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Pi bond
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Pi bond
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Ethylene (ethene), a small organic molecule containing a pi bond, shown in green.

In chemistry, pi bonds (π bonds) are covalent chemical bonds, in each of which two lobes of an orbital on one atom overlap with two lobes of an orbital on another atom, and in which this overlap occurs laterally. Each of these atomic orbitals has an electron density of zero at a shared nodal plane that passes through the two bonded nuclei. This plane also is a nodal plane for the molecular orbital of the pi bond. Pi bonds can form in double and triple bonds but do not form in single bonds in most cases.

The Greek letter π in their name refers to p orbitals, since the orbital symmetry of the pi bond is the same as that of the p orbital when seen down the bond axis. One common form of this sort of bonding involves p orbitals themselves, though d orbitals also engage in pi bonding. This latter mode forms part of the basis for metal-metal multiple bonding.

Properties

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Two p-orbitals forming a π-bond.

Pi bonds are usually weaker than sigma bonds. The C–C double bond, composed of one sigma and one pi bond,[1] has a bond energy less than twice that of a C–C single bond, indicating that the stability added by the pi bond is less than the stability of a sigma bond. From the perspective of quantum mechanics, this bond's weakness is explained by significantly less overlap between the component p-orbitals due to their parallel orientation. This is contrasted by sigma bonds which form bonding orbitals directly between the nuclei of the bonding atoms, resulting in greater overlap and a strong sigma bond.

Pi bonds result from overlap of atomic orbitals that are in contact through two areas of overlap. Most orbital overlaps that do not include the s-orbital, or have different internuclear axes (for example px + py overlap, which does not apply to an s-orbital) are generally all pi bonds. Pi bonds are more diffuse bonds than the sigma bonds. Electrons in pi bonds are sometimes referred to as pi electrons. Molecular fragments joined by a pi bond cannot rotate about that bond without breaking the pi bond, because rotation involves destroying the parallel orientation of the constituent p orbitals.

For homonuclear diatomic molecules, bonding π molecular orbitals have only the one nodal plane passing through the bonded atoms, and no nodal planes between the bonded atoms. The corresponding antibonding, or π* ("pi-star") molecular orbital, is defined by the presence of an additional nodal plane between these two bonded atoms.

Multiple bonds

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A typical double bond consists of one sigma bond and one pi bond; for example, the C=C double bond in ethylene (H2C=CH2). A typical triple bond, for example in acetylene (HC≡CH), consists of one sigma bond and two pi bonds in two mutually perpendicular planes containing the bond axis. Two pi bonds are the maximum that can exist between a given pair of atoms. Quadruple bonds are extremely rare and can be formed only between transition metal atoms, and consist of one sigma bond, two pi bonds and one delta bond.

A pi bond is weaker than a sigma bond, but the combination of pi and sigma bond is stronger than either bond by itself. The enhanced strength of a multiple bond versus a single (sigma bond) is indicated in many ways, but most obviously by a contraction in bond lengths. For example, in organic chemistry, carbon–carbon bond lengths are about 154 pm in ethane,[2][3] 134 pm in ethylene and 120 pm in acetylene. More bonds make the total bond length shorter and the bond becomes stronger.

Comparison of bond-lengths in simple structures
ethane (1 σ bond) ethylene (1 σ bond + 1 π bond) acetylene (1 σ bond + 2 π bonds)

Special cases

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A pi bond can exist between two atoms that do not have a net sigma-bonding effect between them.

In certain metal complexes, pi interactions between a metal atom and alkyne and alkene pi antibonding orbitals form pi-bonds.

In some cases of multiple bonds between two atoms, there is no net sigma-bonding at all, only pi bonds. Examples include diiron hexacarbonyl (Fe2(CO)6), dicarbon (C2), and diborane(2) (B2H2). In these compounds the central bond consists only of pi bonding because of a sigma antibond accompanying the sigma bond itself. These compounds have been used as computational models for analysis of pi bonding itself, revealing that in order to achieve maximum orbital overlap the bond distances are much shorter than expected.[4]

See also

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References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Pi bond

View on Grokipedia
from Grokipedia
A pi bond (π bond) is a covalent chemical bond formed by the sideways (lateral) overlap of two parallel p atomic orbitals on adjacent atoms, resulting in a with concentrated above and below the plane of the nuclei, rather than along the internuclear axis. This type of bond is weaker than a due to the less effective overlap and typically forms only after a has been established between the same pair of atoms, contributing to the structure of double (one pi bond) or triple (two pi bonds) bonds in molecules like ethene (C₂H₄) or ethyne (C₂H₂). In , pioneered by , pi bonds arise from the overlap of unhybridized p orbitals that remain after the formation of hybrid orbitals (such as sp² or sp) for sigma bonding, explaining the geometry and reactivity of unsaturated compounds. The restricted rotation around a carbon-carbon , due to the pi bond's cloud, leads to cis-trans isomerism in alkenes and influences molecular planarity. Pi bonds play a crucial role in conjugation and , where delocalized pi s enhance stability, as seen in . Key properties of pi bonds include their higher reactivity compared to bonds—making them prone to addition reactions—and their contribution to the overall in multiple bonds, where the pi component accounts for a significant but lesser portion of the total strength. These bonds are essential in understanding the electronic structure of organic and inorganic compounds involving transition metals, such as in metal-alkene complexes.

Definition and Formation

Orbital Overlap Mechanism

A pi bond forms through the sideways, or parallel, overlap of atomic p orbitals on adjacent atoms, in contrast to the end-to-end overlap characteristic of sigma bonds. This lateral interaction concentrates above and below the internuclear axis, creating a cylindrical region of shared electrons that stabilizes the molecular structure. In , the sideways overlap of two p orbitals generates a bonding pi (π) and an antibonding pi (π*). The π orbital features constructive interference, resulting in increased lobes above and below the bond axis, while the π* orbital exhibits destructive interference with a nodal plane along the axis, reducing between the nuclei. These orbitals are delocalized across the bonded atoms, with the bonding orbital lowering the overall when occupied by pairs. The quantum mechanical foundation of pi bonding relies on , where the strength of the interaction is quantified by the , defined as S=∫ψAψB dτS = \int \psi_A \psi_B \, d\tau, measuring the extent of orbital overlap between atomic wavefunctions ψA\psi_A and ψB\psi_B. For pi bonds, this integral is positive but smaller than for bonds due to the reduced spatial overlap in the sideways configuration. The resulting pi bond energy contributes to the total bond dissociation energy, though qualitatively, the poorer overlap efficiency makes pi bonds weaker than bonds. Geometrically, pi bond formation requires atoms to adopt sp² or sp hybridization, leaving one or two unhybridized orbitals perpendicular to the plane of the sigma framework for effective sideways overlap. In sp² hybridization, the three hybrid orbitals form sigma bonds in a trigonal planar arrangement, with the remaining orbital oriented for ; in sp hybridization, two hybrid orbitals create a linear skeleton, freeing two orbitals for pi bonding. This alignment ensures maximal overlap and restricts rotation around the bond axis.

Distinction from Sigma Bonds

The concept of the pi bond was introduced by in his 1931 paper "The Nature of the Chemical Bond," as part of , where it was distinguished from the through descriptions of directional orbital overlap to explain and bonding in unsaturated systems. Structurally, sigma bonds form from end-to-end overlap of atomic orbitals, resulting in cylindrical symmetry along the internuclear axis, which permits free rotation around the bond axis without disrupting the overlap. In contrast, pi bonds arise from sideways overlap of p orbitals, concentrating electron density in lobes above and below the internuclear axis with nodal planes perpendicular to this axis, thereby restricting rotation and enforcing planarity in molecules like ethene. In the context of hybridization, sigma bonds typically involve hybrid orbitals such as sp³, sp², or sp, which provide the framework for molecular skeletons in both . Pi bonds, however, utilize unhybridized orbitals perpendicular to the hybridization plane, occurring only in systems with available orbitals, such as sp²-hybridized carbons in alkenes. Regarding reactivity, sigma bonds are stronger and less reactive due to their greater orbital overlap and concentrated , providing stability to single bonds. Pi bonds, with their more exposed and diffuse , are electron-rich and weaker, making them prone to reactions, as seen in the attack on the pi electrons of alkenes by species like HBr./12%3A_Reactions_to_Alkenes/12.3%3A_Nucleophilic_Character_of_the__Pi__Bond%3A__Electrophilic___Addition_of_Hydrogen_Halides)

Physical and Chemical Properties

Bond Strength and Energy

Pi bonds are generally weaker than s due to the nature of their formation through sideways overlap of p orbitals, resulting in less effective accumulation between the nuclei compared to the end-to-end overlap in s. Typical pi bond energies range from 250 to 300 kJ/mol, with the pi component in a carbon-carbon , such as in ethene (H₂C=CH₂), contributing approximately 266 kJ/mol to the total of 614 kJ/mol./Chemical_Bonding/Fundamentals_of_Chemical_Bonding/Bond_Energies) This value is estimated by subtracting the average C-C energy of 348 kJ/mol from the total energy. The strength of pi bonds is influenced by several factors, including the efficiency of p-orbital overlap, which is inherently lower for pi bonds owing to their parallel geometry, leading to bonding interactions that are less stabilizing than those in sigma bonds. Atomic size plays a key role, as larger atoms possess more diffuse p orbitals that reduce overlap efficiency and thus weaken the pi bond; for instance, pi bonds involving third-row elements are typically less strong than those between second-row atoms. Electronegativity differences between bonded atoms can also modulate pi bond strength by introducing polarity, which alters electron distribution and the overall bonding interaction. In quantitative terms, the average sigma bond energy for C-C linkages falls in the 300-400 kJ/mol range, positioning the pi bond as the "weaker link" in unsaturated molecules and explaining its preferential cleavage during reactions. This disparity facilitates stepwise bond dissociation in multiple bonds, where the pi bond breaks more readily than the , as observed in addition reactions to alkenes and alkynes./Chemical_Bonding/Fundamentals_of_Chemical_Bonding/Bond_Energies) The relative weakness of pi bonds also contributes to restricted around double bonds, enhancing molecular rigidity. Experimental determination of pi bond energies often involves measuring overall bond dissociation enthalpies through thermochemical methods like or equilibrium studies, from which the pi contribution is isolated by comparison to values. Computational approaches, such as (DFT), model pi orbital energies and predict bond strengths with high accuracy, often aligning closely with experimental data. provides complementary insights by ionizing pi electrons and revealing their binding energies, which correlate with bond stability.

Bond Length and Geometry

Pi bonds contribute to shortened bond lengths compared to sigma bonds alone, as the additional sideways overlap of p orbitals increases the between nuclei, effectively contracting the bond. For example, in hydrocarbons, the C-C in measures approximately 154 pm, while the in ethene is 134 pm, and the in ethyne is 120 pm, reflecting the progressive shortening with each added pi bond./01%3A_Structure_and_Bonding/1.13%3A_Ethane_Ethylene_and_Acetylene) The presence of a pi bond enforces a planar around the bonded atoms to maximize orbital overlap. In sp²-hybridized carbon atoms, such as those in alkenes, the three bonds adopt a trigonal planar arrangement with bond angles of 120°, allowing the unhybridized p orbitals to align parallel for optimal pi bonding. This planarity restricts rotation about the bond axis, distinguishing pi-containing systems from flexible -only bonds. Deviations from the ideal 120° bond angles in sp² systems weaken pi bonding by misaligning the p orbitals and reducing overlap efficiency. In strained molecules like , the ring forces the double-bonded carbons into angles near 60°, significantly distorting the pi interaction and increasing overall molecular strain. Torsional strain arises in twisted conformations where the pi bond's planar requirement is compromised, leading to partial overlap of p orbitals and a reduced . For instance, in medium-sized cyclic alkenes with non-planar double bonds, this misalignment diminishes the pi contribution, making the bond more sigma-like and less stable. Precise bond lengths in molecules containing pi bonds are determined using techniques such as for solid-state structures and for gas-phase measurements, providing atomic-scale resolution of internuclear distances./05%3A_The_Rigid_Rotor_and_Rotational_Spectroscopy/5.07%3A_Spectroscopy)

Role in Molecular Bonding

Formation of Double Bonds

A double bond in organic molecules, such as alkenes, arises from the combination of one and one pi bond between two carbon atoms. The forms through the end-on overlap of sp² hybrid orbitals from each carbon, providing a strong, cylindrical around the bond axis. The pi bond, in contrast, results from the sideways overlap of unhybridized 2p orbitals perpendicular to the sigma framework, creating a region of above and below the plane of the molecule. This arrangement accommodates four valence electrons in total: two shared in the and two in the pi bond. The pi electrons are delocalized in a parallel to the molecular plane, which restricts rotation around the and imparts rigidity to the structure. In (H₂C=CH₂), the simplest , both carbon atoms adopt sp² hybridization, forming three bonds each (one C-C and two C-H) with 120° bond angles, resulting in a planar trigonal . The C=C bond length in ethene measures 134 pm, shorter than a typical C-C due to the additional pi overlap, with a total bond dissociation energy of 614 kJ/mol reflecting the combined strength of the and pi components. In propene (H₂C=CH-CH₃), the methyl substituent introduces , where adjacent C-H orbitals overlap with the , slightly increasing the C=C to 135 pm and donating to the pi bond, which enhances stability compared to ethene. The formation of these double bonds through orbital overlap is fundamental to the reactivity of alkenes, where the accessible pi electrons serve as sites for addition reactions, such as , while preserving the underlying sigma framework.

Formation of Triple Bonds

A triple bond between two carbon atoms, as found in alkynes, consists of one and two pi bonds. The forms through the head-on overlap of sp-hybrid orbitals from each carbon atom, providing along the bond axis. The two pi bonds arise from the lateral overlap of unhybridized p orbitals: one pair of p_y orbitals overlaps to form one pi bond, and the perpendicular p_z orbitals overlap to form the second pi bond, creating two orthogonal pi systems. This orbital configuration dictates a at the triple-bonded carbons, with bond angles of 180°, which maximizes the overlap efficiency of both pi bonds without steric interference. The resulting distribution features six electrons in bonding orbitals—two in the sigma framework and four delocalized across the two pi bonds—forming a symmetric, cylindrical cloud around the internuclear region that enhances overall bond strength while exposing the pi electrons to external . In ethyne (HC≡CH), the prototypical , the C≡C has a length of approximately 120 pm and a total dissociation energy of 839 kJ/mol, reflecting the cumulative strength of the and pi components. Substituents in terminal alkynes (RC≡CH), such as alkyl or aryl groups, slightly perturb the pi ; for instance, electron-donating groups increase the nucleophilicity of the , while the high s-character (50%) of the sp-hybridized carbon enhances the acidity of the terminal C–H bond (pK_a ≈ 25), facilitating . The linear and rigid nature of triple bonds imparts high thermal stability to the sigma framework but renders the pi bonds more accessible for reactions, such as to form double bonds, due to their exposed .

Advanced and Special Cases

Pi Bonds in Conjugated Systems

In conjugated systems, pi bonds arise from the overlap of p orbitals in a sequence of alternating single and double bonds, enabling the delocalization of pi electrons across multiple atoms. This configuration, known as conjugation, occurs when adjacent pi bonds are separated by a single , allowing lateral overlap of parallel p orbitals perpendicular to the molecular plane. For instance, in 1,3-butadiene (\ceH2C=CH−CH=CH2\ce{H2C=CH-CH=CH2}), the two double bonds are conjugated, resulting in a continuous pi electron cloud that extends over all four carbon atoms. The delocalization of pi electrons in these systems reduces the bond order of individual bonds, making them intermediate between single and double bonds and enhancing overall molecular stability. In 1,3-butadiene, for example, the central C-C bond exhibits partial double-bond character due to electron sharing, with bond lengths of approximately 1.48 compared to 1.54 for a typical and 1.34 for the terminal double bonds. This delocalization lowers the system's energy relative to isolated double bonds; the stabilization energy, quantified via heats of , is approximately 15 kJ/mol for 1,3-butadiene, as its observed heat of hydrogenation (-239 kJ/mol) is less exothermic than the expected value for two isolated s (-254 kJ/mol). For longer conjugated chains, each additional double bond contributes roughly 15-20 kJ/mol of stabilization through extended delocalization./Chapters/Chapter_16%3A_Conjugation_Resonance_and_Dienes/16.07%3A_Stability_of_Conjugated_Dienes) From a perspective, conjugation leads to the formation of delocalized pi s spanning the entire system, where the energy difference between the highest occupied (HOMO) and lowest unoccupied (LUMO) narrows with increasing conjugation length. This reduced HOMO-LUMO gap facilitates lower-energy electronic transitions, observable in spectroscopic properties; for 1,3-butadiene, the pi-to-pi* transition occurs at 217 nm in the region, shifting toward the visible for longer polyenes and imparting color to extended conjugated molecules. Such properties underpin applications in , where delocalized pi electrons enable efficient charge transport in devices like field-effect transistors, as demonstrated in pi-conjugated polymers with mobilities exceeding 16 cm²/V·s as of 2023.

Pi Bonding in Coordination Compounds

In coordination compounds, pi bonding arises primarily through interactions between d-orbitals and orbitals of appropriate , encompassing both ligand-to-metal pi and metal-to-ligand pi . Ligand-to-metal pi donation occurs when filled pi or p orbitals on the , such as those on ions (e.g., Cl⁻), overlap with empty metal d-orbitals, enhancing the by providing additional to the metal center. This is particularly prominent in complexes with pi-donor ligands like or oxide ions, which stabilize higher oxidation states of the metal. Conversely, metal-to-ligand pi backbonding involves from filled metal d-orbitals (typically t₂g in ) to empty pi* antibonding orbitals on the , which weakens the ligand's internal bonds while strengthening the metal-ligand interaction. These processes often operate synergistically with , where initial bonding polarizes the metal-ligand bond to facilitate pi overlap. The orbital symmetry requirements for effective pi bonding demand alignment between metal d-orbitals (such as d_{xy}, d_{xz}, and d_{yz}) and pi or pi* orbitals. For instance, in , the metal's d_{xz} or d_{yz} orbitals match the of the ligand's pi* lobes, enabling sideways overlap that populates the ligand's antibonding manifold. This symmetry matching is crucial in octahedral or square planar geometries, where the t_{2g} set of d-orbitals is non-bonding in frameworks but available for pi interactions. In ligand-to-metal donation, ligand p-orbitals or pi bonds align similarly to donate into metal e_g or t_{2g} orbitals, depending on the complex's electronic configuration. Such overlaps are quantified in , where the net bonding arises from the balance of these pi contributions with sigma interactions. A classic example of pi bonding is found in Zeise's salt, K[PtCl₃(C₂H₄)], prepared in 1827 by William Zeise, the first organometallic compound, whose structure was determined in 1971 by , featuring an ligand bound to Pt(II). Here, the bonding follows the Dewar-Chatt-Duncanson model, involving sigma donation from the ethylene pi orbital to an empty Pt d-orbital and from Pt d-orbitals to the ethylene pi* orbital, which lengthens the C=C bond from 1.337 Å in free to 1.375 Å and rehybridizes the carbon atoms toward sp³ character. The Pt-C distances are approximately 2.13 Å, and the trans Pt-Cl bond is elongated to 2.34 Å due to the pi-acceptor effect of , demonstrating the trans influence in square planar geometry. This pi interaction not only stabilizes the complex but also alters ethylene's reactivity, making it susceptible to nucleophilic attack. In metal carbonyl complexes like Ni(CO)₄, pi backbonding plays a dominant role, with the Ni(0) center donating electron density from its d-orbitals to the low-lying pi* orbitals of CO, strengthening the Ni-C bonds while weakening and lengthening the C-O bonds (typically from 1.13 Å in free CO to ~1.15 Å in the complex). This results in a characteristic red shift of the CO stretching frequency (ν_CO) to around 2050 cm⁻¹, compared to 2143 cm⁻¹ for free CO, as the increased electron density in the pi* orbital reduces the C-O bond order. The synergistic nature of sigma donation from CO's lone pair and pi backbonding enhances overall stability, allowing low-oxidation-state metals like Ni(0) to form stable tetrahedral complexes. Computational studies confirm that d-orbital involvement significantly boosts charge transfer and bond orders, with pi backbonding contributing up to 20-30% of the total metal-ligand interaction energy in such systems. The combined sigma and pi interactions in these complexes lead to shortened metal-ligand bond lengths overall, as the pi backdonation counteracts the lengthening from sigma donation, resulting in net bond strengthening. also increases electron density on the ligands, which explains the preference for pi-acceptor ligands in stabilizing low-oxidation-state metals, as seen in Ni(CO)₄ where the is satisfied through these interactions. In terms of properties, this electron redistribution enhances complex stability against dissociation and influences reactivity, such as facilitating migratory insertion in catalytic cycles. Historically, the synergistic bonding model for pi interactions was formalized in the Dewar-Chatt-Duncanson framework in the for complexes and extended to carbonyls, with further refinements in the 1970s by Malcolm L. H. Green, who developed bonding models for organometallic systems emphasizing d-pi overlaps in metallocenes. Modern organometallic examples, such as [Fe(η⁵-C₅H₅)₂], illustrate pi bonding through delocalized interactions between Fe(II) d-orbitals and the pi systems of the cyclopentadienyl (Cp) rings. The η⁵ hapticity involves overlap of Fe d-orbitals (e.g., d_{z²} and d_{xz/yz}) with symmetry-adapted linear combinations of Cp pi orbitals, forming bonding molecular orbitals that stabilize the 18-electron configuration and confer aromatic-like stability to the Cp ligands. This d-pi bonding accounts for the low rotation barrier (~4 kJ/mol) around the Fe-Cp axis and the compound's thermal robustness, highlighting pi interactions in sandwich complexes beyond simple donor-acceptor models.

References

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