Three-center four-electron bond

The 3-center-4-electron bond is a model used to explain bonding in hypervalent molecules such as phosphorus pentafluoride, sulfur hexafluoride, 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]

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 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 molecules PF5 and SF4 are described, according to this model, as having one 3-center-4-electron bond as well as three and two other more conventionally described bonds, respectively. In SF6 and in the xenon fluorides, all bonds are described with the 3-center-4-electron model.
Bonding in the hypervalent molecule XeF2 according to the 3-center-4-electron bond model.

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.

Older models for explaining hypervalency invoked d orbitals. As of 2010, these models still appear in some beginning-level college texts;[5] 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.[6] The 3-center-4-electron bonding model has the advantage of dispensing with the need for d orbitals, which has led to its acceptance.[7]

Three-center four-electron interactions can also be considered in the transition state of SN2 reactions and in some (resonant) hydrogen bonding:
\bigg[\ F \frac{\quad}{\quad} H\ {}^-\!F \quad \longleftrightarrow \quad F^- \ {}\!H \frac{\quad}{\quad} F\ \bigg]

References

1. ^ Greenwood, Norman N.; Earnshaw, A. (1997), Chemistry of the Elements (2nd ed.), Oxford: Butterworth-Heinemann, ISBN 0080379419 p. 897.
2. ^ Weinhold, F.; Landis, C. Valency and bonding, Cambridge, 2005; pp. 275-306.
3. ^ 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
4. ^ Rundle, R. E. Electron Deficient Compounds. II. Relative Energies of "Half-Bonds". J. Chem. Phys 1949, 17, 671-675.doi:10.1063/1.1747367
5. ^ New Way Chemistry for Hong Kong A-level, 3rd edition by Manhattan
6. ^ 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
7. ^ 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