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<title>Conjugated system</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Conjugated system</span></span>

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<p>In <a href="Physical_organic_chemistry" title="Physical organic chemistry">physical organic chemistry</a>, a <b>conjugated system</b> is a system of connected <a href="P-orbital" class="mw-redirect" title="P-orbital">p-orbitals</a> with <a href="Delocalized_electron" title="Delocalized electron">delocalized electrons</a> in a <a href="Molecule" title="Molecule">molecule</a>, which in general lowers the overall energy of the molecule and increases <a href="Chemical_stability" title="Chemical stability">stability</a>. It is <a href="Resonance_(chemistry)" title="Resonance (chemistry)">conventionally represented</a> as having alternating single and multiple <a href="Covalent_bond" title="Covalent bond">bonds</a>. <a href="Lone_pair" title="Lone pair">Lone pairs</a>, <a href="Radical_(chemistry)" title="Radical (chemistry)">radicals</a> or <a href="Carbenium_ion" title="Carbenium ion">carbenium ions</a> may be part of the system, which may be <a href="Cyclic_molecule" class="mw-redirect" title="Cyclic molecule">cyclic</a>, acyclic, <a href="Linear_molecular_geometry" title="Linear molecular geometry">linear</a> or mixed. The term "conjugated" was coined in 1899 by the German chemist <a href="Johannes_Thiele_(chemist)" title="Johannes Thiele (chemist)">Johannes Thiele</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p><b>Conjugation</b> is the <a href="Orbital_overlap" title="Orbital overlap">overlap</a> of one p-orbital with another across an adjacent <a href="Sigma_bond" title="Sigma bond">σ bond</a>. (In <a href="Transition_metal" title="Transition metal">transition metals</a>, d-orbitals can be involved.)<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup>

</p><p>A conjugated system has a region of overlapping p-orbitals, bridging the interjacent locations that simple diagrams illustrate as not having a π bond. They allow a delocalization of <a href="Pi_electrons" class="mw-redirect" title="Pi electrons">π electrons</a> across all the adjacent aligned p-orbitals.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

The π electrons do not belong to a single bond or <a href="Atom" title="Atom">atom</a>, but rather to a group of atoms.

</p><p>Molecules containing conjugated systems of orbitals and electrons are called <b>conjugated molecules</b>, which have overlapping p orbitals on three or more atoms. Some simple <a href="Organic_chemistry" title="Organic chemistry">organic</a> conjugated molecules are 1,3-butadiene, benzene, and <a href="Allylic" class="mw-redirect" title="Allylic">allylic</a> carbocations.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The largest conjugated systems are found in <a href="Graphene" title="Graphene">graphene</a>, <a href="Graphite" title="Graphite">graphite</a>, <a href="Conductive_polymer" title="Conductive polymer">conductive polymers</a> and <a href="Carbon_nanotube" title="Carbon nanotube">carbon nanotubes</a>.

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<div class="mw-heading mw-heading2"><h2 id="Chemical_bonding_in_conjugated_systems">Chemical bonding in conjugated systems</h2></div>

<p>Conjugation is possible by means of alternating single and <a href="Double_bond" title="Double bond">double bonds</a> in which each atom supplies a p orbital perpendicular to the plane of the molecule. However, that is not the only way for conjugation to take place. As long as each contiguous atom in a chain has an available p orbital, the system can be considered conjugated. For example, <a href="Furan" title="Furan">furan</a> is a five-membered ring with two alternating double bonds flanking an <a href="Oxygen" title="Oxygen">oxygen</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The oxygen has two <a href="Lone_pair" title="Lone pair">lone pairs</a>, one of which occupies a p orbital perpendicular to the ring on that position, thereby maintaining the conjugation of that five-membered ring by overlap with the perpendicular p orbital on each of the adjacent carbon atoms. The other lone pair remains in plane and does not participate in conjugation.

</p><p>In general, any sp<sup>2</sup> or sp-hybridized carbon or <a href="Heteroatom" title="Heteroatom">heteroatom</a>, including ones bearing an empty orbital or lone pair orbital, can participate in conjugated systems. However lone pairs do not always participate in a conjugated system. For example, in <a href="Pyridine" title="Pyridine">pyridine</a>, the nitrogen atom already participates in the conjugated system through a formal double bond with an adjacent carbon, so the lone pair remains in the plane of the ring in an sp<sup>2</sup> hybrid orbital and does not participate in the conjugation. A requirement for conjugation is orbital overlap. Thus, the conjugated system must be planar (or nearly so). As a consequence, lone pairs which do participate in conjugated systems will occupy orbitals of pure p character instead of sp<sup><i>n</i></sup> hybrid orbitals typical for nonconjugated lone pairs.

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<p>A common model for the treatment of conjugated molecules is a composite valence bond / Hückel molecular orbital theory (VB/HMOT) treatment, in which the σ framework of the molecule is separated from the π system (or systems) of the molecule (<i>see the article on the <a href="Sigma-pi_and_equivalent-orbital_models" title="Sigma-pi and equivalent-orbital models">sigma-pi and equivalent-orbital models</a> for this model and an alternative treatment</i>). Although σ bonding can be treated using a delocalized approach as well, it is generally the π bonding that is being considered when delocalized bonding is invoked in the context of simple organic molecules.

</p><p><i>Sigma (σ) framework</i>: The σ framework is described by a strictly localized bonding scheme and consists of σ bonds formed from the interactions between sp<sup>3</sup>-, sp<sup>2</sup>-, and sp-<a href="Orbital_hybridisation" title="Orbital hybridisation">hybridized atomic orbitals</a> on the main group elements (and 1s atomic orbitals on hydrogen), together with localized lone pairs derived from filled, nonbonding hybrid orbitals. The interaction that results in σ bonding takes the form of head-to-head overlap of the larger lobe of each hybrid orbital (or the single spherical lobe of a hydrogen 1s orbital). Each atomic orbital contributes one electron when the orbitals overlap pairwise to form two-electron σ bonds, or two electrons when the orbital constitutes a lone pair. These localized orbitals (bonding and non-bonding) are all located in the plane of the molecule, with σ bonds mainly localized between nuclei along the internuclear axis.

</p><p><i>Pi (π) system or systems</i>: Orthogonal to the σ framework described above, π bonding occurs above and below the plane of the molecule where σ bonding takes place. The π system(s) of the molecule are formed by the interaction of unhybridized p atomic orbitals on atoms employing sp<sup>2</sup>- and sp-hybridization. The interaction that results in π bonding takes place between p orbitals that are adjacent by virtue of a σ bond joining the atoms and takes the form of side-to-side overlap of the two equally large lobes that make up each p orbital. Atoms that are sp<sup>3</sup>-hybridized do not have an unhybridized p orbital available for participation in π bonding and their presence necessarily terminates a π system or separates two π systems. A basis p orbital that takes part in a π system can contribute one electron (which corresponds to half of a formal "double bond"), two electrons (which corresponds to a delocalized "lone pair"), or zero electrons (which corresponds to a formally "empty" orbital). Bonding for π systems formed from the overlap of more than two p orbitals is handled using the <a href="H%C3%BCckel_method" title="Hückel method">Hückel approach</a> to obtain a zeroth order (qualitative) approximation of the π symmetry molecular orbitals that result from delocalized π bonding.

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<p>This simple model for chemical bonding is successful for the description of most normal-valence molecules consisting of only s- and p-block elements, although systems that involve electron-deficient bonding, including nonclassical carbocations, lithium and boron clusters, and hypervalent centers require significant modifications in which σ bonds are also allowed to delocalize and are perhaps better treated with canonical molecular orbitals that are delocalized over the entire molecule. Likewise, d- and f-block organometallics are also inadequately described by this simple model. Bonds in strained small rings (such as cyclopropane or epoxide) are not well-described by strict σ/π separation, as bonding between atoms in the ring consists of "<a href="Bent_bond" title="Bent bond">bent bonds</a>" or "banana bonds" that are bowed outward and are intermediate in nature between σ and π bonds. Nevertheless, organic chemists frequently use the language of this model to rationalize the structure and reactivity of typical organic compounds.

</p><p>Electrons in conjugated π systems are shared by all adjacent sp<sup>2</sup>- and sp-hybridized atoms that contribute overlapping, parallel p atomic orbitals. As such, the atoms and π-electrons involved behave as one large bonded system. These systems are often referred to '<i>n</i>-center <i>k-</i>electron π-bonds,' compactly denoted by the symbol Π<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"><i>k</i></sup><br><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><i>n</i></sub></span></span>, to emphasize this behavior. For example, the delocalized π electrons in acetate anion and benzene are said to be involved in Π<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sup><br><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sub></span></span> and Π<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">6</sup><br><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">6</sub></span></span> systems, respectively (<i>see the article on <a href="Three-center_four-electron_bond" title="Three-center four-electron bond">three-center four-electron bonding</a></i>). Generally speaking, these multi-center bonds correspond to the occupation of several molecular orbitals (MOs) with varying degrees of bonding or non-bonding character (filling of orbitals with antibonding character is uncommon). Each one is occupied by one or two electrons in accordance with the <a href="Aufbau_principle" title="Aufbau principle">Aufbau principle</a> and <a href="Hund's_rule_of_maximum_multiplicity" title="Hund's rule of maximum multiplicity">Hund's rule</a>. Cartoons showing overlapping p orbitals, like the one for benzene below, show the basis p atomic orbitals <i>before</i> they are combined to form molecular orbitals. In compliance with the <a href="Pauli_exclusion_principle" title="Pauli exclusion principle">Pauli exclusion principle</a>, overlapping p orbitals <i>do not</i> result in the formation of one large MO containing more than two electrons.

</p><p><a href="H%C3%BCckel_method" title="Hückel method">Hückel MO theory</a> is commonly used approach to obtain a zeroth order picture of delocalized π molecular orbitals, including the mathematical sign of the wavefunction at various parts of the molecule and the locations of nodal planes. It is particularly easy to apply for conjugated hydrocarbons and provides a reasonable approximation as long as the molecule is assumed to be planar with good overlap of p orbitals.

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<div class="mw-heading mw-heading2"><h2 id="Stabilization_energy">Stabilization energy</h2></div>

<p>The quantitative estimation of stabilization from conjugation is notoriously contentious and depends on the implicit assumptions that are made when comparing reference systems or reactions. The energy of stabilization is known as the <b>resonance energy</b> when formally defined as the difference in energy between the real chemical species and the hypothetical species featuring localized π bonding that corresponds to the most stable <a href="Resonance_(chemistry)" title="Resonance (chemistry)">resonance form</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> This energy cannot be measured, and a precise definition accepted by most chemists will probably remain elusive. Nevertheless, some broad statements can be made. In general, stabilization is more significant for cationic systems than neutral ones. For <a href="Butadiene" title="Butadiene">buta-1,3-diene</a>, a crude measure of stabilization is the <a href="Activation_energy" title="Activation energy">activation energy</a> for rotation of the C2-C3 bond. This places the resonance stabilization at around 6 kcal/mol.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Comparison of heats of hydrogenation of <a href="Pentadiene" title="Pentadiene">1,4-pentadiene</a> and 1,3-pentadiene estimates a slightly more modest value of 3.5 kcal/mol.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> For comparison, allyl cation has a gas-phase rotation barrier of around 38 kcal/mol,<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> a much greater penalty for loss of conjugation. Comparison of hydride ion affinities of propyl cation and allyl cation, corrected for inductive effects, results in a considerably lower estimate of the resonance energy at 20–22 kcal/mol.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Nevertheless, it is clear that conjugation stabilizes allyl cation to a much greater extent than buta-1,3-diene. In contrast to the usually minor effect of neutral conjugation, aromatic stabilization can be considerable. Estimates for the resonance energy of benzene range from around 36–73 kcal/mol.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Generalizations_and_related_concepts">Generalizations and related concepts</h2></div>

<p>There are also other types of interactions that generalize the idea of interacting p orbitals in a conjugated system. The concept of <i>hyperconjugation</i> holds that certain σ bonds can also delocalize into a low-lying unoccupied orbital of a π system or an unoccupied p orbital. <a href="Hyperconjugation" title="Hyperconjugation">Hyperconjugation</a> is commonly invoked to explain the stability of alkyl substituted radicals and carbocations. Hyperconjugation is less important for species in which all atoms satisfy the octet rule, but a recent computational study supports hyperconjugation as the origin of the increased stability of alkenes with a higher degree of substitution (<a href="Zaitsev's_rule" class="mw-redirect" title="Zaitsev's rule">Zaitsev's rule</a>).<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>

</p><p><i>Homoconjugation</i><sup id="cite_ref-IUPAC_14-0" class="reference"><a href="#cite_note-IUPAC-14"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> is an overlap of two π-systems separated by a non-conjugating group, such as CH<sub>2</sub>. Unambiguous examples are comparatively rare in neutral systems, due to a comparatively minor energetic benefit that is easily overridden by a variety of other factors; however, they are common in cationic systems in which a large energetic benefit can be derived from delocalization of positive charge (<i>see the article on <a href="Homoaromaticity" title="Homoaromaticity">homoaromaticity</a> for details.</i>).<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Neutral systems generally require constrained geometries favoring interaction to produce significant degrees of homoconjugation.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> In the example below, the carbonyl stretching frequencies of the IR spectra of the respective compounds demonstrate homoconjugation, or lack thereof, in the neutral ground state molecules.

</p><p>Due to the partial π character of formally σ bonds in a cyclopropane ring, evidence for transmission of "conjugation" through cyclopropanes has also been obtained.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup>

</p><p>Two appropriately aligned π systems whose ends meet at right angles can engage in spiroconjugation<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> or in homoconjugation across the spiro atom.

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<p><a href="Vinylogy" title="Vinylogy">Vinylogy</a> is the extension of a functional group through a conjugated organic bonding system, which transmits <a href="Electronic_effects" class="mw-redirect" title="Electronic effects">electronic effects</a>.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Conjugated_cyclic_compounds">Conjugated cyclic compounds</h2></div>

<p><a href="Cyclic_compound" title="Cyclic compound">Cyclic compounds</a> can be partly or completely conjugated. <a href="Annulenes" class="mw-redirect" title="Annulenes">Annulenes</a>, completely conjugated monocyclic hydrocarbons, may be aromatic, nonaromatic or antiaromatic.

</p><div class="mw-heading mw-heading3"><h3 id="Aromatic_compounds">Aromatic compounds</h3></div>

<p>Compounds that have a monocyclic, planar conjugated system containing <a href="4n%2B2_rule" class="mw-redirect" title="4n+2 rule">(4<i>n</i> + 2) π-electrons</a> for whole numbers <i>n</i> are <a href="Aromaticity" title="Aromaticity">aromatic</a> and exhibit an unusual stability. The classic example <a href="Benzene" title="Benzene">benzene</a> has a system of six π electrons, which, together with the planar ring of C–C σ bonds containing 12 electrons and radial C–H σ bonds containing six electrons, forms the thermodynamically and kinetically stable <i><a href="Benzene_ring" class="mw-redirect" title="Benzene ring">benzene ring</a></i>, the common core of the benzenoid aromatic compounds. For benzene itself, there are two equivalent conjugated contributing Lewis structures (the so-called Kekulé structures) that predominate.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> The true electronic structure is therefore a quantum-mechanical combination (resonance hybrid) of these contributors, which results in the experimentally observed C–C bonds which are intermediate between single and double bonds and of equal strength and length. In the molecular orbital picture, the six p atomic orbitals of benzene combine to give six molecular orbitals. Three of these orbitals, which lie at lower energies than the isolated p orbital and are therefore net bonding in character (one molecular orbital is strongly bonding, while the other two are equal in energy but bonding to a lesser extent) are occupied by six electrons, while three destabilized orbitals of overall antibonding character remain unoccupied. The result is strong thermodynamic and kinetic aromatic stabilization. Both models describe rings of π electron density above and below the framework of C–C σ bonds.

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<div class="mw-heading mw-heading3"><h3 id="Nonaromatic_and_antiaromatic_compounds">Nonaromatic and antiaromatic compounds</h3></div>

<p>Not all compounds with alternating double and single bonds are aromatic. <a href="Cyclooctatetraene" title="Cyclooctatetraene">Cyclooctatetraene</a>, for example, possesses alternating single and double bonds. The molecule typically adopts a "tub" <a href="Conformational_isomerism" class="mw-redirect" title="Conformational isomerism">conformation</a>. Because the p orbitals of the molecule do not align themselves well in this non-planar molecule, the π bonds are essentially isolated and not conjugated. The lack of conjugation allows the 8 π electron molecule to avoid <a href="Antiaromaticity" title="Antiaromaticity">antiaromaticity</a>, a destabilizing effect associated with cyclic, conjugated systems containing 4<i>n</i> π (<i>n</i> = 0, 1, 2, ...) electrons. This effect is due to the placement of two electrons into two degenerate nonbonding (or nearly nonbonding) orbitals of the molecule, which, in addition to drastically reducing the thermodynamic stabilization of delocalization, would either force the molecule to take on triplet diradical character, or cause it to undergo <a href="Jahn%E2%80%93Teller_effect" title="Jahn–Teller effect">Jahn-Teller distortion</a> to relieve the degeneracy. This has the effect of greatly increasing the kinetic reactivity of the molecule. Because of the lack of long-range interactions, cyclooctatetraene takes on a nonplanar conformation and is nonaromatic in character, behaving as a typical alkene. In contrast, derivatives of the cyclooctatetraene dication and dianion have been found to be planar experimentally, in accord with the prediction that they are stabilized aromatic systems with 6 and 10 π electrons, respectively. Because antiaromaticity is a property that molecules try to avoid whenever possible, only a few experimentally observed species are believed to be antiaromatic. <a href="Cyclobutadiene" title="Cyclobutadiene">Cyclobutadiene</a> and cyclopentadienyl cation are commonly cited as examples of antiaromatic systems.

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<div class="mw-heading mw-heading2"><h2 id="In_pigments">In pigments</h2></div>

<p>In a conjugated pi-system, electrons are able to capture certain photons as the electrons resonate along a certain distance of p-orbitals, similar to how a <a href="Antenna_(radio)" title="Antenna (radio)">radio antenna</a> detects radio signals along its length. Typically, the more conjugated (longer) the pi-system is, the longer the wavelength of photon can be captured. Compounds whose molecules contain a sufficient number of conjugated bonds can absorb light in the visible region, and therefore appear colorful to the eye, usually appearing yellow or red.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup>

</p><p>Many <a href="Dye" title="Dye">dyes</a> make use of conjugated electron systems to absorb <a href="Visible_light" class="mw-redirect" title="Visible light">visible light</a>, giving rise to strong colors. For example, the long conjugated <a href="Hydrocarbon" title="Hydrocarbon">hydrocarbon</a> chain in <a href="Beta-carotene" class="mw-redirect" title="Beta-carotene">beta-carotene</a> leads to its strong orange color. When an electron in the system absorbs a <a href="Photon" title="Photon">photon</a> of light of the right <a href="Wavelength" title="Wavelength">wavelength</a>, it can be promoted to a higher energy level. A simple model of the energy levels is provided by the <a href="Quantum_mechanics" title="Quantum mechanics">quantum-mechanical</a> problem of a one-dimensional <a href="Particle_in_a_box" title="Particle in a box">particle in a box</a> of length L, representing the movement of a π electron along a long conjugated chain of carbon atoms. In this model the lowest possible absorption energy corresponds to the energy difference between the highest occupied molecular orbital (<a href="HOMO/LUMO" class="mw-redirect" title="HOMO/LUMO">HOMO</a>) and the lowest unoccupied molecular orbital (LUMO). For a chain of <i>n</i> C=C bonds or 2<i>n</i> carbon atoms in the molecular <a href="Ground_state" title="Ground state">ground state</a>, there are 2<i>n</i> π electrons occupying <i>n</i> molecular orbitals, so that the energy gap is<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup>

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<annotation encoding="application/x-tex">{\displaystyle E_{n+1}-E_{n}={\frac {(2n+1)\hbar ^{2}\pi ^{2}}{2mL^{2}}}}</annotation>

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</math></span><img src="./df2b81c8ab3541e056d98b3ad5f9d1a93a32108b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:27.877ex; height:6.176ex;" alt="{\displaystyle E_{n+1}-E_{n}={\frac {(2n+1)\hbar ^{2}\pi ^{2}}{2mL^{2}}}}" loading="lazy"></span></dd></dl>

<p>Since the box length <i>L</i> increases approximately linearly with the number of C=C bonds <i>n</i>, this means that the energy Δ<i>E</i> of a photon absorbed in the HOMO–LUMO transition is approximately proportional to 1/<i>n</i>. The photon <a href="Wavelength" title="Wavelength">wavelength</a> λ = <i>hc</i>/Δ<i>E</i> is then approximately proportional to <i>n</i>. Although this model is very approximate, λ does in general increase with <i>n</i> (or <i>L</i>) for similar molecules. For example, the HOMO–LUMO absorption wavelengths for conjugated <a href="1%2C3-Butadiene" class="mw-redirect" title="1,3-Butadiene">butadiene</a>, hexatriene and octatetraene are 217 nm, 252 nm and 304 nm respectively.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> However, for good numerical agreement of the particle in a box model with experiment, the single-bond/double-bond bond length alternations of the polyenes must be taken into account.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Alternatively, one can use the <a href="H%C3%BCckel_method" title="Hückel method">Hückel method</a> which is also designed to model the electronic structure of conjugated systems.

</p><p>Many electronic transitions in conjugated π-systems are from a predominantly <a href="Covalent_bond" title="Covalent bond">bonding</a> <a href="Molecular_orbital" title="Molecular orbital">molecular orbital</a> (MO) to a predominantly <a href="Antibonding_molecular_orbital" title="Antibonding molecular orbital">antibonding</a> MO (π to π<sup>*</sup>), but electrons from non-bonding <a href="Lone_pair" title="Lone pair">lone pairs</a> can also be promoted to a π-system MO (n to π<sup>*</sup>) as often happens in <a href="Charge-transfer_complex" title="Charge-transfer complex">charge-transfer complexes</a>. A HOMO to LUMO transition is made by an electron if it is allowed by the <a href="Selection_rules" class="mw-redirect" title="Selection rules">selection rules</a> for <a href="Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic transitions</a>. Conjugated systems of fewer than eight conjugated double bonds absorb only in the ultraviolet region and are colorless to the human eye. With every double bond added, the system absorbs <a href="Photon" title="Photon">photons</a> of longer wavelength (and lower energy), and the compound ranges from yellow to red in color. Compounds that are blue or green typically do not rely on conjugated double bonds alone.

</p><p>This absorption of light in the ultraviolet to visible spectrum can be quantified using <a href="Ultraviolet%E2%80%93visible_spectroscopy" title="Ultraviolet–visible spectroscopy">ultraviolet–visible spectroscopy</a>, and forms the basis for the entire field of <a href="Photochemistry" title="Photochemistry">photochemistry</a>.

</p><p>Conjugated systems that are widely used for synthetic <a href="Pigment" title="Pigment">pigments</a> and <a href="Dye" title="Dye">dyes</a> are <a href="Diazo" title="Diazo">diazo</a> and <a href="Azo_compound" title="Azo compound">azo compounds</a> and phthalocyanine compounds.

</p>

<div class="mw-heading mw-heading3"><h3 id="Phthalocyanine_compounds">Phthalocyanine compounds</h3></div>

<p>Conjugated systems not only have low energy excitations in the visible spectral region but they also accept or donate electrons easily. <a href="Phthalocyanine" title="Phthalocyanine">Phthalocyanines</a>, which, like <a href="Phthalocyanine_Blue_BN" class="mw-redirect" title="Phthalocyanine Blue BN">Phthalocyanine Blue BN</a> and <a href="Phthalocyanine_Green_G" title="Phthalocyanine Green G">Phthalocyanine Green G</a>, often contain a transition metal ion, exchange an electron with the complexed <a href="Transition_metal#Characteristic_properties" title="Transition metal">transition metal ion</a> that easily changes its <a href="Oxidation_state" title="Oxidation state">oxidation state</a>. Pigments and dyes like these are <a href="Charge-transfer_complex" title="Charge-transfer complex">charge-transfer complexes</a>.

</p>

<div class="mw-heading mw-heading3"><h3 id="Porphyrins_and_similar_compounds">Porphyrins and similar compounds</h3></div>

<p><a href="Porphyrin" title="Porphyrin">Porphyrins</a> have conjugated molecular ring systems (<a href="Macrocycle" title="Macrocycle">macrocycles</a>) that appear in many <a href="Enzyme" title="Enzyme">enzymes</a> of biological systems. As a <a href="Ligand" title="Ligand">ligand</a>, porphyrin forms numerous <a href="Complex_(chemistry)" class="mw-redirect" title="Complex (chemistry)">complexes</a> with metallic ions like <a href="Iron" title="Iron">iron</a> in <a href="Hemoglobin" title="Hemoglobin">hemoglobin</a> that colors blood red. Hemoglobin transports oxygen to the cells of our bodies. Porphyrin–metal complexes often have strong colors. A similar molecular structural ring unit called <a href="Chlorin" title="Chlorin">chlorin</a> is similarly complexed with <a href="Magnesium" title="Magnesium">magnesium</a> instead of iron when forming part of the most common forms of <a href="Chlorophyll" title="Chlorophyll">chlorophyll</a> molecules, giving them a green color. Another similar macrocycle unit is <a href="Corrin" title="Corrin">corrin</a>, which complexes with <a href="Cobalt" title="Cobalt">cobalt</a> when forming part of <a href="Cobalamin" class="mw-redirect" title="Cobalamin">cobalamin</a> molecules, constituting <a href="Vitamin_B12" title="Vitamin B12">Vitamin B12</a>, which is intensely red. The corrin unit has six conjugated double bonds but is not conjugated all the way around its macrocycle ring.

</p>

</td></tr>

<tr>

<td><small><a href="Heme" title="Heme">Heme</a> group of <a href="Hemoglobin" title="Hemoglobin">hemoglobin</a></small></td>

<td><small>The <a href="Chlorin" title="Chlorin">chlorin</a> section of the <a href="Chlorophyll_a" title="Chlorophyll a">chlorophyll a</a> molecule. The green box shows a <a href="Functional_group" title="Functional group">group</a> that varies between <a href="Chlorophyll" title="Chlorophyll">chlorophyll</a> types.</small></td>

<td><small><a href="Cobalamin" class="mw-redirect" title="Cobalamin">Cobalamin</a> structure includes a <a href="Corrin" title="Corrin">corrin</a> macrocycle.</small>

</td></tr></tbody></table>

<div class="mw-heading mw-heading3"><h3 id="Chromophores">Chromophores</h3></div>

<p>Conjugated systems form the basis of <a href="Chromophore" title="Chromophore">chromophores</a>, which are light-absorbing parts of a molecule that can cause a compound to be colored. Such chromophores are often present in various organic compounds and sometimes present in <a href="Polymer" title="Polymer">polymers</a> that are colored or glow in the dark. Chromophores often consist of a series of conjugated bonds and/or ring systems, commonly aromatic, which can include C–C, C=C, C=O, or N=N bonds.

</p>

<p>Conjugated chromophores are found in many <a href="Organic_compound" title="Organic compound">organic compounds</a> including <a href="Azo_dyes" class="mw-redirect" title="Azo dyes">azo dyes</a> (also <a href="Food_coloring" title="Food coloring">artificial food additives</a>), compounds in fruits and vegetables (<a href="Lycopene" title="Lycopene">lycopene</a> and <a href="Anthocyanidin" title="Anthocyanidin">anthocyanidins</a>), <a href="Photoreceptor_cell" title="Photoreceptor cell">photoreceptors</a> of the eye, and some pharmaceutical compounds such as the following:

</p>

<p>Conjugated polymer <a href="Nanoparticle" title="Nanoparticle">nanoparticles</a> (PDots) are assembled from hydrophobic fluorescent conjugated polymers, along with <a href="Amphiphilic" class="mw-redirect" title="Amphiphilic">amphiphilic</a> polymers to provide water solubility. Pdots are important labels for <a href="Single-molecule_experiment" title="Single-molecule experiment">single-molecule</a> <a href="Fluorescence_microscopy" class="mw-redirect" title="Fluorescence microscopy">fluorescence microscopy</a>, based on high brightness, lack of <a href="Fluorescence_intermittency_in_colloidal_nanocrystals" title="Fluorescence intermittency in colloidal nanocrystals">blinking</a> or <a href="Fluorophore" title="Fluorophore">dark fraction</a>, and slow <a href="Photobleaching" title="Photobleaching">photobleaching</a>.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup>

</p>

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<div class="side-box-text plainlist">Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Conjugated_system" class="extiw external" title="q:Special:Search/Conjugated system">Conjugated system</a></b></i>.</div></div>

</div>

<ul><li><a href="Conjugated_microporous_polymer" title="Conjugated microporous polymer">Conjugated microporous polymer</a></li>

<li><a href="Cross-conjugation" title="Cross-conjugation">Cross-conjugation</a></li>

<li><a href="Hyperconjugation" title="Hyperconjugation">Hyperconjugation</a></li>

<li><a href="List_of_conjugated_polymers" title="List of conjugated polymers">List of conjugated polymers</a></li>

<li><a href="Metallic_bond" class="mw-redirect" title="Metallic bond">Metallic bond</a></li>

<li><a href="Polyene" title="Polyene">Polyene</a></li>

<li><a href="Resonance_(chemistry)" title="Resonance (chemistry)">Resonance</a></li>

<li><a href="Vinylogy" title="Vinylogy">Vinylogy</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2></div>

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<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">For the purposes of this article, we are primarily concerned with delocalized orbitals with π-symmetry. This is in line with the typical usage of 'conjugated system' to refer to π (and not σ) delocalization. Canonical molecular orbitals are fully delocalized, so in a sense, all electrons involved in bonding, including ones making up the σ bonds and lone pairs, are delocalized throughout the molecule. However, while treating π electrons as delocalized yields many useful insights into chemical reactivity, treatment of σ and nonbonding electrons in the same way is generally less profitable, except in cases of multicenter σ-bonding as found in cluster compounds of Li and B. Moreover, the added complexity tends to impede chemical intuition. Hence, for most <a href="Organic_molecule" class="mw-redirect" title="Organic molecule">organic molecules</a>, chemists commonly use a localized orbital model to describe the σ-bonds and lone pairs, while superimposing delocalized molecular orbitals to describe the π-bonding. This view has the added advantage that there is a clear correspondence between the <a href="Lewis_structure" title="Lewis structure">Lewis structure</a> of a molecule and the orbitals used to describe its bonding.</span>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFThiele1899" class="citation journal cs1 cs1-prop-foreign-lang-source">Thiele, Johannes (1899). <a rel="nofollow" class="external text" href="https://babel.hathitrust.org/cgi/pt?id=mdp.39015026322779;view=1up;seq=473">"Zur Kenntnis der ungesättigten Verbindungen"</a> [[Contribution] to our knowledge of unsaturated compounds]. <i>Justus Liebig's Annalen der Chemie</i> (in German). <b>306</b>: <span class="nowrap">87–</span>142. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fjlac.18993060107">10.1002/jlac.18993060107</a>.</cite> On p. 90, Thiele coined the term "conjugated": <span title="German-language text"><i lang="de">"Ein solches System benachbarter Doppelbindungen mit ausgeglichenen inneren Partialvalenzen sei als 'conjugirt' bezeichnet."</i></span> (Such a system of adjacent double bonds with equalized inner partial valences shall be termed "conjugated".)</span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><a href="International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a>, <i><a href="IUPAC_books" class="mw-redirect" title="IUPAC books">Compendium of Chemical Terminology</a></i>, 5th ed. (the "Gold Book") (2025). Online version: (2006–) "<a rel="nofollow" class="external text" href="https://goldbook.iupac.org/terms/view/C01267.html">conjugated system (conjugation)</a>". <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fgoldbook.C01267">10.1351/goldbook.C01267</a></span>

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<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFMarch1985" class="citation book cs1">March, Jerry (1985). <i>Advanced Organic Chemistry reactions, mechanisms and structure</i> (3rd ed.). New York: John Wiley & Sons, Inc. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-471-85472-7</bdi>.</cite></span>

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<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite class="citation book cs1">"16 Conjugation, Resonance, and Dienes". <a rel="nofollow" class="external text" href="http://icvcollege.edu.in/sites/default/files/Conjugation%2C%20Resonance%2C.pdf"><i>Organic Chemistry</i></a> <span class="cs1-format">(PDF)</span> (3rd ed.). Belonia, South Tripura, India: <a href="Iswar_Chandra_Vidyasagar_College" title="Iswar Chandra Vidyasagar College">Iswar Chandra Vidyasagar College</a><span class="reference-accessdate">. Retrieved <span class="nowrap">19 April</span> 2022</span>.</cite></span>

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<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://chem.libretexts.org/Courses/Purdue/Chem_26505:_Organic_Chemistry_I_(Lipton)/Chapter_1._Electronic_Structure_and_Chemical_Bonding/1.10:_Pi_Conjugation#:~:text=Conjugation%20is%20possible%20by%20means,an%20oxygen%20in%20position%201.">"1.10: Pi Conjugation"</a>. <i>Chemistry LibreTexts</i>. 2014-08-01<span class="reference-accessdate">. Retrieved <span class="nowrap">2024-10-07</span></span>.</cite></span>

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<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><a href="International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a>, <i><a href="IUPAC_books" class="mw-redirect" title="IUPAC books">Compendium of Chemical Terminology</a></i>, 5th ed. (the "Gold Book") (2025). Online version: (2006–) "<a rel="nofollow" class="external text" href="https://goldbook.iupac.org/terms/view/R05333.html">resonance energy</a>". <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fgoldbook.R05333">10.1351/goldbook.R05333</a></span>

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<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><cite id="CITEREFFellerCraig2009" class="citation journal cs1">Feller, David; Craig, Norman C. (2009-02-05). "High Level ab Initio Energies and Structures for the Rotamers of 1,3-Butadiene". <i>The Journal of Physical Chemistry A</i>. <b>113</b> (8): <span class="nowrap">1601–</span>1607. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009JPCA..113.1601F">2009JPCA..113.1601F</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fjp8095709">10.1021/jp8095709</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/19199679">19199679</a>.</cite></span>

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<li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><cite id="CITEREFCareyGuiliano2013" class="citation book cs1">Carey, Francis A.; Guiliano, Robert M. (2013-01-07). <i>Organic chemistry</i> (Ninth ed.). New York, NY. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780073402741</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/822971422">822971422</a>.</cite><span class="cs1-maint citation-comment"><code class="cs1-code">{{cite book}}</code>: CS1 maint: location missing publisher (link)</span></span>

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<li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><cite id="CITEREFGobbiFrenking1994" class="citation journal cs1">Gobbi, Alberto; Frenking, Gernot (1994-10-01). "Resonance Stabilization in Allyl Cation, Radical, and Anion". <i>Journal of the American Chemical Society</i>. <b>116</b> (20): <span class="nowrap">9275–</span>9286. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1994JAChS.116.9275G">1994JAChS.116.9275G</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fja00099a052">10.1021/ja00099a052</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0002-7863">0002-7863</a>.</cite></span>

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<li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><cite id="CITEREFBarbourKarty2004" class="citation journal cs1">Barbour, Josiah B.; Karty, Joel M. (2004-01-14). "Resonance Energies of the Allyl Cation and Allyl Anion: Contribution by Resonance and Inductive Effects toward the Acidity and Hydride Abstraction Enthalpy of Propene". <i>The Journal of Organic Chemistry</i>. <b>69</b> (3): <span class="nowrap">648–</span>654. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fjo035189m">10.1021/jo035189m</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/14750787">14750787</a>.</cite></span>

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<li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><cite id="CITEREFCotton1990" class="citation book cs1">Cotton, Frank Albert (1990). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/isbn_9780471510949"><i>Chemical applications of group theory</i></a></span> (3rd ed.). New York: Wiley. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0471510949</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/19975337">19975337</a>.</cite></span>

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<li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><cite id="CITEREFBraidaPranaHiberty2009" class="citation journal cs1">Braida, Benoit; Prana, Vinca; Hiberty, Philippe C. (2009-07-20). "The Physical Origin of Saytzeff's Rule". <i>Angewandte Chemie International Edition</i>. <b>48</b> (31): <span class="nowrap">5724–</span>5728. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fanie.200901923">10.1002/anie.200901923</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1433-7851">1433-7851</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/19562814">19562814</a>.</cite></span>

</li>

<li id="cite_note-IUPAC-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-IUPAC_14-0">^</a></b></span> <span class="reference-text"><a href="International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a>, <i><a href="IUPAC_books" class="mw-redirect" title="IUPAC books">Compendium of Chemical Terminology</a></i>, 5th ed. (the "Gold Book") (2025). Online version: (2006–) "<a rel="nofollow" class="external text" href="https://goldbook.iupac.org/terms/view/H02842.html">homoconjugation</a>". <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fgoldbook.H02842">10.1351/goldbook.H02842</a></span>

</li>

<li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">Some orbital overlap is possible even between bonds separated by one (or more) CH<sub>2</sub> because the bonding electrons occupy orbitals which are quantum-mechanical functions and extend indefinitely in space. Macroscopic drawings and models with sharp boundaries are misleading because they do not show this aspect.</span>

</li>

<li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><cite id="CITEREFScott1986" class="citation journal cs1">Scott, L. T. (1986-01-01). "Cyclic homoconjugation in neutral organic molecules". <i>Pure and Applied Chemistry</i>. <b>58</b> (1): <span class="nowrap">105–</span>110. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.562.8748">10.1.1.562.8748</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fpac198658010105">10.1351/pac198658010105</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1365-3075">1365-3075</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:98131188">98131188</a>.</cite></span>

</li>

<li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><cite id="CITEREFStewartPagenkopf1969" class="citation journal cs1">Stewart, John Mathews; Pagenkopf, Gordon K. (January 1969). "Transmission of conjugation by the cyclopropane ring". <i>The Journal of Organic Chemistry</i>. <b>34</b> (1): <span class="nowrap">7–</span>11. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fjo00838a003">10.1021/jo00838a003</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0022-3263">0022-3263</a>.</cite></span>

</li>

<li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><cite id="CITEREFMaslak1994" class="citation journal cs1">Maslak, Przemyslaw (May 1994). "Spiroconjugation: An added dimension in the design of organic molecular materials". <i>Advanced Materials</i>. <b>6</b> (5): <span class="nowrap">405–</span>407. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1994AdM.....6..405M">1994AdM.....6..405M</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fadma.19940060515">10.1002/adma.19940060515</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0935-9648">0935-9648</a>.</cite></span>

</li>

<li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><i>The Vinylogous Aldol Reaction: A Valuable, Yet Understated Carbon-Carbon Bond-Forming Maneuver</i> Giovanni Casiraghi, Franca Zanardi, Giovanni Appendino, and Gloria Rassu <a href="Chem._Rev." class="mw-redirect" title="Chem. Rev.">Chem. Rev.</a> <b>2000</b>; 100(6) pp 1929 – 1972; (Review) <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fcr990247i">10.1021/cr990247i</a></span>

</li>

<li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><cite id="CITEREFRashidvan_Lenthe2011" class="citation journal cs1">Rashid, Zahid; van Lenthe, Joop H. (March 2011). "Generation of Kekulé valence structures and the corresponding valence bond wave function". <i>Journal of Computational Chemistry</i>. <b>32</b> (4): <span class="nowrap">696–</span>708. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fjcc.21655">10.1002/jcc.21655</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1096-987X">1096-987X</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/20941739">20941739</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:16526798">16526798</a>.</cite></span>

</li>

<li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text">While the two Kekulé resonance forms contribute to most (>90%) of the π bond energy, there are also a number of other minor contributors to the wavefunction in the valence bond treatment, including the three Dewar resonance forms, and even smaller contributions from various ionic and singlet diradical forms. See article by Rashid and van Lenthe for a recent computational treatment.</span>

</li>

<li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><cite id="CITEREFLipton2017" class="citation book cs1">Lipton, Mark (Jan 31, 2017). "Chapter 1. Electronic Structure and Chemical Bonding". <a rel="nofollow" class="external text" href="https://chem.libretexts.org/Courses/Purdue/Purdue%3A_Chem_26505%3A_Organic_Chemistry_I_(Lipton)/Chapter_1._Electronic_Structure_and_Chemical_Bonding/1.10%3A_Pi_Conjugation"><i>Purdue: Chem 26505: Organic Chemistry I (Lipton)</i></a> (LibreTexts ed.). Purdue University.</cite></span>

</li>

<li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text">P. Atkins and J. de Paula <i>Physical Chemistry</i> (8th ed., W.H.Freeman 2006), p.281 <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-7167-8759-8</bdi></span>

</li>

<li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text">Atkins and de Paula p.398</span>

</li>

<li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><cite id="CITEREFAutschbach2007" class="citation journal cs1">Autschbach, Jochen (November 2007). "Why the Particle-in-a-Box Model Works Well for Cyanine Dyes but Not for Conjugated Polyenes". <i>Journal of Chemical Education</i>. <b>84</b> (11): 1840. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007JChEd..84.1840A">2007JChEd..84.1840A</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fed084p1840">10.1021/ed084p1840</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0021-9584">0021-9584</a>.</cite></span>

</li>

<li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><cite id="CITEREFWuHansenHouYu2011" class="citation journal cs1">Wu C, Hansen SJ, Hou Q, Yu J, Zeigler M, Jin Y, Burnham DR, McNeill JD, Olson JM, Chiu DT (2011). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3095208">"Design of highly emissive polymer dot bioconjugates for in vivo tumor targeting"</a>. <i>Angewandte Chemie</i>. <b>50</b> (15): <span class="nowrap">3430–</span>4. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fanie.201007461">10.1002/anie.201007461</a></span>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3095208">3095208</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/21381164">21381164</a>.</cite></span>

</li>

<li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><cite id="CITEREFKonerKrndijaHouSherratt2013" class="citation journal cs1">Koner AL, Krndija D, Hou Q, Sherratt DJ, Howarth M (2013). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3584654">"Hydroxy-terminated conjugated polymer nanoparticles have near-unity bright fraction and reveal cholesterol-dependence of IGF1R nanodomains"</a>. <i>ACS Nano</i>. <b>7</b> (2): <span class="nowrap">1137–</span>1144. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fnn3042122">10.1021/nn3042122</a></span>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3584654">3584654</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/23330847">23330847</a>.</cite></span>

</li>

</ol></div></div>

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</style><div id="Chemical_bonds164" style="font-size:114%;margin:0 4em"><a href="Chemical_bond" title="Chemical bond">Chemical bonds</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Intramolecular_force" title="Intramolecular force">Intramolecular</a><br>(strong)</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Covalent_bond" title="Covalent bond">Covalent</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Electron_deficiency" title="Electron deficiency">Electron deficiency</a>

<li><a href="Hypervalent_molecule" title="Hypervalent molecule">Hypervalence</a>

<li><a href="Agostic_interaction" title="Agostic interaction">Agostic</a></li>

<li><a href="Coordinate_covalent_bond" title="Coordinate covalent bond">Coordinate (dipolar)</a></li>

<li><a href="Pi_backbonding" title="Pi backbonding">Pi backbond</a></li>

<li><a href="Metal%E2%80%93ligand_multiple_bond" title="Metal–ligand multiple bond">Metal–ligand multiple bond</a></li>

<li><a href="Charge-shift_bond" title="Charge-shift bond">Charge-shift</a></li>

<li><a href="Hapticity" title="Hapticity">Hapticity</a></li>

<li><a href="Hyperconjugation" title="Hyperconjugation">Hyperconjugation</a></li>

<li><a href="Aromaticity" title="Aromaticity">Aromaticity</a>

<li><a href="Bicycloaromaticity" title="Bicycloaromaticity">bicyclo</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Metallic_bonding" title="Metallic bonding">Metallic</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Metal_aromaticity" title="Metal aromaticity">Metal aromaticity</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Ionic_bonding" title="Ionic bonding">Ionic</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

</div></td></tr></tbody></table><div></div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Intermolecular_force" title="Intermolecular force">Intermolecular</a><br>(weak)</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Van_der_Waals_force" title="Van der Waals force">Van der Waals<br>forces</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="London_dispersion_force" title="London dispersion force">London dispersion</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Hydrogen_bond" title="Hydrogen bond">Hydrogen</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Low-barrier_hydrogen_bond" title="Low-barrier hydrogen bond">Low-barrier</a></li>

<li><a href="Resonance-assisted_hydrogen_bond" class="mw-redirect" title="Resonance-assisted hydrogen bond">Resonance-assisted</a></li>

<li><a href="Symmetric_hydrogen_bond" title="Symmetric hydrogen bond">Symmetric</a></li>

<li><a href="Dihydrogen_bond" title="Dihydrogen bond">Dihydrogen bonds</a></li>

<li><a href="C%E2%80%93H%C2%B7%C2%B7%C2%B7O_interaction" title="C–H···O interaction">C–H···O interaction</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Non-covalent_interactions" class="mw-redirect" title="Non-covalent interactions">Noncovalent</a><br>other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Mechanically_interlocked_molecular_architectures" title="Mechanically interlocked molecular architectures">Mechanical</a></li>

<li><a href="Halogen_bond" title="Halogen bond">Halogen</a></li>

<li><a href="Chalcogen_bond" title="Chalcogen bond">Chalcogen</a></li>

<li><a href="Metallophilic_interaction" title="Metallophilic interaction">Metallophilic</a> (<a href="Aurophilicity" title="Aurophilicity">aurophilic</a>)</li>

<li><a href="Intercalation_(chemistry)" title="Intercalation (chemistry)">Intercalation</a></li>

<li><a href="Stacking_(chemistry)" title="Stacking (chemistry)">Stacking</a></li>

<li><a href="Cation%E2%80%93pi_interaction" class="mw-redirect" title="Cation–pi interaction">Cation–pi</a></li>

<li><a href="Cation%E2%80%93pi_interaction" class="mw-redirect" title="Cation–pi interaction">Anion–pi</a></li>

<li><a href="Salt_bridge_(protein_and_supramolecular)" title="Salt bridge (protein and supramolecular)">Salt bridge</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Bond_cleavage" title="Bond cleavage">Bond cleavage</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Heterolysis_(chemistry)" title="Heterolysis (chemistry)">Heterolysis</a></li>

<li><a href="Homolysis_(chemistry)" title="Homolysis (chemistry)">Homolysis</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Electron_counting" title="Electron counting">Electron counting</a> rules</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Aromaticity" title="Aromaticity">Aromaticity</a>

<ul><li><a href="H%C3%BCckel's_rule" title="Hückel's rule">Hückel's rule</a></li>

<li><a href="Baird's_rule" title="Baird's rule">Baird's rule</a></li>

<li><a href="M%C3%B6bius_aromaticity" title="Möbius aromaticity">Möbius</a></li>

<li><a href="Spherical_aromaticity" title="Spherical aromaticity">spherical</a></li></ul></li>

<li><a href="Polyhedral_skeletal_electron_pair_theory" title="Polyhedral skeletal electron pair theory">Polyhedral skeletal electron pair theory</a></li>

<li><a href="Jemmis_mno_rules" title="Jemmis mno rules">Jemmis mno rules</a></li></ul>

</div></td></tr></tbody></table></div>

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