Delocalized Bond

In theoretical chemistry, a conjugated system is a system of connected p-orbitals with delocalized electrons in a molecule, which in general lowers the overall energy of the molecule and increases stability. It is conventionally represented as having alternating single and multiple bonds. Lone pairs, radicals or carbenium ions may be part of the system, which may be cyclic, acyclic, linear or mixed. The term "conjugated" was coined in 1899 by the German chemist Johannes Thiele.

Conjugation is the overlap of one p-orbital with another across an adjacent σ bond (in transition metals, d-orbitals can be involved).

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 π electrons across all the adjacent aligned p-orbitals.
The π electrons do not belong to a single bond or atom, but rather to a group of atoms.

Molecules containing conjugated systems of orbitals and electrons are called conjugated molecules, which have overlapping p orbitals on three or more atoms. Some simple organic conjugated molecules are 1,3-butadiene, benzene, and allylic carbocations. The largest conjugated systems are found in graphene, graphite, conductive polymers and carbon nanotubes.

Chemical bonding in conjugated systems

Conjugation is possible by means of alternating single and double bonds 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. The oxygen has two lone pairs, 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 sp² or sp-hybridized carbon or heteroatom, including ones bearing an empty orbital or lone pair orbital, can participate in conjugated systems, though 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 sp² 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^''n'' hybrid orbitals typical for nonconjugated lone pairs.

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 sp³-, sp²-, and sp- 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 sp²- 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 sp³-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 approach to obtain a zeroth order (qualitative) approximation of the π symmetry molecular orbitals that result from delocalized π bonding.

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 a