Physics:Quantum delta bond - Revision history

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	The Greek letter δ in their name refers to d orbitals, since the orbital symmetry of the δ bond is the same as that of the usual (4-lobed) type of d orbital when seen down the bond axis. This type of bonding is observed in atoms that have occupied d orbitals with low enough energy to participate in covalent bonding, for example, in organometallic species of transition metals. Some rhenium, molybdenum, technetium, and chromium compounds contain a quadruple bond, consisting of one σ bond, two π bonds and one δ bond. In the case of the [Re<sub>2</sub>Cl<sub>8</sub>]<sup>2-</sup> ion in the D<sub>4h</sub> Point group, the bonding delta interaction is the highest energy bonding interaction, followed by the bonding pi, and sigma interactions. The resultant antibonding delta interaction is the least destabilized, followed by the antibonding pi and sigma interactions.<ref>{{Cite journal \|last=Falvello \|first=Larry R. \|last2=Foxman \|first2=Bruce M. \|last3=Murillo \|first3=Carlos A. \|date=2014-09-15 \|title=Fitting the Pieces of the Puzzle: The δ Bond \|url=https://pubs.acs.org/doi/10.1021/ic500119h \|journal=Inorganic Chemistry \|language=en \|volume=53 \|issue=18 \|pages=9441–9456 \|doi=10.1021/ic500119h \|issn=0020-1669}}</ref>		The Greek letter δ in their name refers to d orbitals, since the orbital symmetry of the δ bond is the same as that of the usual (4-lobed) type of d orbital when seen down the bond axis. This type of bonding is observed in atoms that have occupied d orbitals with low enough energy to participate in covalent bonding, for example, in organometallic species of transition metals. Some rhenium, molybdenum, technetium, and chromium compounds contain a quadruple bond, consisting of one σ bond, two π bonds and one δ bond. In the case of the [Re<sub>2</sub>Cl<sub>8</sub>]<sup>2-</sup> ion in the D<sub>4h</sub> Point group, the bonding delta interaction is the highest energy bonding interaction, followed by the bonding pi, and sigma interactions. The resultant antibonding delta interaction is the least destabilized, followed by the antibonding pi and sigma interactions.<ref>{{Cite journal \|last=Falvello \|first=Larry R. \|last2=Foxman \|first2=Bruce M. \|last3=Murillo \|first3=Carlos A. \|date=2014-09-15 \|title=Fitting the Pieces of the Puzzle: The δ Bond \|url=https://pubs.acs.org/doi/10.1021/ic500119h \|journal=Inorganic Chemistry \|language=en \|volume=53 \|issue=18 \|pages=9441–9456 \|doi=10.1021/ic500119h \|issn=0020-1669}}</ref>

	[[File:Molecular orbital diagram of d orbitals in D4h Re2Cl8.jpg\|thumb\|Molecular Orbital Diagram of D<sub>4h</sub> [Re<sub>2</sub>Cl<sub>8</sub><nowiki>]</nowiki><sup>2-</sup> showing the bonding and antibonding d orbital interactions and their relative energies. the d<sub>x</sub><sup>2</sup><sub>-y</sub><sup>2</sup> is omitted from d-d interactions due to its engagement with chloride ligands]]
	The orbital symmetry of the δ bonding orbital is different from that of a π antibonding orbital, which has one nodal plane containing the internuclear axis and a second nodal plane perpendicular to this axis between the atoms.		The orbital symmetry of the δ bonding orbital is different from that of a π antibonding orbital, which has one nodal plane containing the internuclear axis and a second nodal plane perpendicular to this axis between the atoms.

WikiHarold: Remove imported red links from Quantum page

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	== References ==		== References ==
	{{Reflist}}		{{Reflist}}

	~~{{Chemical bonding theory}}~~

	{{DEFAULTSORT:Delta Bond}}		{{DEFAULTSORT:Delta Bond}}
	~~[[Category:Chemical bonding]]~~

	{{Sourceattribution\|Delta bond}}		{{Sourceattribution\|Delta bond}}

WikiHarold: Clean Quantum page image and red links

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Clean Quantum page image and red links

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	[[File:Dimolybdenum-Mo2-delta-bond-Spartan-HF-3-21G-3D-side.png\|thumb\|right\|200px\|3D model of a boundary surface of a δ bond in Mo<sub>2</sub>]]		[[File:Dimolybdenum-Mo2-delta-bond-Spartan-HF-3-21G-3D-side.png\|thumb\|right\|200px\|3D model of a boundary surface of a δ bond in Mo<sub>2</sub>]]

	In ~~[[HandWiki:Chemistry\|~~chemistry]], a '''delta bond''' ('''δ bond''') is a ~~[[Chemistry:Covalent bond\|~~covalent~~]] [[Chemistry:Chemical bond\|~~chemical bond]], in which four lobes of an ~~[[Physics:Atomic orbital\|~~atomic orbital]] on one atom ~~[[Orbital~~ overlap~~\|overlap]]~~ four lobes of an atomic orbital on another atom. This overlap leads to the formation of a bonding ~~[[Chemistry:Molecular orbital\|~~molecular orbital]] with two nodal planes which contain the internuclear axis and go through both atoms.<ref>{{cite book\|title=Advanced Inorganic Chemistry\|last2=Wilkinson\|first2=G.\|date=1988\|publisher=John Wiley\|isbn=0-471-84997-9\|edition=5th\|pages=1087–1091\|first1=F. A.\|last1=Cotton\|author2-link=Geoffrey Wilkinson}}</ref><ref>{{cite book\|title=Concepts and Models of Inorganic Chemistry\|url=https://archive.org/details/conceptsmodelsof0000doug\|url-access=registration\|last2=McDaniel\|first2=D. H.\|last3=Alexander\|first3=J. J.\|date=1983\|publisher=Wiley\|isbn=9780471895053\|edition=2nd\|page=[https://archive.org/details/conceptsmodelsof0000doug/page/137 137]\|first1=B.\|last1=Douglas}}</ref><ref>{{cite book\|title=Inorganic Chemistry\|last=Huheey\|first=J. E.\|date=1983\|publisher=Harper and Row\|isbn=9780060429874\|edition=3rd\|pages=743–744}}</ref><ref>{{cite book\|title=Inorganic Chemistry\|last2=Tarr\|first2=D. A.\|date=1998\|publisher=Prentice-Hall\|isbn=978-0138418915\|edition=2nd\|pages=123–124\|first1=G. L.\|last1=Miessler}}</ref>		In chemistry, a '''delta bond''' ('''δ bond''') is a covalent chemical bond, in which four lobes of an atomic orbital on one atom overlap four lobes of an atomic orbital on another atom. This overlap leads to the formation of a bonding molecular orbital with two nodal planes which contain the internuclear axis and go through both atoms.<ref>{{cite book\|title=Advanced Inorganic Chemistry\|last2=Wilkinson\|first2=G.\|date=1988\|publisher=John Wiley\|isbn=0-471-84997-9\|edition=5th\|pages=1087–1091\|first1=F. A.\|last1=Cotton\|author2-link=Geoffrey Wilkinson}}</ref><ref>{{cite book\|title=Concepts and Models of Inorganic Chemistry\|url=https://archive.org/details/conceptsmodelsof0000doug\|url-access=registration\|last2=McDaniel\|first2=D. H.\|last3=Alexander\|first3=J. J.\|date=1983\|publisher=Wiley\|isbn=9780471895053\|edition=2nd\|page=[https://archive.org/details/conceptsmodelsof0000doug/page/137 137]\|first1=B.\|last1=Douglas}}</ref><ref>{{cite book\|title=Inorganic Chemistry\|last=Huheey\|first=J. E.\|date=1983\|publisher=Harper and Row\|isbn=9780060429874\|edition=3rd\|pages=743–744}}</ref><ref>{{cite book\|title=Inorganic Chemistry\|last2=Tarr\|first2=D. A.\|date=1998\|publisher=Prentice-Hall\|isbn=978-0138418915\|edition=2nd\|pages=123–124\|first1=G. L.\|last1=Miessler}}</ref>

	The Greek letter δ in their name refers to d orbitals, since the orbital symmetry of the δ bond is the same as that of the usual (4-lobed) type of d orbital when seen down the bond axis. This type of bonding is observed in atoms that have occupied d orbitals with low enough energy to participate in covalent bonding, for example, in organometallic species of ~~[[Chemistry:Transition metal\|~~transition ~~metal]]s~~. Some ~~[[Chemistry:Rhenium\|~~rhenium]], ~~[[Chemistry:Molybdenum\|~~molybdenum]], ~~[[Chemistry:Technetium\|~~technetium]], and ~~[[Chemistry:Chromium\|~~chromium]] compounds contain a ~~[[Chemistry:Quadruple bond\|~~quadruple bond]], consisting of one ~~[[Chemistry:Sigma bond\|~~σ bond]], two ~~[[Chemistry:Pi bond\|~~π ~~bond]]s~~ and one δ bond. In the case of the [Re<sub>2</sub>Cl<sub>8</sub>]<sup>2-</sup> ion in the D<sub>4h</sub> [[Point group]], the ~~[[Chemistry:Bonding molecular orbital\|~~bonding]] delta interaction is the highest energy bonding interaction, followed by the bonding pi, and sigma interactions. The resultant ~~[[Chemistry:Antibonding molecular orbital\|~~antibonding]] delta interaction is the least destabilized, followed by the antibonding pi and sigma interactions.<ref>{{Cite journal \|last=Falvello \|first=Larry R. \|last2=Foxman \|first2=Bruce M. \|last3=Murillo \|first3=Carlos A. \|date=2014-09-15 \|title=Fitting the Pieces of the Puzzle: The δ Bond \|url=https://pubs.acs.org/doi/10.1021/ic500119h \|journal=Inorganic Chemistry \|language=en \|volume=53 \|issue=18 \|pages=9441–9456 \|doi=10.1021/ic500119h \|issn=0020-1669}}</ref>		The Greek letter δ in their name refers to d orbitals, since the orbital symmetry of the δ bond is the same as that of the usual (4-lobed) type of d orbital when seen down the bond axis. This type of bonding is observed in atoms that have occupied d orbitals with low enough energy to participate in covalent bonding, for example, in organometallic species of transition metals. Some rhenium, molybdenum, technetium, and chromium compounds contain a quadruple bond, consisting of one σ bond, two π bonds and one δ bond. In the case of the [Re<sub>2</sub>Cl<sub>8</sub>]<sup>2-</sup> ion in the D<sub>4h</sub> Point group, the bonding delta interaction is the highest energy bonding interaction, followed by the bonding pi, and sigma interactions. The resultant antibonding delta interaction is the least destabilized, followed by the antibonding pi and sigma interactions.<ref>{{Cite journal \|last=Falvello \|first=Larry R. \|last2=Foxman \|first2=Bruce M. \|last3=Murillo \|first3=Carlos A. \|date=2014-09-15 \|title=Fitting the Pieces of the Puzzle: The δ Bond \|url=https://pubs.acs.org/doi/10.1021/ic500119h \|journal=Inorganic Chemistry \|language=en \|volume=53 \|issue=18 \|pages=9441–9456 \|doi=10.1021/ic500119h \|issn=0020-1669}}</ref>

	[[File:Molecular orbital diagram of d orbitals in D4h Re2Cl8.jpg\|thumb\|Molecular Orbital Diagram of D<sub>4h</sub> [Re<sub>2</sub>Cl<sub>8</sub><nowiki>]</nowiki><sup>2-</sup> showing the bonding and antibonding d orbital interactions and their relative energies. the d<sub>x</sub><sup>2</sup><sub>-y</sub><sup>2</sup> is omitted from d-d interactions due to its engagement with chloride ligands]]		[[File:Molecular orbital diagram of d orbitals in D4h Re2Cl8.jpg\|thumb\|Molecular Orbital Diagram of D<sub>4h</sub> [Re<sub>2</sub>Cl<sub>8</sub><nowiki>]</nowiki><sup>2-</sup> showing the bonding and antibonding d orbital interactions and their relative energies. the d<sub>x</sub><sup>2</sup><sub>-y</sub><sup>2</sup> is omitted from d-d interactions due to its engagement with chloride ligands]]
	The orbital symmetry of the δ bonding orbital is different from that of a ~~[[Chemistry:Pi bond\|~~π]] antibonding orbital, which has one nodal plane containing the internuclear axis and a second nodal plane perpendicular to this axis between the atoms.		The orbital symmetry of the δ bonding orbital is different from that of a π antibonding orbital, which has one nodal plane containing the internuclear axis and a second nodal plane perpendicular to this axis between the atoms.

	The δ notation was introduced by Robert Mulliken in 1931.<ref>{{cite journal\|title=The Origin of the Sigma, Pi, Delta Notation for Chemical Bonds\|first=William B.\|last=Jensen\|journal=J. Chem. Educ.\|date=2013\|volume=90\|issue=6\|pages=802–803\|doi=10.1021/ed200298h\|bibcode=2013JChEd..90..802J}}</ref><ref>{{cite journal\|title=Bonding Power of Electrons and Theory of Valence\|first=Robert S.\|last=Mulliken\|journal=~~[[Chemistry:Chemical Reviews\|~~Chem. Rev.]]\|date=1931\|volume=9\|issue=3\|pages=347–388\|doi=10.1021/cr60034a001}}</ref> The first compound identified as having a δ bond was ~~[[Chemistry:Potassium octachlorodirhenate\|~~potassium octachlorodirhenate(III)]]. In 1965, F. A. Cotton reported that there was δ-bonding as part of the rhenium–rhenium ~~[[Chemistry:Quadruple bond\|~~quadruple bond]] in the [Re<sub>2</sub>Cl<sub>8</sub>]<sup>2−</sup> ion.<ref>{{cite journal\|title=Metal–Metal Bonding in [Re<sub>2</sub>X<sub>8</sub>]<sup>2−</sup> Ions and Other Metal Atom Clusters\|first=F. A.\|last=Cotton\|journal=Inorg. Chem.\|date=1965\|volume=4\|issue=3\|pages=334–336\|doi=10.1021/ic50025a016}}</ref> Another example of a δ bond is proposed in ~~[[Chemistry:Cyclobutadieneiron tricarbonyl\|~~cyclobutadieneiron tricarbonyl]] between an iron d orbital and the four p orbitals of the attached cyclobutadiene molecule.		The δ notation was introduced by Robert Mulliken in 1931.<ref>{{cite journal\|title=The Origin of the Sigma, Pi, Delta Notation for Chemical Bonds\|first=William B.\|last=Jensen\|journal=J. Chem. Educ.\|date=2013\|volume=90\|issue=6\|pages=802–803\|doi=10.1021/ed200298h\|bibcode=2013JChEd..90..802J}}</ref><ref>{{cite journal\|title=Bonding Power of Electrons and Theory of Valence\|first=Robert S.\|last=Mulliken\|journal=Chem. Rev.\|date=1931\|volume=9\|issue=3\|pages=347–388\|doi=10.1021/cr60034a001}}</ref> The first compound identified as having a δ bond was potassium octachlorodirhenate(III). In 1965, F. A. Cotton reported that there was δ-bonding as part of the rhenium–rhenium quadruple bond in the [Re<sub>2</sub>Cl<sub>8</sub>]<sup>2−</sup> ion.<ref>{{cite journal\|title=Metal–Metal Bonding in [Re<sub>2</sub>X<sub>8</sub>]<sup>2−</sup> Ions and Other Metal Atom Clusters\|first=F. A.\|last=Cotton\|journal=Inorg. Chem.\|date=1965\|volume=4\|issue=3\|pages=334–336\|doi=10.1021/ic50025a016}}</ref> Another example of a δ bond is proposed in cyclobutadieneiron tricarbonyl between an iron d orbital and the four p orbitals of the attached cyclobutadiene molecule.
	</div>		</div>

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 {{Short description|Type of chemical bond}}
-[[File:Delta-bond-formation-2D.png|thumb|right|200px|Formation of a δ bond by the overlap of two d orbitals]]
 [[File:Dimolybdenum-Mo2-delta-bond-Spartan-HF-3-21G-3D-side.png|thumb|right|200px|3D model of a boundary surface of a δ bond in Mo<sub>2</sub>]]
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 The δ notation was introduced by Robert Mulliken in 1931.<ref>{{cite journal|title=The Origin of the Sigma, Pi, Delta Notation for Chemical Bonds|first=William B.|last=Jensen|journal=J. Chem. Educ.|date=2013|volume=90|issue=6|pages=802–803|doi=10.1021/ed200298h|bibcode=2013JChEd..90..802J}}</ref><ref>{{cite journal|title=Bonding Power of Electrons and Theory of Valence|first=Robert S.|last=Mulliken|journal=[[Chemistry:Chemical Reviews|Chem. Rev.]]|date=1931|volume=9|issue=3|pages=347–388|doi=10.1021/cr60034a001}}</ref> The first compound identified as having a δ bond was [[Chemistry:Potassium octachlorodirhenate|potassium octachlorodirhenate(III)]]. In 1965, F. A. Cotton reported that there was δ-bonding as part of the rhenium–rhenium [[Chemistry:Quadruple bond|quadruple bond]] in the [Re<sub>2</sub>Cl<sub>8</sub>]<sup>2−</sup> ion.<ref>{{cite journal|title=Metal–Metal Bonding in [Re<sub>2</sub>X<sub>8</sub>]<sup>2−</sup> Ions and Other Metal Atom Clusters|first=F. A.|last=Cotton|journal=Inorg. Chem.|date=1965|volume=4|issue=3|pages=334–336|doi=10.1021/ic50025a016}}</ref> Another example of a δ bond is proposed in [[Chemistry:Cyclobutadieneiron tricarbonyl|cyclobutadieneiron tricarbonyl]] between an iron d orbital and the four p orbitals of the attached cyclobutadiene molecule.
 == References ==

imported>WikiHarold: WikiHarold moved page Chemistry:Delta bond to Physics:Quantum delta bond without leaving a redirect

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WikiHarold moved page Chemistry:Delta bond to Physics:Quantum delta bond without leaving a redirect

← Older revision	Revision as of 17:10, 4 May 2026
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imported>WikiHarold: WikiHarold moved page Chemistry:Delta bond to Physics:Quantum delta bond without leaving a redirect

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WikiHarold moved page Chemistry:Delta bond to Physics:Quantum delta bond without leaving a redirect

New page

{{Short description|Type of chemical bond}}
[[File:Delta-bond-formation-2D.png|thumb|right|200px|Formation of a δ bond by the overlap of two d orbitals]]
[[File:Dimolybdenum-Mo2-delta-bond-Spartan-HF-3-21G-3D-side.png|thumb|right|200px|3D model of a boundary surface of a δ bond in Mo2]]

In [[HandWiki:Chemistry|chemistry]], a '''delta bond''' ('''δ bond''') is a [[Chemistry:Covalent bond|covalent]] [[Chemistry:Chemical bond|chemical bond]], in which four lobes of an [[Physics:Atomic orbital|atomic orbital]] on one atom [[Orbital overlap|overlap]] four lobes of an atomic orbital on another atom. This overlap leads to the formation of a bonding [[Chemistry:Molecular orbital|molecular orbital]] with two nodal planes which contain the internuclear axis and go through both atoms.<ref>{{cite book|title=Advanced Inorganic Chemistry|last2=Wilkinson|first2=G.|date=1988|publisher=John Wiley|isbn=0-471-84997-9|edition=5th|pages=1087–1091|first1=F. A.|last1=Cotton|author2-link=Geoffrey Wilkinson}}</ref><ref>{{cite book|title=Concepts and Models of Inorganic Chemistry|url=https://archive.org/details/conceptsmodelsof0000doug|url-access=registration|last2=McDaniel|first2=D. H.|last3=Alexander|first3=J. J.|date=1983|publisher=Wiley|isbn=9780471895053|edition=2nd|page=[https://archive.org/details/conceptsmodelsof0000doug/page/137 137]|first1=B.|last1=Douglas}}</ref><ref>{{cite book|title=Inorganic Chemistry|last=Huheey|first=J. E.|date=1983|publisher=Harper and Row|isbn=9780060429874|edition=3rd|pages=743–744}}</ref><ref>{{cite book|title=Inorganic Chemistry|last2=Tarr|first2=D. A.|date=1998|publisher=Prentice-Hall|isbn=978-0138418915|edition=2nd|pages=123–124|first1=G. L.|last1=Miessler}}</ref>

The Greek letter δ in their name refers to d orbitals, since the orbital symmetry of the δ bond is the same as that of the usual (4-lobed) type of d orbital when seen down the bond axis. This type of bonding is observed in atoms that have occupied d orbitals with low enough energy to participate in covalent bonding, for example, in organometallic species of [[Chemistry:Transition metal|transition metal]]s. Some [[Chemistry:Rhenium|rhenium]], [[Chemistry:Molybdenum|molybdenum]], [[Chemistry:Technetium|technetium]], and [[Chemistry:Chromium|chromium]] compounds contain a [[Chemistry:Quadruple bond|quadruple bond]], consisting of one [[Chemistry:Sigma bond|σ bond]], two [[Chemistry:Pi bond|π bond]]s and one δ bond. In the case of the [Re2Cl8]2- ion in the D4h [[Point group]], the [[Chemistry:Bonding molecular orbital|bonding]] delta interaction is the highest energy bonding interaction, followed by the bonding pi, and sigma interactions. The resultant [[Chemistry:Antibonding molecular orbital|antibonding]] delta interaction is the least destabilized, followed by the antibonding pi and sigma interactions.<ref>{{Cite journal |last=Falvello |first=Larry R. |last2=Foxman |first2=Bruce M. |last3=Murillo |first3=Carlos A. |date=2014-09-15 |title=Fitting the Pieces of the Puzzle: The δ Bond |url=https://pubs.acs.org/doi/10.1021/ic500119h |journal=Inorganic Chemistry |language=en |volume=53 |issue=18 |pages=9441–9456 |doi=10.1021/ic500119h |issn=0020-1669}}</ref>

[[File:Molecular orbital diagram of d orbitals in D4h Re2Cl8.jpg|thumb|Molecular Orbital Diagram of D4h [Re2Cl8<nowiki>]</nowiki>2- showing the bonding and antibonding d orbital interactions and their relative energies. the dx2-y2 is omitted from d-d interactions due to its engagement with chloride ligands]]
The orbital symmetry of the δ bonding orbital is different from that of a [[Chemistry:Pi bond|π]] antibonding orbital, which has one nodal plane containing the internuclear axis and a second nodal plane perpendicular to this axis between the atoms.

The δ notation was introduced by Robert Mulliken in 1931.<ref>{{cite journal|title=The Origin of the Sigma, Pi, Delta Notation for Chemical Bonds|first=William B.|last=Jensen|journal=J. Chem. Educ.|date=2013|volume=90|issue=6|pages=802–803|doi=10.1021/ed200298h|bibcode=2013JChEd..90..802J}}</ref><ref>{{cite journal|title=Bonding Power of Electrons and Theory of Valence|first=Robert S.|last=Mulliken|journal=[[Chemistry:Chemical Reviews|Chem. Rev.]]|date=1931|volume=9|issue=3|pages=347–388|doi=10.1021/cr60034a001}}</ref> The first compound identified as having a δ bond was [[Chemistry:Potassium octachlorodirhenate|potassium octachlorodirhenate(III)]]. In 1965, F. A. Cotton reported that there was δ-bonding as part of the rhenium–rhenium [[Chemistry:Quadruple bond|quadruple bond]] in the [Re2Cl8]2− ion.<ref>{{cite journal|title=Metal–Metal Bonding in [Re2X8]2− Ions and Other Metal Atom Clusters|first=F. A.|last=Cotton|journal=Inorg. Chem.|date=1965|volume=4|issue=3|pages=334–336|doi=10.1021/ic50025a016}}</ref> Another example of a δ bond is proposed in [[Chemistry:Cyclobutadieneiron tricarbonyl|cyclobutadieneiron tricarbonyl]] between an iron d orbital and the four p orbitals of the attached cyclobutadiene molecule.

== References ==
{{Reflist}}

{{Chemical bonding theory}}

{{DEFAULTSORT:Delta Bond}}
[[Category:Chemical bonding]]

{{Sourceattribution|Delta bond}}