Pi Bond

A pi bond (π bond) is a component of a covalent bond characterized, in a localized two-atom description, by a nodal plane containing the axis joining the bonded nuclei. It commonly arises from sideways overlap of parallel atomic orbitals, especially p orbitals. Unlike a sigma bond, its bonding electron density lies on either side of a plane through the bond axis. Pi bonding accounts for the additional bonding components in ordinary double and triple bonds and is central to the description of conjugated molecules. (goldbook.iupac.org)

Orbital overlap and symmetry

In valence bond theory, a typical π bond forms when two adjacent atoms each supply a p orbital oriented perpendicular to the internuclear axis. The orbitals overlap laterally rather than end to end. Their two regions of overlap—often drawn above and below the molecular plane—constitute one π bond, not two separate bonds. (openstax.org)

The nodal plane is a surface where the orbital wave function is zero. On opposite sides of this plane, the wave function has opposite algebraic signs. These signs indicate orbital phase, not positive and negative electric charge. A π bonding orbital retains this plane through the bond axis while providing constructive overlap between corresponding lobes on neighboring atoms. (goldbook.iupac.org)

The labels σ and π are fundamentally symmetry designations, rather than names restricted to particular atomic orbital types. IUPAC distinguishes their use for localized two-center bonds from their use for orbitals extending over a whole molecule. For molecular orbitals, the relevant distinction concerns symmetry or antisymmetry under reflection in a defining plane; for a two-center π bond, the defining nodal plane contains the internuclear axis. (goldbook.iupac.org)

Double and triple bonds

In the conventional localized description of ordinary multiple bonds, their components are:

These components describe different orbital overlaps between the same atoms, not separate connections to different atoms. (openstax.org)

Ethene, H₂C=CH₂, illustrates a double bond. In the orbital hybridization model, each carbon atom has three sp² hybrid orbitals forming its σ bonds and one unhybridized p orbital perpendicular to that framework. Sideways overlap of the two p orbitals produces the carbon–carbon π bond. The ground-state molecule is planar, allowing effective parallel alignment of those orbitals. (openstax.org)

Ethyne, HC≡CH, illustrates a triple bond. Each carbon is described as sp-hybridized, leaving two mutually perpendicular p orbitals. Corresponding p orbitals overlap to produce two π components, while the carbon–carbon σ bond lies along the molecular axis. The molecule is linear. (openstax.org)

Molecular orbital description

Molecular orbital theory describes π bonding through orbitals extending over the participating atoms. Combining two suitably oriented p orbitals produces a lower-energy π bonding orbital and a higher-energy π antibonding orbital*, pronounced “pi star.” In the bonding combination, corresponding lobes overlap constructively. The antibonding combination has an additional node separating the nuclei, reducing electron density in the bonding region. (openstax.org)

For ground-state ethene, two electrons occupy the π bonding orbital, and the π* orbital is empty. In a simple molecular-orbital treatment, the contribution of this pair of orbitals to bond order is

where $N_{\pi}$ and $N_{\pi^*}$ are their respective electron populations. An occupied bonding orbital with two electrons and an empty antibonding orbital therefore contributes one unit of bond order. Occupation of π* reduces that contribution. (openstax.org)

Geometry and restricted rotation

Pi bonding imposes an orientational requirement: the participating orbitals must remain appropriately aligned. Twisting the two ends of an ordinary carbon–carbon double bond reduces their lateral overlap. A large twist substantially disrupts the π interaction, making rotation about a double bond much more difficult than rotation about an isolated σ bond. This restriction is a key structural distinction between single and multiple bonds. (openstax.org)

The contrast does not mean that rotation about every single bond is energetically unrestricted. Rather, the σ overlap itself can be maintained during rotation, whereas localized π overlap depends strongly on the relative orientation of the orbitals. (openstax.org)

Conjugation and delocalization

Pi electrons need not belong to one isolated pair of atoms. In a conjugated system, adjacent p orbitals interact across a sequence of atoms. For example, the four p orbitals of 1,3-butadiene combine into four π molecular orbitals: two bonding and two antibonding. Its π system is consequently described more fully by orbitals spanning the conjugated framework than by two independent localized π bonds. (openstax.org)

Resonance provides a complementary representation of delocalized bonding through multiple Lewis structures. In benzene, six p orbitals form a cyclic π system containing six electrons. Its localized alternating-bond drawings are representations of a delocalized electronic structure. Benzene is an example of aromaticity, which, for simple planar monocyclic conjugated systems, is associated with the Hückel $4n+2$ π-electron rule. (openstax.org)

Reactivity and spectroscopy

Pi bonds help explain the characteristic reactions of alkenes. Their π electrons can interact with electrophilic reagents, initiating electrophilic addition reactions. Such reactions transform the bonding pattern of a double bond into products containing new σ bonds; the precise mechanism depends on the reagent and reaction conditions. (openstax.org)

Pi orbitals also provide an important basis for interpreting electronic spectroscopy. Absorption of suitable radiation can promote an electron from a π orbital to a π* orbital, producing a π → π* transition. Increasing conjugation commonly decreases the energy separation relevant to absorption and shifts absorption toward longer wavelengths. These relationships make electronic spectra useful for investigating conjugated molecular structures. (openstax.org)

Scope of the model

The familiar sideways-overlap picture is especially useful for localized multiple bonds, but it should not be confused with a complete description of every π-electron system. In conjugated molecules, assigning each electron pair to one particular bond can obscure delocalization. Likewise, the symmetry label of an orbital extending over an entire molecule must be distinguished from the symmetry of a localized two-center bonding component. The localized and molecular-orbital descriptions address related aspects of bonding at different levels of representation. (goldbook.iupac.org)

References

1. 3 Multiple Bonds — Chemistry, OpenStaxopenstax.org
2. 3 Multiple Bonds — Chemistry 2e, OpenStaxopenstax.org
3. 1 Valence Bond Theory — Chemistry: Atoms First 2e, OpenStaxopenstax.org
4. 8 sp2 Hybrid Orbitals and the Structure of Ethylene — Organic Chemistry, OpenStaxopenstax.org
5. 11 Describing Chemical Bonds: Molecular Orbital Theory — Organic Chemistry, OpenStaxopenstax.org
6. 4 Molecular Orbital Theory — Chemistry: Atoms First 2e, OpenStaxopenstax.org
7. 1 Molecular Orbitals of Conjugated Pi Systems — Organic Chemistry, OpenStaxopenstax.org
8. 3 Aromaticity and the Hückel 4n + 2 Rule — Organic Chemistry, OpenStaxopenstax.org
9. Ch. 7 Summary — Organic Chemistry, OpenStaxopenstax.org
10. 7 Ultraviolet Spectroscopy — Organic Chemistry, OpenStaxopenstax.org
11. 8 Interpreting Ultraviolet Spectra: The Effect of Conjugation — Organic Chemistry, OpenStaxopenstax.org