thus become ''delocalization energy'' and a resonance structure becomes a ''contributing structure''. The double headed arrows would be replaced by commas to illustrate a set of structures rather than suggesting that there is a reaction that converts among them.
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| == General characteristics of resonance ==
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| Molecules and ions with resonance (also called mesomerism) have the following basic characteristics:
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| [[File:Carbonate-ion-resonance-2D.png|thumb|380px|Contributing structures of the [[carbonate]] ion]]
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| *They can be represented by several correct Lewis formulas, called "contributing structures", "resonance structures" or "canonical forms". However, the real structure is not a rapid interconversion of contributing structures. Several Lewis structures are used together, because none of them exactly represents the actual structure. To represent the intermediate, a resonance hybrid is used instead.
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| *The contributing structures are not [[isomer]]s. They differ only in the position of electrons, not in the position of nuclei.
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| *Each Lewis formula must have the same number of valence electrons (and thus the same total charge), and the same number of unpaired electrons, if any.<ref>Linus Pauling: [http://osulibrary.oregonstate.edu/specialcollections/coll/pauling/bond/notes/1946a.3-ts-13-large.html ''Resonance''] Manuscript for publication in Encyclopædia Britannica, p.13; July 29, 1946.</ref>
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| *Bonds that have different [[bond order]]s in different contributing structures do not have typical bond lengths. Measurements reveal intermediate bond lengths.
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| *The real structure has a lower total potential energy than each of the contributing structures would have. This means that it is more stable than each separate contributing structure would be.
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| == Use of contributing structures ==
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| In Lewis formulas, covalent bonds are represented in accordance with the [[valence bond theory]].
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| Each single bond is made by two [[valence electron]]s, localized between the two bonded atoms. Each [[double bond]] has two additional localized [[π electron]]s, while each [[triple bond]] has four additional π electrons (two pairs) between the bonded atoms.
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| In molecules or ions that have a combination of one or more single and multiple bonds, often the ''exact'' position of the respective bonds in the Lewis formula cannot be indicated. The π electrons appear to be [[delocalized]] and the multiple bonds could be in different positions. In those cases the molecule cannot be represented by one single Lewis formula. To solve this problem, in valence bond theory the concept of resonance is used, and the molecule is represented by several contributing structures, each showing a possible distribution of single and multiple bonds. The [[molecular orbital theory]] already includes the concept of delocalized electrons and therefore has no need of the concept of resonance.
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| None of the contributing structures are considered to represent the actual structure, since bonds that have a different [[bond order]] in different contributing structures do not have, if measured, a bond length that is typical for a normal single or multiple bond. Moreover, the overall energy of the actual structure is lowered with the resonance energy.
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| === Resonance hybrids ===
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| The actual structure of a molecule in the ''normal quantum state'' has the lowest possible value of total energy. This structure is called the "resonance hybrid" of that molecule. The resonance hybrid is the approximate intermediate of the contributing structures, but the overall energy is lower than each of the contributors, due to the resonance energy. Any molecule or ion exists in only one form - the resonance hybrid. It does not jump back and forth between its resonance contributors- looking like one this moment and like another the next moment.
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| <ref name='Pauling'>Linus Pauling: [http://books.google.com/books?id=L-1K9HmKmUUC&pg=PA10 ''The Nature of the chemical bond - An Introduction to Modern Structural Chemistry''] Cornell University Press, third Edition 1960, ''The Concept of Resonance'', pp.10-13</ref> | |
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| === Major and minor contributors ===
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| One contributing structure may resemble the actual molecule more than another (in the sense of energy and stability). Structures with a low value of potential energy are more stable than those with high values and resemble the actual structure more. The most stable contributing structures are called ''major contributors''. Energetically unfavourable and therefore less probable structures are ''minor contributors''.<br />
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| Major contributors are generally structures
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| *that obey as much as possible the [[octet rule]] (8 valence electrons around each atom rather than having deficiencies or surplus)
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| *that have a maximum number of covalent bonds
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| *that carry a minimum of charged atoms. If unlike charges are present their separation must be least while for like charges the separation must be maximum.
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| *with negative charge, if any, on the most [[electronegativity|electronegative]] atoms and positive charge, if any, on the most electropositive.
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| The greater the number of contributing structures, the more stable the molecule. This is because the more states at lower energy are available to the electrons in a particular molecule, the more stable the electrons are. Also the more volume electrons can occupy at lower energy the more stable the molecule is. We can also understand this concept by borrowing a concept of physics. As we know that charge dispersed is directly proportional to stability. Here, electrons can be termed as charged bodies and the more volume they occupy, more the charge gets dispersed ultimately leading to stability.{{cn|date=December 2011}} <!-- Can we have a reference that deals with molecules? I suggest this is true only for the free electron gas. -->
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| Equivalent contributors contribute equally to the actual structure; those with low potential energy (the major contributors) contribute more to the resonance hybrid than the less stable minor contributors. Especially when there is more than one major contributor, the resonance stabilization is high. High values of resonance energy are found in [[Aromaticity|aromatic molecules]].
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| === Contributing structures in diagrams ===
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| [[File:Thiocyanate-resonance-2.png|thumb|upright=1.4|Contributing structures of the [[thiocyanate ion]], enclosed in square brackets.]]
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| {{double image|right|Nitrate-ion-resonance-hybrid-2D.png|130|Benzene circle.svg|100|Hybrid of the [[nitrate]] ion|Hybrid of [[benzene]].}}
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| In diagrams, contributing structures are typically separated by double-headed arrows ([[File:Arrowlr.svg|30px]]). The arrow should not be confused with the right and left pointing ''equilibrium arrow'' ([[File:U+21CC.svg|25px]]).
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| All structures together may be enclosed in large square brackets, to indicate they picture one single molecule or ion, not different species in a [[chemical equilibrium]].
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| Alternatively to the use of resonance structures in diagrams, a hybrid diagram can be used. In a hybrid diagram, pi bonds that are involved in resonance are usually pictured as curves
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| <ref>[http://www.iupac.org/publications/pac/2008/pdf/8002x0277.pdf Graphical representation for chemical structure diagrams (IUPAC Recommendations 2008)] GR-8, p.387</ref> or dashed lines, indicating that these are partial rather than normal complete pi bonds. In benzene and other aromatic rings, the delocalized pi-electrons are sometimes pictured as a solid circle.<ref>[http://www.iupac.org/publications/pac/2008/pdf/8002x0277.pdf Graphical representation for chemical structure diagrams (IUPAC Recommendations 2008)] GR-6, pp.379-382</ref>
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| {{Clear}}
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| ==Bond lengths==
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| [[Image:Benz3.svg|thumb|350px|right|Resonance structures of [[benzene]]]]
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| Comparing the two contributing structures of [[benzene]], all single and double bonds are interchanged. [[Bond length]]s can be measured, for example using [[X-ray diffraction]]. The average length of a C-C single bond is 154 [[picometres|pm]]; that of a C=C double bond is 133 pm. In localized cyclohexatriene, the carbon-carbon bonds should be alternating 154 and 133 pm. Instead, all carbon-carbon bonds in benzene are found to be about 139 pm, a bond length intermediate between single and double bond. This mixed single and double bond (or triple bond) character is typical for all molecules in which bonds have a different [[bond order]] in different contributing structures. Bond lengths can be compared using bond orders. For e.g. in cyclohexane the bond order is 1 while that in benzene is 1+(3/6)= 1.5 . Consequently, benzene has more double bond character and hence has a shorter bond length than cyclohexane.
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| {{clear}}
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| ==Resonance energy ==
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| Every structure is associated with a certain quantity of energy, which determines the stability of the molecule or ion (the lower energy, the greater stability). A resonance hybrid has a ''structure'' that is intermediate between the contributing structures; the total quantity of ''potential energy'', however, is lower than the intermediate. Hybrids are therefore always more stable than any of the contributing structures would be.<ref>{{cite book |author= Robert Morrison, Robert Boyd|title=Organic Chemistry|edition=Fifth Edition|year=1989|publisher=Prentice Hall of India|isbn=0-87692-560-3|pages=372|chapter=Chapter 10|quote=The resonance hybrid is more stable than any of the contributing structures.}}</ref>
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| The molecule is sometimes said to be "stabilized by resonance" or "resonance-stabilized," but the stabilization derives from electron delocalization, of which "resonance" is only a description. Delocalization of the π-electrons lowers the orbital energies, imparting this stability. The difference between the potential energy of the actual structure (the resonance hybrid) and that of the contributing structure with the lowest potential energy is called the "resonance energy".<ref name='resonance energy'/>
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| ===Resonance energy of benzene===
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| Resonance (or delocalization) energy is the amount of energy needed to convert the true delocalized structure into that of the most stable contributing structure. The ''empirical resonance energy'' can be estimated by comparing the [[enthalpy change]] of [[hydrogenation]] of the real substance with that estimated for the contributing structure.
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| The complete hydrogenation of benzene to [[cyclohexane]] via [[1,3-cyclohexadiene]] and [[cyclohexene]] is [[exothermic]]; 1 mole benzene delivers 208.4 kJ (49.8 kcal).
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| [[File:Benzene hydrogenation.svg|800px]]
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| Hydrogenation of one mole of double bonds delivers 119.7 kJ (28.6 kcal), as can be deduced from the last step, the hydrogenation of cyclohexene. In benzene, however, 23.4 kJ (5.6 kcal) are needed to hydrogenate one mole of double bonds. The difference, being 143.1 kJ (34.2 kcal), is the empirical resonance energy of benzene. Because 1,3-cyclohexadiene also has a small delocalization energy (7.6 kJ or 1.8 kcal/mol) the net resonance energy, relative to the localized cyclohexatriene, is a bit higher: 151 kJ or 36 kcal/mol.
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| <ref>Wiberg, Nakaji and Morgan [http://pubs.acs.org/doi/abs/10.1021/ja00062a017 ''Heat of hydrogenation of a cis imine. An experimental and theoretical study''] J. Am. Chem. Soc., 1993, 115 (9), pp 3527–3532; {{doi|10.1021/ja00062a017}}</ref>
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| This measured resonance energy is also the difference between the hydrogenation energy of three 'non-resonance' double bonds and the measured hydrogenation energy:
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| :(3 × 119.7) − 208.4 = 150.7 kJ/mol (36 kcal).<ref>J. Sherman [http://resources.metapress.com/pdf-preview.axd?code=xg78062p2312q56g&size=largest ''The heats of hydrogenation of unsaturated hydrocarbons.''] Journal of the American Oil Chemists' Society; Volume 16, Number 2; February, 1939; {{doi|10.1007/BF02543208}}</ref>
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| == Resonance in quantum mechanics ==
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| Resonance has a deeper significance in the mathematical formalism of [[valence bond theory]] (VB). When a molecule cannot be represented by the standard tools of valence bond theory (promotion, [[orbital hybridisation|hybridisation]], orbital overlap, [[sigma bond|sigma]] and [[pi bond|π bond]] formation) because no single structure predicted by VB can account for all the properties of the molecule, one invokes the concept of resonance.
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| Valence bond theory gives us a model for benzene where each carbon atom makes two sigma bonds with its neighbouring carbon atoms and one with a hydrogen atom. But since carbon is tetravalent, it has the ability to form one more bond. In VB it can form this extra bond with either of the neighbouring carbon atoms, giving rise to the familiar [[Friedrich August Kekulé von Stradonitz|Kekulé]] ring structure. But this cannot account for all carbon-carbon bond lengths being equal in benzene. A solution is to write the actual [[wavefunction]] of the molecule as a linear superposition of the two possible Kekulé structures (or rather the wavefunctions representing these structures), creating a wavefunction that is neither of its components but rather a superposition of them.
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| In benzene both Kekulé structures have equal energy and are equal contributors to the overall structure—the superposition is an equally-weighted average, or a 1:1 linear combination of the two—but this need not be the case. In general, the superposition is written with undetermined coefficients, which are then variationally [[optimization (mathematics)|optimized]] to find the lowest possible energy for the given set of basis wavefunctions. This is taken to be the best approximation that can be made to the real structure, though a better one may be made with addition of more structures.
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| === Molecular orbital (MO) versus valence bond (VB) theory ===
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| In [[molecular orbital theory]], the main alternative to [[valence bond theory]], resonance often (but not always) translates to a [[delocalized electron|delocalization of electrons]] in π orbitals (which are a separate concept from π bonds in VB). In MO theory, the molecular orbitals (MOs) are approximated as sums of all the atomic orbitals (AOs) on all the atoms; there are as many MOs as AOs. Each AO<sub>i</sub> has a ''weighting'' coefficient c<sub>i</sub> that indicates the AO's contribution to a particular MO. For example, in benzene, the MO model gives us 6 π MOs which are combinations of the 2p<sub>z</sub> AOs on each of the 6 C atoms. Thus, each π MO is delocalized over the whole benzene molecule and any electron ''occupying'' an MO will be delocalized over the whole molecule. This MO interpretation has inspired the picture of the benzene ring as a hexagon with a circle inside. When describing benzene, the VB concept of localized sigma 'bonds' and the MO concept of 'delocalized' π electrons are frequently combined in elementary chemistry courses.
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| The resonance structures in the VB model are particularly useful in predicting the effect of [[substituents]] on π systems such as benzene. They lead to the models of resonance structures for an [[electron-withdrawing group]] and [[electron-releasing group]] on benzene. The utility of MO theory is that a quantitative indication of the charge from the π system on an atom can be obtained from the squares of the ''weighting'' coefficient c<sub>i</sub> on atom C<sub>i</sub>. Charge ''q<sub>i</sub>'' ≈ c<sub>i</sub><sup>2</sup>. The reason for squaring the coefficient is that if an electron is described by an AO, then the square of the AO gives the [[electron density]]. The AOs are adjusted ([[Normalizing constant|normalized]]) so that AO<sup>2</sup> =1, and ''q<sub>i</sub>'' ≈ (c<sub>i</sub>AO<sub>i</sub>)<sup>2</sup> ≈ c<sub>i</sub><sup>2</sup>. In benzene, q<sub>i</sub> = 1 on each C atom. With an [[electron-withdrawing group]] q<sub>i</sub> < 1 on the ''ortho'' and ''para'' C atoms and > 1 for an [[electron-releasing group]].
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| === Coefficients ===
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| Weighting of the of resonance structures in terms of their contribution to the overall structure can be calculated in multiple ways, using ''"Ab initio"'' methods derived from Valence Bond theory, or else from the [[Natural Bond Orbital]]s (NBO) approaches of Weinhold [http://www.chem.wisc.edu/~nbo5 NBO5], or finally from empirical calculations based on the Hückel method. A Hückel method-based software for teaching resonance is available on the [http://www.hulis.free.fr HuLiS] Web site.
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| == Representations ==
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| ===Ionic-covalent molecules===
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| The [[ozone]] molecule is represented by two resonance structures. In reality the two terminal oxygen atoms are equivalent and the hybrid structure is drawn on the right with a charge of -1/2 on both oxygen atoms and partial double bonds with a full and dashed line and [[bond order]] 1.5.<ref>''Organic Chemistry'' (6th Edition)
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| L. G. Wade</ref><ref>''Organic Chemistry'' (4th Edition) Paula Y. Bruice</ref>
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| :[[File:Delocalization ozone.svg|Delocalization ozone]]
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| For [[hypervalent molecule]]s such as xenon difluoride, the rationalization described above can be applied to generate resonance structures to explain the bonding in such molecules. This has been shown by quantum chemical calculations to be the correct description instead of the common expanded octet model.
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| <center><math>\bigg[\ F \frac{\quad}{\quad} Xe^+ \ {}^-\!F \quad \longleftrightarrow \quad F^- \ {}^+\!Xe \frac{\quad}{\quad} F\ \bigg]</math></center>
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| ===Aromatic molecules===
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| {{main|Aromaticity}}
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| In [[benzene]] the two cyclohexatriene ''Kekulé'' structures first proposed by [[Friedrich August Kekulé von Stradonitz|Kekulé]] are taken together as contributing structures to represent the total structure. In the hybrid structure on the right the dashed hexagon replaces three double bonds, and represents six electrons in a set of three [[molecular orbital]]s of [[pi orbital|π]] symmetry, with a [[node (physics)|nodal plane]] in the plane of the molecule.
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| :[[File:Benzene delocalization.svg|Benzene delocalization]]
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| In [[furan]] a [[lone pair]] of the oxygen atom interacts with the π orbitals of the carbon atoms.
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| The [[curved arrow]]s depicture the move of [[delocalized electron|delocalized π electrons]], which results in different contributors.
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| :[[File:Furan Resonance.png|700px|Contributing structures of furan]]
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| === Electron-deficient molecules ===
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| The [[diborane]] molecule is described by resonance structures, each with electron-deficiency on different atoms. This reduces the electron-deficiency on each atom and stabilizes the molecule. Below are the resonance structures of an individual [[three-center two-electron bond|3c-2e]] bond in diborane.
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| [[File:Diborane resonance.svg|500px|Contributing structures of diborane.]]
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| The [[allyl cation]] has two contributing structures with a positive charge on the terminal carbon atoms. In the hybrid structure their charge is +1/2. The full positive charge can also be depicted as delocalized among three carbon atoms.
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| :[[File:Delocalization allyl cation.svg|Delocalization allyl cation]]
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| === Reactive intermediates ===
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| {{Main|Reactive intermediate}}
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| Often, reactive intermediates such as [[carbocations]] and [[free radicals]] have more delocalized structure than their parent reactants, giving rise to unexpected products. The classical example is [[allylic rearrangement]]. When 1 mole of HCl adds to 1 mole of 1,3-butadiene, in addition to the ordinarily expected product 3-chloro-1-butene, we also find 1-chloro-2-butene. Isotope labelling experiments have shown that what happens here is that the additional double bond shifts from 1,2 position to 2,3 position in some of the product. This and other evidence (such as [[NMR]] in [[superacid]] solutions) shows that the intermediate carbocation must have a highly delocalized structure, different from its mostly classical (delocalization exists but is small) parent molecule. This cation (an allylic cation) can be represented using resonance, as shown above.
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| This observation of greater delocalization in less stable molecules is quite general. The excited states of conjugated [[diene]]s are stabilised more by conjugation than their ground states, causing them to become organic dyes.
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| A well-studied example of delocalization that does not involve π electrons ([[hyperconjugation]]) can be observed in the [[non-classical ion]] [[norbornane|norbornyl cation]]. Other examples are [[diborane]] (see above) and [[methanium]] (CH<sub>5</sub><sup>+</sup>). These can be viewed as containing [[three-center two-electron bond]]s and are represented either by contributing structures involving rearrangement of sigma electrons or by a special notation, a Y that has the three nuclei at its three points.
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| ==See also==
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| {{Commons category|Mesomerism}}
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| * [[Aromaticity]]
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| * [[Conjugated system]]
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| * [[Delocalization]]
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| * [[Hyperconjugation]]
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| * [[Tautomerism]]
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| * [[Avoided crossing]]
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| ==External links==
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| * {{fr}} {{cite web
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| | url = http://www.hulis.free.fr
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| | title = HuLiS : Java Applet - Simple Hückel Theory and Mesomery - program logiciel software
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| | author = N. Goudard, Y. Carissan, D. Hagebaum-Reignier, S. Humbel
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| | year = 2008
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| | accessdate = 29 October 2010
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| }}
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| == References ==
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| {{Reflist}}
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| {{DEFAULTSORT:Resonance (Chemistry)}}
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| [[Category:Chemical bonding]]
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| [[ru:Химический резонанс]]
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| [[tr:Rezonans (fizik)]]
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| [[zh:共振论]]
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