Three-center four-electron bond

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The 3-center 4-electron 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] 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 pi-bonding such as ozone and sulfur trioxide.

Description

Molecular orbital theory

The model considers bonding of three colinear atoms. For example in XeF₂, the linear F−Xe−F subunit is described by a set of three molecular orbitals (MOs) derived from colinear p-orbitals on each atom. The Xe−F bonds result from the combination of a filled p orbital in the central atom (Xe) with two half-filled p orbitals on the axial atoms (F), resulting in a filled bonding orbital, a filled non-bonding orbital, and an empty antibonding orbital. The two lower energy MO's are doubly occupied. The bond order for each Xe-F bonds is 1/2, since the only bonding orbital is delocalized over the two Xe-F bonds.^[5]

The HOMO is localized on the two terminal atoms. This localization of charge is accommodated by the fact that the terminal ligands are highly electronegative in hypervalent molecules. The linear F−A−F axis of the molecules SF₄ and ClF₃ is described as a 3-center 4-electron bond. In the xenon fluorides, all bonds are described with the 3-center 4-electron model. Molecules without an s-orbital lone pair such as PF₅ and SF₆ are described by an extended version of the 3-center 4-electron model (See hypervalent molecule).

Bonding in the hypervalent molecule XeF₂ according to the 3-center 4-electron bond model.

Valence bond theory

The bonding in XeF₂ can also be shown qualitatively using resonant Lewis structures as shown below:

${\bigg [}\ F{\frac {\quad }{\quad }}Xe^{+}\ {}^{-}\!F\quad \longleftrightarrow \quad F^{-}\ {}^{+}\!Xe{\frac {\quad }{\quad }}F\ {\bigg ]}$

In this representation, the octet rule is not broken, the bond orders are 1/2, and there is increased electron density in the fluorine atoms. These results are consistent with the molecular orbital picture discussed above.

Hypervalent description with d orbitals

Older models for explaining hypervalency invoked d orbitals. As of 2010, these models still appear in some beginning-level college texts;^[6] however, quantum chemical calculations suggest that d-orbital participation is negligible due to the large energy difference between the relevant p (filled) and d (empty) orbitals. Furthermore, a distinction should be made between "d orbitals" in the valence bond sense and "d functions" that are included in the QM calculation as polarization functions.^[7] The 3-center-4-electron bonding model has the advantage of dispensing with the need for d orbitals, which has led to its acceptance.^[8]

Other systems

Three-center four-electron interactions can also be considered in the transition state of S_N2 reactions and in some (resonant) hydrogen bonding (as in the bifluoride anion):

${\bigg [}\ F{\frac {\quad }{\quad }}H\ {}^{-}\!F\quad \longleftrightarrow \quad F^{-}\ {}\!H{\frac {\quad }{\quad }}F\ {\bigg ]}$

References

↑ Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. ISBN 0080379419. p. 897.
↑ Weinhold, F.; Landis, C. Valency and bonding, Cambridge, 2005; pp. 275-306.
↑ Pimentel, G. C. The Bonding of Trihalide and Bifluoride Ions by the Molecular Orbital Method. J. Chem. Phys. 1951, 19, 446-448. doi:10.1063/1.1748245
↑ Rundle, R. E. Electron Deficient Compounds. II. Relative Energies of "Half-Bonds". J. Chem. Phys 1949, 17, 671–675.doi:10.1063/1.1747367
↑ B.E. Douglas, D.H. McDaniel and J.J. Alexander, Concepts and Models of Inorganic Chemistry, 2nd edition (Wiley 1983) p.164
↑ New Way Chemistry for Hong Kong A-level, 3rd edition by Manhattan
↑ E. Magnusson. Hypercoordinate molecules of second-row elements: d functions or d orbitals? J. Am. Chem. Soc. 1990, 112, 7940-7951. doi:10.1021/ja00178a014
↑ Ramsden, C. A. Non-bonding molecular orbitals and the chemistry of non-classical organic molecules. Chem. Soc. Rev. 1994, 111-118. doi:10.1039/CS9942300111

Chemical bonds

Intramolecular
("strong")

Covalent
bonds

By symmetry	Sigma (σ) Pi (π) Delta (δ) Phi (φ)

By multiplicity	1 (single) 2 (double) 3 (triple) 4 (quadruple) 5 (quintuple) 6 (sextuple)

Miscellaneous	Agostic bond Bent bond Dipolar bond Pi backbond Hapticity Conjugation Hyperconjugation Antibonding

Resonant bonds	Electron-deficient 3c–2e 4c–2e Hypercoordination 3c–4e Aromaticity

Metallic bonds

Metal aromaticity

Ionic bonding

Intermolecular
("weak")

van der Waals forces	London dispersion force

Hydrogen bond	Low-barrier Resonance-assisted Symmetric Dihydrogen bonds

Other noncovalent	Mechanical bond Halogen bond Aurophilicity Intercalation Stacking Cation–pi bond Anion–pi bond Salt bridge

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