Conjugated system

In physical organic 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.
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. 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 sp² hybrid orbital and does not participate in the conjugation. A requirement for conjugation is orbital overlap. Thus, the conjugated system must be planar. As a consequence, lone pairs which do participate in conjugated systems will occupy orbitals of pure p character instead of spⁿ 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 treatment, in which the σ framework of the molecule is separated from the π system of the molecule. 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 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, 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. 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 are all located in the plane of the molecule, with σ bonds mainly localized between nuclei along the internuclear axis.
Pi 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 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, two electrons, or zero electrons. 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 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 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 are not well-described by strict σ/π separation, as bonding between atoms in the ring consists of "bent bonds" 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 sp²- 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, to emphasize this behavior. For example, the delocalized π electrons in acetate anion and benzene are said to be involved in Π and Π systems, respectively. Generally speaking, these multi-center bonds correspond to the occupation of several molecular orbitals with varying degrees of bonding or non-bonding character. Each one is occupied by one or two electrons in accordance with the Aufbau principle and 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 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.

Stabilization energy

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 resonance energy 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 resonance form. 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 buta-1,3-diene, a crude measure of stabilization is the activation energy for rotation of the C2-C3 bond. This places the resonance stabilization at around 6 kcal/mol. Comparison of heats of hydrogenation of 1,4-pentadiene and 1,3-pentadiene estimates a slightly more modest value of 3.5 kcal/mol. For comparison, allyl cation has a gas-phase rotation barrier of around 38 kcal/mol, 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. 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.

Generalizations and related concepts

There are also other types of interactions that generalize the idea of interacting p orbitals in a conjugated system. The concept of hyperconjugation holds that certain σ bonds can also delocalize into a low-lying unoccupied orbital of a π system or an unoccupied p orbital. Hyperconjugation 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.
Homoconjugation is an overlap of two π-systems separated by a non-conjugating group, such as CH₂. 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. Neutral systems generally require constrained geometries favoring interaction to produce significant degrees of homoconjugation. 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.
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.
Two appropriately aligned π systems whose ends meet at right angles can engage in spiroconjugation or in homoconjugation across the spiro atom.
Image:Vinylogous.png|class=skin-invert-image|300px|thumb|Delocalization of negative charge in a generic carboxylate anion, derived from an organic carboxylic acid, and the corresponding vinylogous carboxylate anion, where a vinyl group now separates the charged oxygen from the carbonyl group. The validity of the theoretical concept of vinylogy is supported by the pKa of such vinylogs, which approach that of the analogous carboxylic acid.
Vinylogy is the extension of a functional group through a conjugated organic bonding system, which transmits electronic effects.