Three-center four-electron bond

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The 3-center 4-electron (3c–4e) bond is a model used to explain bonding in certain hypervalent molecules such as tetratomic and hexatomic interhalogen compounds, sulfur tetrafluoride, the xenon fluorides, and the bifluoride ion. [1] [2] It is also known as the Pimentel–Rundle three-center model after the work published by George C. Pimentel in 1951, [3] which built on concepts developed earlier by Robert E. Rundle for electron-deficient bonding. [4] [5] An extended version of this model is used to describe the whole class of hypervalent molecules such as phosphorus pentafluoride and sulfur hexafluoride as well as multi-center π-bonding such as ozone and sulfur trioxide.


There are also molecules such as diborane (B2H6) and dialane (Al2H6) which have three-center two-electron bond (3c-2e) bonds.


While the term "hypervalent" was not introduced in the chemical literature until 1969, [6] Irving Langmuir and G. N. Lewis debated the nature of bonding in hypervalent molecules as early as 1921. [7] [8] While Lewis supported the viewpoint of expanded octet, invoking s-p-d hybridized orbitals and maintaining 2c–2e bonds between neighboring atoms, Langmuir instead opted for maintaining the octet rule, invoking an ionic basis for bonding in hypervalent compounds (see Hypervalent molecule, valence bond theory diagrams for PF5 and SF6). [9]

In a 1951 seminal paper, [3] Pimentel rationalized the bonding in hypervalent trihalide ions (X
, X = F, Br, Cl, I) via a molecular orbital (MO) description, building on the concept of the "half-bond" introduced by Rundle in 1947. [4] [5] In this model, two of the four electrons occupy an all in-phase bonding MO, while the other two occupy a non-bonding MO, leading to an overall bond order of 0.5 between adjacent atoms (see Molecular orbital description).

More recent theoretical studies on hypervalent molecules support the Langmuir view, confirming that the octet rule serves as a good first approximation to describing bonding in the s- and p-block elements. [10] [11]

Examples of molecules exhibiting three-center four-electron bonding

σ 3c–4e

π 3c–4e

Structure and bonding

Molecular orbital description

Figure 1: Diagram illustrating s molecular orbitals of the triiodide anion. Triiodide molecular orbitals.png
Figure 1: Diagram illustrating σ molecular orbitals of the triiodide anion.

The σ molecular orbitals (MOs) of triiodide can be constructed by considering the in-phase and out-of-phase combinations of the central atom's p orbital (collinear with the bond axis) with the p orbitals of the peripheral atoms. [12] This exercise generates the diagram at right (Figure 1). Three molecular orbitals result from the combination of the three relevant atomic orbitals, with the four electrons occupying the two MOs lowest in energy – a bonding MO delocalized across all three centers, and a non-bonding MO localized on the peripheral centers. Using this model, one sidesteps the need to invoke hypervalent bonding considerations at the central atom, since the bonding orbital effectively consists of two 2-center-1-electron bonds (which together do not violate the octet rule), and the other two electrons occupy the non-bonding orbital.

Valence bond (natural bond orbital) description

Figure 2: A donor-acceptor interaction diagram illustrating construction of the triiodide anion s natural bond orbitals from I2 and I fragments. I3-NBOs.png
Figure 2: A donor-acceptor interaction diagram illustrating construction of the triiodide anion σ natural bond orbitals from I2 and I fragments.

In the natural bond orbital viewpoint of 3c–4e bonding, the triiodide anion is constructed from the combination of the diiodine (I2) σ molecular orbitals and an iodide (I) lone pair. The I lone pair acts as a 2-electron donor, while the I2 σ* antibonding orbital acts as a 2-electron acceptor. [12] Combining the donor and acceptor in in-phase and out-of-phase combinations results in the diagram depicted at right (Figure 2). Combining the donor lone pair with the acceptor σ* antibonding orbital results in an overall lowering in energy of the highest-occupied orbital (ψ2). While the diagram depicted in Figure 2 shows the right-hand atom as the donor, an equivalent diagram can be constructed using the left-hand atom as the donor. This bonding scheme is succinctly summarized by the following two resonance structures: I—I···I ↔ I···I—I (where "—" represents a single bond and "···" represents a "dummy bond" with formal bond order 0 whose purpose is only to indicate connectivity), which when averaged reproduces the I—I bond order of 0.5 obtained both from natural bond orbital analysis and from molecular orbital theory.

Figure 3: Diagram depicting the natural bond orbital donor-acceptor interaction in neon difluoride. The central Ne atom acts as the donor, while the out-of-phase combination of the peripheral F atoms acts as the acceptor. The two orbitals have been overlaid on the same molecule framework. NeF2-DA.tif
Figure 3: Diagram depicting the natural bond orbital donor-acceptor interaction in neon difluoride. The central Ne atom acts as the donor, while the out-of-phase combination of the peripheral F atoms acts as the acceptor. The two orbitals have been overlaid on the same molecule framework.

More recent theoretical investigations suggest the existence of a novel type of donor-acceptor interaction that may dominate in triatomic species with so-called "inverted electronegativity"; [13] that is, a situation in which the central atom is more electronegative than the peripheral atoms. Molecules of theoretical curiosity such as neon difluoride (NeF2) and berylium dilithide (BeLi2) represent examples of inverted electronegativity. [13] As a result of unusual bonding situation, the donor lone pair ends up with significant electron density on the central atom, while the acceptor is the "out-of-phase" combination of the p orbitals on the peripheral atoms. This bonding scheme is depicted in Figure 3 for the theoretical noble gas dihalide NeF2.

SN2 transition state modeling

The valence bond description and accompanying resonance structures A—B···C ↔ A···B—C suggest that molecules exhibiting 3c–4e bonding can serve as models for studying the transition states of bimolecular nucleophilic substitution reactions. [12]

See also

Related Research Articles

Chemical bond Lasting attraction between atoms that enables the formation of chemical compounds

A chemical bond is a lasting attraction between atoms, ions or molecules that enables the formation of chemical compounds. The bond may result from the electrostatic force of attraction between oppositely charged ions as in ionic bonds or through the sharing of electrons as in covalent bonds. The strength of chemical bonds varies considerably; there are "strong bonds" or "primary bonds" such as covalent, ionic and metallic bonds, and "weak bonds" or "secondary bonds" such as dipole–dipole interactions, the London dispersion force and hydrogen bonding.

Covalent bond Chemical bond that involves the sharing of electron pairs between atoms

A covalent bond is a chemical bond that involves the sharing of electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs, and the stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding. For many molecules, the sharing of electrons allows each atom to attain the equivalent of a full outer shell, corresponding to a stable electronic configuration. In organic chemistry, covalent bonds are much more common than ionic bonds.

Conjugated system

In 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.

Octet rule Chemical rule of thumblets

The octet rule is a chemical rule of thumb that reflects the theory that main group elements tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. The rule is especially applicable to carbon, nitrogen, oxygen, and the halogens, but also to metals such as sodium or magnesium.

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A hypervalent molecule (the phenomenon is sometimes colloquially known as expanded octet) is a molecule that contains one or more main group elements apparently bearing more than eight electrons in their valence shells. Phosphorus pentachloride (PCl5), sulfur hexafluoride (SF6), chlorine trifluoride (ClF3), the chlorite (ClO2) ion, and the triiodide (I3) ion are examples of hypervalent molecules.

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A three-center two-electron (3c–2e) bond is an electron-deficient chemical bond where three atoms share two electrons. The combination of three atomic orbitals form three molecular orbitals: one bonding, one non-bonding, and one anti-bonding. The two electrons go into the bonding orbital, resulting in a net bonding effect and constituting a chemical bond among all three atoms. In many common bonds of this type, the bonding orbital is shifted towards two of the three atoms instead of being spread equally among all three. An example of a 3c–2e bond is the trihydrogen cation H+
. This type of bond is also called banana bond.

Quadruple bond

A quadruple bond is a type of chemical bond between two atoms involving eight electrons. This bond is an extension of the more familiar types double bonds and triple bonds. Stable quadruple bonds are most common among the transition metals in the middle of the d-block, such as rhenium, tungsten, technetium, molybdenum and chromium. Typically the ligands that support quadruple bonds are π-donors, not π-acceptors.

The 18-electron rule is a chemical rule of thumb used primarily for predicting and rationalizing formulas for stable transition metal complexes, especially organometallic compounds. The rule is based on the fact that the valence orbitals of transition metals consist of five d orbitals, one s orbital and three p orbitals which can collectively accommodate 18 electrons as either bonding or nonbonding electron pairs. This means that the combination of these nine atomic orbitals with ligand orbitals creates nine molecular orbitals that are either metal-ligand bonding or non-bonding. When a metal complex has 18 valence electrons, it is said to have achieved the same electron configuration as the noble gas in the period. The rule is not helpful for complexes of metals that are not transition metals, and interesting or useful transition metal complexes will violate the rule because of the consequences deviating from the rule bears on reactivity. The rule was first proposed by American chemist Irving Langmuir in 1921.

The bifluoride ion is an inorganic anion with the chemical formula HF
. The anion is colorless. Salts of bifluoride are commonly encountered in the reactions of fluoride salts with hydrofluoric acid. The commercial production of fluorine involves electrolysis of bifluoride salts.

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Stereoelectronic effect

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Nontrigonal pnictogen compounds

Nontrigonal pnictogen compounds refer to tricoordinate trivalent pnictogen compounds that are not of typical trigonal pyramidal molecular geometry. By virtue of their geometric constraint, these compounds exhibit distinct electronic structures and reactivities, which bestow on them potential to provide unique nonmetal platforms for bond cleavage reactions.


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