Editing Conjugated system (section)

==Chemical bonding in conjugated systems==
[[File:Delocalization-updated.png|class=skin-invert-image|alt=|thumb|400x400px|Some prototypical examples of species with delocalized bonding. Top row: [[pyridine]], [[furan]], [[tropylium cation]]. Second row: [[allyl group|allyl radical]], [[acetate|acetate ion]], [[acrolein]]. Atoms involved are in bold red, while electrons involved in delocalized bonding are in blue. (Particular attention should be paid to the involvement or non-involvement of "non-bonding" electrons.)]]
Conjugation is possible by means of alternating single and [[double bond]]s 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, [[furan]] is a five-membered ring with two alternating double bonds flanking an [[oxygen]].<ref>{{Cite web |date=2014-08-01 |title=1.10: Pi Conjugation |url=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. |access-date=2024-10-07 |website=Chemistry LibreTexts |language=en}}</ref> The oxygen has two [[lone pair]]s, 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.

In general, any sp<sup>2</sup> or sp-hybridized carbon or [[heteroatom]], 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 [[pyridine]], 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>''n''</sup> hybrid orbitals typical for nonconjugated lone pairs.
[[File:Furan-pi-system.png|thumb|275x275px|The π system of furan and lone pairs. Note that one of the oxygen lone pairs participates in conjugation in a p orbital, while the other lone pair is  in an sp<sup>2</sup> hybridized orbital in the plane of the molecule and ''not'' part of the π system.  The participation of six electrons in the π system makes furan aromatic (see below).]]
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 (''see the article on the [[sigma-pi and equivalent-orbital models]] for this model and an alternative treatment'').  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.

''Sigma (σ) framework'': 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-[[Orbital hybridisation|hybridized atomic orbitals]] 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.

''Pi (π) system or systems'': 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 [[Hückel method|Hückel approach]] to obtain a zeroth order (qualitative) approximation of the π symmetry molecular orbitals that result from delocalized π bonding.
[[File:Diazomethane-bonding scheme.png|thumb|450x450px|Using the σ/π-separation scheme to describe bonding, the Lewis resonance structures of a molecule like diazomethane can be translated into a bonding picture consisting of π-systems and localized lone pairs superimposed on a localized framework of σ-bonds.]]
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 "[[bent bond]]s" 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.

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 '''n''-center ''k-''electron π-bonds,' compactly denoted by the symbol Π{{su|p=''k''|b=''n''}}, to emphasize this behavior.  For example, the delocalized π electrons in acetate anion and benzene are said to be involved in Π{{su|p=4|b=3}} and Π{{su|p=6|b=6}} systems, respectively (''see the article on [[three-center four-electron bond]]ing''). 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 [[Aufbau principle]] and [[Hund's rule of maximum multiplicity|Hund's rule]]. Cartoons showing overlapping p orbitals, like the one for benzene below, show the basis p atomic orbitals ''before'' they are combined to form molecular orbitals. In compliance with the [[Pauli exclusion principle]], overlapping p orbitals ''do not'' result in the formation of one large MO containing more than two electrons.

[[Hückel method|Hückel MO theory]] 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.