• 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.

• A simple model of the energy levels is provided by the quantum-mechanical problem of a one-dimensional particle in a box of length L, representing the movement of a π electron
  along a long conjugated chain of carbon atoms.

• 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 hybrid orbital and does not participate in the conjugation.

• 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.

• Phthalocyanine compounds[edit] Conjugated systems not only have low energy excitations in the visible spectral region but they also accept or donate electrons easily.

• 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.

• The classic example benzene 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 benzene ring, the common core of the benzenoid aromatic compounds.

• Many electronic transitions in conjugated π-systems are from a predominantly bonding molecular orbital (MO) to a predominantly antibonding MO (π to π*), but electrons from
  non-bonding lone pairs can also be promoted to a π-system MO (n to π*) as often happens in charge-transfer complexes.

• A similar molecular structural ring unit called chlorin is similarly complexed with magnesium instead of iron when forming part of the most common forms of chlorophyll molecules,
  giving them a green color.

• [17][18] 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.

• 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.

• Atoms that are sp-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.

• Lone pairs, radicals or carbenium ions may be part of the system, which may be cyclic, acyclic, linear or mixed.

• The participation of six electrons in the π system makes furan aromatic (see below).

• In general, any sp 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.

• 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.

• 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).

• For example, the delocalized π electrons in acetate anion and benzene are said to be involved in Π 3 and Π 6 systems, respectively (see the article on three-center four-electron
  bonding).

• 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.

• 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).

• As long as each contiguous atom in a chain has an available p orbital, the system can be considered conjugated.

• 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 Jahn-Teller distortion to relieve the degeneracy.

• In pigments 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 radio
  antenna detects photons along its length.

• 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.

• [14] 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.

• The lack of conjugation allows the 8 π electron molecule to avoid antiaromaticity, a destabilizing effect associated with cyclic, conjugated systems containing 4n π electrons.

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

• Chromophores[edit] Conjugated systems form the basis of chromophores, which are light-absorbing parts of a molecule that can cause a compound to be colored.

• It is important to recognize that, 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).

• 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.

• 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.

• 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.

• 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.

• 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.

• As such, the atoms and π-electrons involved behave as one large bonded system.

• Aromatic compounds[edit] Compounds that have a monocyclic, planar conjugated system containing electrons for whole numbers n are aromatic and exhibit an unusual stability.

• 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.

• 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.

• Note that one of the oxygen lone pairs participates in conjugation in a p orbital, while the other lone pair is in an sp hybridized orbital in the plane of the molecule and
  not part of the π system.

• [22] Alternatively, one can use the Hückel method which is also designed to model the electronic structure of conjugated systems.

• 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.

• [19] Many dyes make use of conjugated electron systems to absorb visible light, giving rise to strong colors.

• 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.

• Phthalocyanines, which, like Phthalocyanine Blue BN and Phthalocyanine Green G, often contain a transition metal ion, exchange an electron with the complexed transition metal
  ion that easily changes its oxidation state.

• 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-, sp-, 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.

 

Works Cited

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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 organic molecules, 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
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Photo credit: https://www.flickr.com/photos/crobj/2093263381/’]