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The '''3-center 4-electron bond''' is a model used to explain bonding in certain [[hypervalent molecule]]s such as tetratomic and hexatomic [[interhalogen]] compounds, [[sulfur tetrafluoride]], the [[xenon fluorides]], and the [[bifluoride]] ion.<ref>{{Greenwood&Earnshaw}} p. 897.</ref><ref>Weinhold, F.; Landis, C. ''Valency and bonding'', Cambridge, '''2005'''; pp. 275-306.</ref> It is also known as the '''Pimentel–Rundle three-center model''' after the work published by [[George C. Pimentel]] in 1951,<ref>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}}</ref> which built on concepts developed earlier by Robert E. Rundle for electron-deficient bonding.<ref>Rundle, R. E. Electron Deficient Compounds. II. Relative Energies of "Half-Bonds". ''J. Chem. Phys'' '''1949''', ''17'', 671–675.{{doi|10.1063/1.1747367}}</ref> 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 XeF<sub>2</sub>, 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.<ref>B.E. Douglas, D.H. McDaniel and J.J. Alexander, ''Concepts and Models of Inorganic Chemistry'', 2nd edition (Wiley 1983) p.164</ref> | |||
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 SF<sub>4</sub> and ClF<sub>3</sub> 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 PF<sub>5</sub> and SF<sub>6</sub> are described by an extended version of the 3-center 4-electron model (See [[hypervalent molecule]]). | |||
[[Image:XeF2.png|400px||thumb|center|Bonding in the hypervalent molecule XeF<sub>2</sub> according to the 3-center 4-electron bond model.]] | |||
===Valence bond theory=== | |||
The bonding in XeF<sub>2</sub> can also be shown qualitatively using [[resonance (chemistry)|resonant]] [[Lewis structure]]s as shown below: | |||
<center><math>\bigg[\ F \frac{\quad}{\quad} Xe^+ \ {}^-\!F \quad \longleftrightarrow \quad F^- \ {}^+\!Xe \frac{\quad}{\quad} F\ \bigg]</math></center> | |||
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;<ref>New Way Chemistry for Hong Kong A-level, 3rd edition by Manhattan</ref> however, [[quantum chemistry|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 function]]s.<ref>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}}</ref> The 3-center-4-electron bonding model has the advantage of dispensing with the need for d orbitals, which has led to its acceptance.<ref>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}}</ref> | |||
==Other systems== | |||
Three-center four-electron interactions can also be considered in the transition state of [[SN2 reaction|S<sub>N</sub>2 reaction]]s and in some (resonant) hydrogen bonding (as in the [[bifluoride]] anion): | |||
<center><math>\bigg[\ F \frac{\quad}{\quad} H\ {}^-\!F \quad \longleftrightarrow \quad F^- \ {}\!H \frac{\quad}{\quad} F\ \bigg]</math></center> | |||
==References== | |||
{{reflist}} | |||
{{Chemical bonds}} | |||
[[Category:Chemical bonding]] | |||
Latest revision as of 22:51, 14 November 2013
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).
Valence bond theory
The bonding in XeF2 can also be shown qualitatively using resonant Lewis structures as shown below:
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 SN2 reactions and in some (resonant) hydrogen bonding (as in the bifluoride anion):
References
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- ↑ Template:Greenwood&Earnshaw 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. 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.
- ↑ Rundle, R. E. Electron Deficient Compounds. II. Relative Energies of "Half-Bonds". J. Chem. Phys 1949, 17, 671–675.21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.
- ↑ 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. 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.
- ↑ Ramsden, C. A. Non-bonding molecular orbitals and the chemistry of non-classical organic molecules. Chem. Soc. Rev. 1994, 111-118. 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.