Three-center four-electron bond
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. It is also known as the Pimentel–Rundle three-center model after the work published by George C. Pimentel in 1951, which built on concepts developed earlier by Robert E. Rundle for electron-deficient bonding. 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.
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.
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).
Valence bond theory 
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; 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. The 3-center-4-electron bonding model has the advantage of dispensing with the need for d orbitals, which has led to its acceptance.
Other systems 
- 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