Physics:Quantum bonding molecular orbital - Revision history

WikiHarold: Remove imported red links from Quantum page

2026-05-23T23:46:48Z

Remove imported red links from Quantum page

← Older revision		Revision as of 23:46, 23 May 2026
Line 39:		Line 39:

	=== Localized molecular orbitals ===		=== Localized molecular orbitals ===
	~~{{main\|Chemistry:Localized molecular orbitals}}~~
	[[File:MethaneMObondingmo.jpg\|thumb\|The MO diagram for methane]]		[[File:MethaneMObondingmo.jpg\|thumb\|The MO diagram for methane]]

Line 50:		Line 49:
	== References ==		== References ==
	<references />		<references />

	~~{{Chemical bonding theory}}~~

	~~[[Category:Chemical bonding]]~~

	{{Sourceattribution\|Bonding molecular orbital}}		{{Sourceattribution\|Bonding molecular orbital}}

WikiHarold: Clean Quantum page image and red links

2026-05-23T23:33:40Z

Clean Quantum page image and red links

← Older revision		Revision as of 23:33, 23 May 2026
Line 10:		Line 10:

	<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">		<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">
	In ~~[[Chemistry:Theoretical chemistry\|~~theoretical chemistry]], the '''bonding orbital''' is used in ~~[[Chemistry:Molecular orbital\|~~molecular orbital]] (MO) theory to describe the ~~[[Chemistry:Chemical bond\|~~attractive ~~interaction]]s~~ between the ~~[[Physics:Atomic orbital\|~~atomic ~~orbital]]s~~ of two or more ~~[[Physics:Atom\|atom]]s~~ in a ~~[[Physics:Molecule\|~~molecule]]. In MO theory, ~~[[Physics:Electron\|electron]]s~~ are portrayed to move in ~~[[Wave\|wave]]s~~.<ref>{{Cite journal\|last=Mulliken\|first=Robert S.\|date=1932\|title=Electronic Structures of Polyatomic Molecules and Valence. II. General Considerations\|journal=Physical Review\|volume=41\|issue=1\|pages=49–71\|doi=10.1103/physrev.41.49\|bibcode=1932PhRv...41...49M}}</ref> When more than one of these waves come close together, the in-phase combination of these waves produces an interaction that leads to a species that is greatly stabilized. The result of the waves’ ~~[[Physics:Constructive interference\|~~constructive interference]] causes the ~~[[Physics:Electron density\|~~density of the electrons]] to be found within the binding region, creating a stable bond between the two species.<ref>{{Cite journal\|last1=Sannigrahi\|first1=A. B.\|last2=Kar\|first2=Tapas\|date=1988-08-01\|title=Molecular orbital theory of bond order and valency\|journal=Journal of Chemical Education\|volume=65\|issue=8\|page=674\|doi=10.1021/ed065p674\|bibcode=1988JChEd..65..674S\|issn=0021-9584}}</ref>		In theoretical chemistry, the '''bonding orbital''' is used in molecular orbital (MO) theory to describe the attractive interactions between the atomic orbitals of two or more atoms in a molecule. In MO theory, electrons are portrayed to move in waves.<ref>{{Cite journal\|last=Mulliken\|first=Robert S.\|date=1932\|title=Electronic Structures of Polyatomic Molecules and Valence. II. General Considerations\|journal=Physical Review\|volume=41\|issue=1\|pages=49–71\|doi=10.1103/physrev.41.49\|bibcode=1932PhRv...41...49M}}</ref> When more than one of these waves come close together, the in-phase combination of these waves produces an interaction that leads to a species that is greatly stabilized. The result of the waves’ constructive interference causes the density of the electrons to be found within the binding region, creating a stable bond between the two species.<ref>{{Cite journal\|last1=Sannigrahi\|first1=A. B.\|last2=Kar\|first2=Tapas\|date=1988-08-01\|title=Molecular orbital theory of bond order and valency\|journal=Journal of Chemical Education\|volume=65\|issue=8\|page=674\|doi=10.1021/ed065p674\|bibcode=1988JChEd..65..674S\|issn=0021-9584}}</ref>
	</div>		</div>

	<div style="width:300px;">		<div style="width:300px;">
	[[File:~~File not found~~.png\|thumb\|280px\|~~No image available~~.]]		[[File:H2wikibondingmo.png\|thumb\|280px\|bonding molecular orbital in the Quantum Collection.]]
	</div>		</div>

Line 22:		Line 22:
	[[File:H2wikibondingmo.png\|thumb\|The MO diagram for dihydrogen]]		[[File:H2wikibondingmo.png\|thumb\|The MO diagram for dihydrogen]]

	In the classic example of the H<sub>2</sub> MO, the two separate H atoms have identical atomic orbitals. When creating the molecule dihydrogen, the individual valence orbitals, 1''s'', either: merge in phase to get bonding orbitals, where the ~~[[Physics:Electron density\|~~electron density]] is in between the nuclei of the atoms; or, merge out of phase to get antibonding orbitals, where the electron density is everywhere around the atom except for the space between the nuclei of the two atoms.<ref name="Sausalito 2006">{{Cite book\|title=Modern physical organic chemistry\|last=Anslyn\|first=Eric V.\|date=2006\|publisher=University Science\|others=Dougherty, Dennis A., 1952-\|isbn=978-1891389313\|location=Sausalito, CA\|oclc=55600610}}</ref> Bonding orbitals lead to a more stable species than when the two hydrogens are monatomic. ~~[[Chemistry:Antibonding molecular orbital\|~~Antibonding orbitals]] are less stable because, with very little to no electron density in the middle, the two nuclei (holding the same charge) repulse each other. Therefore, it would require more energy to hold the two atoms together through the antibonding orbital. Each electron in the ~~[[Physics:Electron shell\|~~valence]] 1''s'' shell of hydrogen come together to fill in the stabilizing bonding orbital. So, hydrogen prefers to exist as a diatomic, and not monatomic, molecule.<ref>{{Cite journal\|last=Lennard-Jones\|first=J. E.\|date=1929-01-01\|title=The electronic structure of some diatomic molecules\|journal=Transactions of the Faraday Society\|language=en\|volume=25\|pages=668\|doi=10.1039/tf9292500668\|bibcode=1929FaTr...25..668L\|issn=0014-7672}}</ref>		In the classic example of the H<sub>2</sub> MO, the two separate H atoms have identical atomic orbitals. When creating the molecule dihydrogen, the individual valence orbitals, 1''s'', either: merge in phase to get bonding orbitals, where the electron density is in between the nuclei of the atoms; or, merge out of phase to get antibonding orbitals, where the electron density is everywhere around the atom except for the space between the nuclei of the two atoms.<ref name="Sausalito 2006">{{Cite book\|title=Modern physical organic chemistry\|last=Anslyn\|first=Eric V.\|date=2006\|publisher=University Science\|others=Dougherty, Dennis A., 1952-\|isbn=978-1891389313\|location=Sausalito, CA\|oclc=55600610}}</ref> Bonding orbitals lead to a more stable species than when the two hydrogens are monatomic. Antibonding orbitals are less stable because, with very little to no electron density in the middle, the two nuclei (holding the same charge) repulse each other. Therefore, it would require more energy to hold the two atoms together through the antibonding orbital. Each electron in the valence 1''s'' shell of hydrogen come together to fill in the stabilizing bonding orbital. So, hydrogen prefers to exist as a diatomic, and not monatomic, molecule.<ref>{{Cite journal\|last=Lennard-Jones\|first=J. E.\|date=1929-01-01\|title=The electronic structure of some diatomic molecules\|journal=Transactions of the Faraday Society\|language=en\|volume=25\|pages=668\|doi=10.1039/tf9292500668\|bibcode=1929FaTr...25..668L\|issn=0014-7672}}</ref>
	[[File:He2wikibondingmo.jpg\|thumb\|The MO diagram for helium]]		[[File:He2wikibondingmo.jpg\|thumb\|The MO diagram for helium]]

	When looking at helium, the atom holds two electrons in each valence 1''s'' shell. When the two atomic orbitals come together, they first fill in the bonding orbital with two electrons, but unlike hydrogen, it has two electrons left, which must then go to the antibonding orbital. The instability of the antibonding orbital cancels out the stabilizing effect provided by the bonding orbital; therefore, dihelium's ~~[[Chemistry:Bond order\|~~bond order]] is 0. This is why helium would prefer to be monatomic over diatomic.<ref>{{Cite book\|title=Inorganic chemistry\|last=Housecroft\|first=Catherine E.\|publisher=Pearson\|others=Sharpe, A. G.\|year=2012\|isbn=9780273742753\|edition=4th\|location=Harlow, England\|oclc=775664094}}</ref>		When looking at helium, the atom holds two electrons in each valence 1''s'' shell. When the two atomic orbitals come together, they first fill in the bonding orbital with two electrons, but unlike hydrogen, it has two electrons left, which must then go to the antibonding orbital. The instability of the antibonding orbital cancels out the stabilizing effect provided by the bonding orbital; therefore, dihelium's bond order is 0. This is why helium would prefer to be monatomic over diatomic.<ref>{{Cite book\|title=Inorganic chemistry\|last=Housecroft\|first=Catherine E.\|publisher=Pearson\|others=Sharpe, A. G.\|year=2012\|isbn=9780273742753\|edition=4th\|location=Harlow, England\|oclc=775664094}}</ref>

	== Polyatomic molecules ==		== Polyatomic molecules ==
Line 32:		Line 32:
	=== Bonding MOs of pi bonds ===		=== Bonding MOs of pi bonds ===

	~~[[Chemistry:~~Pi ~~bond\|Pi bond]]s~~ are created by the “side-on” interactions of the orbitals.<ref name="Sausalito 2006" /> Once again, in molecular orbitals, bonding pi (π) electrons occur when the interaction of the two π atomic orbitals are in-phase. In this case, the ~~[[Physics:Electron density\|~~electron density]] of the π orbitals needs to be symmetric along the mirror plane in order to create the bonding interaction. Asymmetry along the mirror plane will lead to a node in that plane and is described in the antibonding orbital, π*.<ref name="Sausalito 2006" />		Pi bonds are created by the “side-on” interactions of the orbitals.<ref name="Sausalito 2006" /> Once again, in molecular orbitals, bonding pi (π) electrons occur when the interaction of the two π atomic orbitals are in-phase. In this case, the electron density of the π orbitals needs to be symmetric along the mirror plane in order to create the bonding interaction. Asymmetry along the mirror plane will lead to a node in that plane and is described in the antibonding orbital, π*.<ref name="Sausalito 2006" />

	[[File:MObutadienebondingmo.jpg\|thumb\|The MO diagram for butadiene]]		[[File:MObutadienebondingmo.jpg\|thumb\|The MO diagram for butadiene]]

	An example of a MO of a simple ~~[[Chemistry:Conjugated system\|~~conjugated π system]] is butadiene. To create the MO for ~~[[Chemistry:Butadiene\|~~butadiene]], the resulting π and π* orbitals of the previously described system will interact with each other. This mixing will result in the creation of 4 group orbitals (which can also be used to describe the π MO of any diene):<ref name="Sausalito 2006" /> π<sub>1</sub> contains no vertical ~~[[Physics:Node\|~~nodes]], π<sub>2</sub> contains one and both are considered bonding orbitals; π<sub>3</sub> contains 2 vertical nodes, π<sub>4</sub> contains 3 and are both considered antibonding orbitals.<ref name="Sausalito 2006" />		An example of a MO of a simple conjugated π system is butadiene. To create the MO for butadiene, the resulting π and π* orbitals of the previously described system will interact with each other. This mixing will result in the creation of 4 group orbitals (which can also be used to describe the π MO of any diene):<ref name="Sausalito 2006" /> π<sub>1</sub> contains no vertical nodes, π<sub>2</sub> contains one and both are considered bonding orbitals; π<sub>3</sub> contains 2 vertical nodes, π<sub>4</sub> contains 3 and are both considered antibonding orbitals.<ref name="Sausalito 2006" />

	=== Localized molecular orbitals ===		=== Localized molecular orbitals ===
Line 42:		Line 42:
	[[File:MethaneMObondingmo.jpg\|thumb\|The MO diagram for methane]]		[[File:MethaneMObondingmo.jpg\|thumb\|The MO diagram for methane]]

	The spherical 3D shape of ''s'' orbitals have no directionality in space and ''p<sub>x</sub>'', ''p<sub>y</sub>'', and ''p<sub>z</sub>'' orbitals are all 90<sup>o</sup> with respect to each other. Therefore, in order to obtain orbitals corresponding to ~~[[Chemistry:Chemical bond\|~~chemical ~~bond]]s~~ to describe chemical reactions, Edmiston and Ruedenberg pioneered the development of localization procedures.<ref name="Cohen 1969">{{Cite journal\|last1=Cohen\|first1=Irwin\|last2=Del Bene\|first2=Janet\|date=1969-08-01\|title=Hybrid orbitals in molecular orbital theory\|journal=Journal of Chemical Education\|volume=46\|issue=8\|page=487\|doi=10.1021/ed046p487\|bibcode=1969JChEd..46..487C\|issn=0021-9584}}</ref><ref>{{Cite journal\|last=Edmiston\|first=Clyde\|date=1963\|title=Localized Atomic and Molecular Orbitals\|journal=Reviews of Modern Physics\|volume=35\|issue=3\|pages=457–464\|doi=10.1103/revmodphys.35.457\|bibcode=1963RvMP...35..457E}}</ref> For example, in CH<sub>4</sub>, the four electrons from the 1''s'' orbitals of the hydrogen atoms and the ~~[[Physics:Valence electron\|~~valence ~~electron]]s~~ from the carbon atom (2 in ''s'' and 2 in ''p'') occupy the bonding molecular orbitals, σ and π.<ref name="Cohen 1969"/> The delocalized MOs of the carbon atom in the molecule of methane can then be ~~[[Chemistry:Localized molecular orbitals\|~~localized]] to give four ''sp''<sup>3</sup> ~~[[Physics:Orbital hybridisation\|~~hybrid orbitals]].		The spherical 3D shape of ''s'' orbitals have no directionality in space and ''p<sub>x</sub>'', ''p<sub>y</sub>'', and ''p<sub>z</sub>'' orbitals are all 90<sup>o</sup> with respect to each other. Therefore, in order to obtain orbitals corresponding to chemical bonds to describe chemical reactions, Edmiston and Ruedenberg pioneered the development of localization procedures.<ref name="Cohen 1969">{{Cite journal\|last1=Cohen\|first1=Irwin\|last2=Del Bene\|first2=Janet\|date=1969-08-01\|title=Hybrid orbitals in molecular orbital theory\|journal=Journal of Chemical Education\|volume=46\|issue=8\|page=487\|doi=10.1021/ed046p487\|bibcode=1969JChEd..46..487C\|issn=0021-9584}}</ref><ref>{{Cite journal\|last=Edmiston\|first=Clyde\|date=1963\|title=Localized Atomic and Molecular Orbitals\|journal=Reviews of Modern Physics\|volume=35\|issue=3\|pages=457–464\|doi=10.1103/revmodphys.35.457\|bibcode=1963RvMP...35..457E}}</ref> For example, in CH<sub>4</sub>, the four electrons from the 1''s'' orbitals of the hydrogen atoms and the valence electrons from the carbon atom (2 in ''s'' and 2 in ''p'') occupy the bonding molecular orbitals, σ and π.<ref name="Cohen 1969"/> The delocalized MOs of the carbon atom in the molecule of methane can then be localized to give four ''sp''<sup>3</sup> hybrid orbitals.

	== Applications ==		== Applications ==

	Molecular orbitals and, more specifically, the bonding orbital is a theory that is taught in all different areas of chemistry, from organic to physical and even analytical, because it is widely applicable. Organic chemists use molecular orbital theory in their thought rationale for reactions;<ref name="Dannenberg 1999">{{Cite journal\|last=Dannenberg\|first=J. J.\|date=1999-05-12\|title=Using Perturbation and Frontier Molecular Orbital Theory To Predict Diastereofacial Selectivity\|journal=Chemical Reviews\|volume=99\|issue=5\|pages=1225–1242\|doi=10.1021/cr980382f\|pmid=11749445\|issn=0009-2665}}</ref><ref>{{Cite journal\|last1=Li\|first1=Yongjun\|last2=Jia\|first2=Zhiyu\|last3=Xiao\|first3=Shengqiang\|last4=Liu\|first4=Huibiao\|last5=Li\|first5=Yuliang\|date=2016-05-16\|title=A method for controlling the synthesis of stable twisted two-dimensional conjugated molecules\|journal=Nature Communications\|language=En\|volume=7\|page=11637\|doi=10.1038/ncomms11637\|pmid=27181692\|pmc=4873669\|bibcode=2016NatCo...711637L}}</ref> analytical chemists use it in different spectroscopy methods;<ref>{{Cite journal\|last=Smith\|first=Wendell F.\|title=Application of molecular orbital theory to the electronic absorption spectra of schiff bases\|journal=Tetrahedron\|volume=19\|issue=3\|pages=445–454\|doi=10.1016/s0040-4020(01)99192-6\|year=1963}}</ref><ref>{{Cite journal\|last=Mulliken\|first=Robert S.\|date=1967-07-07\|title=Spectroscopy, Molecular Orbitals, and Chemical Bonding\|journal=Science\|language=en\|volume=157\|issue=3784\|pages=13–24\|doi=10.1126/science.157.3784.13\|issn=0036-8075\|pmid=5338306\|bibcode=1967Sci...157...13M}}</ref> physical chemists use it in calculations;<ref name="Dannenberg 1999" /><ref>{{Cite journal\|last=Gimarc\|first=Benjamin M.\|date=1974\|title=Applications of qualitative molecular orbital theory\|journal=Accounts of Chemical Research\|volume=7\|issue=11\|pages=384–392\|doi=10.1021/ar50083a004}}</ref> it is even seen in materials chemistry through ~~[[Physics:Electronic~~ band ~~structure\|band theory]]—an~~ extension of molecular orbital theory.<ref>{{Cite journal\|last1=Brédas\|first1=J. L.\|last2=Calbert\|first2=J. P.\|last3=da Silva Filho\|first3=D. A.\|last4=Cornil\|first4=J.\|date=2002-04-30\|title=Organic semiconductors: A theoretical characterization of the basic parameters governing charge transport\|journal=Proceedings of the National Academy of Sciences\|volume=99\|issue=9\|pages=5804–5809\|doi=10.1073/pnas.092143399\|pmid=11972059\|pmc=122857\|bibcode=2002PNAS...99.5804B\|doi-access=free}}</ref>		Molecular orbitals and, more specifically, the bonding orbital is a theory that is taught in all different areas of chemistry, from organic to physical and even analytical, because it is widely applicable. Organic chemists use molecular orbital theory in their thought rationale for reactions;<ref name="Dannenberg 1999">{{Cite journal\|last=Dannenberg\|first=J. J.\|date=1999-05-12\|title=Using Perturbation and Frontier Molecular Orbital Theory To Predict Diastereofacial Selectivity\|journal=Chemical Reviews\|volume=99\|issue=5\|pages=1225–1242\|doi=10.1021/cr980382f\|pmid=11749445\|issn=0009-2665}}</ref><ref>{{Cite journal\|last1=Li\|first1=Yongjun\|last2=Jia\|first2=Zhiyu\|last3=Xiao\|first3=Shengqiang\|last4=Liu\|first4=Huibiao\|last5=Li\|first5=Yuliang\|date=2016-05-16\|title=A method for controlling the synthesis of stable twisted two-dimensional conjugated molecules\|journal=Nature Communications\|language=En\|volume=7\|page=11637\|doi=10.1038/ncomms11637\|pmid=27181692\|pmc=4873669\|bibcode=2016NatCo...711637L}}</ref> analytical chemists use it in different spectroscopy methods;<ref>{{Cite journal\|last=Smith\|first=Wendell F.\|title=Application of molecular orbital theory to the electronic absorption spectra of schiff bases\|journal=Tetrahedron\|volume=19\|issue=3\|pages=445–454\|doi=10.1016/s0040-4020(01)99192-6\|year=1963}}</ref><ref>{{Cite journal\|last=Mulliken\|first=Robert S.\|date=1967-07-07\|title=Spectroscopy, Molecular Orbitals, and Chemical Bonding\|journal=Science\|language=en\|volume=157\|issue=3784\|pages=13–24\|doi=10.1126/science.157.3784.13\|issn=0036-8075\|pmid=5338306\|bibcode=1967Sci...157...13M}}</ref> physical chemists use it in calculations;<ref name="Dannenberg 1999" /><ref>{{Cite journal\|last=Gimarc\|first=Benjamin M.\|date=1974\|title=Applications of qualitative molecular orbital theory\|journal=Accounts of Chemical Research\|volume=7\|issue=11\|pages=384–392\|doi=10.1021/ar50083a004}}</ref> it is even seen in materials chemistry through band theory—an extension of molecular orbital theory.<ref>{{Cite journal\|last1=Brédas\|first1=J. L.\|last2=Calbert\|first2=J. P.\|last3=da Silva Filho\|first3=D. A.\|last4=Cornil\|first4=J.\|date=2002-04-30\|title=Organic semiconductors: A theoretical characterization of the basic parameters governing charge transport\|journal=Proceedings of the National Academy of Sciences\|volume=99\|issue=9\|pages=5804–5809\|doi=10.1073/pnas.092143399\|pmid=11972059\|pmc=122857\|bibcode=2002PNAS...99.5804B\|doi-access=free}}</ref>

	== References ==		== References ==

Harold: Add missing image fallback to Quantum header

2026-05-17T22:32:52Z

Add missing image fallback to Quantum header

← Older revision		Revision as of 22:32, 17 May 2026
Line 14:		Line 14:

	<div style="width:300px;">		<div style="width:300px;">
	~~<!--~~ No ~~lead~~ image available ~~in existing page~~. ~~-->~~		[[File:File not found.png\|thumb\|280px\|No image available.]]
	</div>		</div>

Harold: Restore Quantum article header template

2026-05-17T21:51:44Z

Restore Quantum article header template

@@ Line 1: / Line 1: @@
 {{Short description|Quantum-mechanical explanation of chemical bonding}}
 In [[Chemistry:Theoretical chemistry|theoretical chemistry]], the '''bonding orbital''' is used in [[Chemistry:Molecular orbital|molecular orbital]] (MO) theory to describe the [[Chemistry:Chemical bond|attractive interaction]]s between the [[Physics:Atomic orbital|atomic orbital]]s of two or more [[Physics:Atom|atom]]s in a [[Physics:Molecule|molecule]]. In MO theory, [[Physics:Electron|electron]]s are portrayed to move in [[Wave|wave]]s.<ref>{{Cite journal|last=Mulliken|first=Robert S.|date=1932|title=Electronic Structures of Polyatomic Molecules and Valence. II. General Considerations|journal=Physical Review|volume=41|issue=1|pages=49–71|doi=10.1103/physrev.41.49|bibcode=1932PhRv...41...49M}}</ref> When more than one of these waves come close together, the in-phase combination of these waves produces an interaction that leads to a species that is greatly stabilized. The result of the waves’ [[Physics:Constructive interference|constructive interference]] causes the [[Physics:Electron density|density of the electrons]] to be found within the binding region, creating a stable bond between the two species.<ref>{{Cite journal|last1=Sannigrahi|first1=A. B.|last2=Kar|first2=Tapas|date=1988-08-01|title=Molecular orbital theory of bond order and valency|journal=Journal of Chemical Education|volume=65|issue=8|page=674|doi=10.1021/ed065p674|bibcode=1988JChEd..65..674S|issn=0021-9584}}</ref>
 == Diatomic molecules ==

imported>WikiHarold: WikiHarold moved page Chemistry:Bonding molecular orbital to Physics:Quantum bonding molecular orbital without leaving a redirect

2026-05-04T14:01:00Z

WikiHarold moved page Chemistry:Bonding molecular orbital to Physics:Quantum bonding molecular orbital without leaving a redirect

← Older revision	Revision as of 14:01, 4 May 2026
(No difference)

imported>WikiHarold: WikiHarold moved page Chemistry:Bonding molecular orbital to Physics:Quantum bonding molecular orbital without leaving a redirect

2026-05-04T14:01:00Z

WikiHarold moved page Chemistry:Bonding molecular orbital to Physics:Quantum bonding molecular orbital without leaving a redirect

New page

{{Short description|Quantum-mechanical explanation of chemical bonding}}
In [[Chemistry:Theoretical chemistry|theoretical chemistry]], the '''bonding orbital''' is used in [[Chemistry:Molecular orbital|molecular orbital]] (MO) theory to describe the [[Chemistry:Chemical bond|attractive interaction]]s between the [[Physics:Atomic orbital|atomic orbital]]s of two or more [[Physics:Atom|atom]]s in a [[Physics:Molecule|molecule]]. In MO theory, [[Physics:Electron|electron]]s are portrayed to move in [[Wave|wave]]s.<ref>{{Cite journal|last=Mulliken|first=Robert S.|date=1932|title=Electronic Structures of Polyatomic Molecules and Valence. II. General Considerations|journal=Physical Review|volume=41|issue=1|pages=49–71|doi=10.1103/physrev.41.49|bibcode=1932PhRv...41...49M}}</ref> When more than one of these waves come close together, the in-phase combination of these waves produces an interaction that leads to a species that is greatly stabilized. The result of the waves’ [[Physics:Constructive interference|constructive interference]] causes the [[Physics:Electron density|density of the electrons]] to be found within the binding region, creating a stable bond between the two species.<ref>{{Cite journal|last1=Sannigrahi|first1=A. B.|last2=Kar|first2=Tapas|date=1988-08-01|title=Molecular orbital theory of bond order and valency|journal=Journal of Chemical Education|volume=65|issue=8|page=674|doi=10.1021/ed065p674|bibcode=1988JChEd..65..674S|issn=0021-9584}}</ref>

== Diatomic molecules ==
[[File:H2wikibondingmo.png|thumb|The MO diagram for dihydrogen]]

In the classic example of the H2 MO, the two separate H atoms have identical atomic orbitals. When creating the molecule dihydrogen, the individual valence orbitals, 1''s'', either: merge in phase to get bonding orbitals, where the [[Physics:Electron density|electron density]] is in between the nuclei of the atoms; or, merge out of phase to get antibonding orbitals, where the electron density is everywhere around the atom except for the space between the nuclei of the two atoms.<ref name="Sausalito 2006">{{Cite book|title=Modern physical organic chemistry|last=Anslyn|first=Eric V.|date=2006|publisher=University Science|others=Dougherty, Dennis A., 1952-|isbn=978-1891389313|location=Sausalito, CA|oclc=55600610}}</ref> Bonding orbitals lead to a more stable species than when the two hydrogens are monatomic. [[Chemistry:Antibonding molecular orbital|Antibonding orbitals]] are less stable because, with very little to no electron density in the middle, the two nuclei (holding the same charge) repulse each other. Therefore, it would require more energy to hold the two atoms together through the antibonding orbital. Each electron in the [[Physics:Electron shell|valence]] 1''s'' shell of hydrogen come together to fill in the stabilizing bonding orbital. So, hydrogen prefers to exist as a diatomic, and not monatomic, molecule.<ref>{{Cite journal|last=Lennard-Jones|first=J. E.|date=1929-01-01|title=The electronic structure of some diatomic molecules|journal=Transactions of the Faraday Society|language=en|volume=25|pages=668|doi=10.1039/tf9292500668|bibcode=1929FaTr...25..668L|issn=0014-7672}}</ref>
[[File:He2wikibondingmo.jpg|thumb|The MO diagram for helium]]

When looking at helium, the atom holds two electrons in each valence 1''s'' shell. When the two atomic orbitals come together, they first fill in the bonding orbital with two electrons, but unlike hydrogen, it has two electrons left, which must then go to the antibonding orbital. The instability of the antibonding orbital cancels out the stabilizing effect provided by the bonding orbital; therefore, dihelium's [[Chemistry:Bond order|bond order]] is 0. This is why helium would prefer to be monatomic over diatomic.<ref>{{Cite book|title=Inorganic chemistry|last=Housecroft|first=Catherine E.|publisher=Pearson|others=Sharpe, A. G.|year=2012|isbn=9780273742753|edition=4th|location=Harlow, England|oclc=775664094}}</ref>

== Polyatomic molecules ==
[[File:PibondingMObondingmo.jpg|thumb|The MO diagram for a pi bond]]

=== Bonding MOs of pi bonds ===

[[Chemistry:Pi bond|Pi bond]]s are created by the “side-on” interactions of the orbitals.<ref name="Sausalito 2006" /> Once again, in molecular orbitals, bonding pi (π) electrons occur when the interaction of the two π atomic orbitals are in-phase. In this case, the [[Physics:Electron density|electron density]] of the π orbitals needs to be symmetric along the mirror plane in order to create the bonding interaction. Asymmetry along the mirror plane will lead to a node in that plane and is described in the antibonding orbital, π*.<ref name="Sausalito 2006" />

[[File:MObutadienebondingmo.jpg|thumb|The MO diagram for butadiene]]

An example of a MO of a simple [[Chemistry:Conjugated system|conjugated π system]] is butadiene. To create the MO for [[Chemistry:Butadiene|butadiene]], the resulting π and π* orbitals of the previously described system will interact with each other. This mixing will result in the creation of 4 group orbitals (which can also be used to describe the π MO of any diene):<ref name="Sausalito 2006" /> π1 contains no vertical [[Physics:Node|nodes]], π2 contains one and both are considered bonding orbitals; π3 contains 2 vertical nodes, π4 contains 3 and are both considered antibonding orbitals.<ref name="Sausalito 2006" />

=== Localized molecular orbitals ===
{{main|Chemistry:Localized molecular orbitals}}
[[File:MethaneMObondingmo.jpg|thumb|The MO diagram for methane]]

The spherical 3D shape of ''s'' orbitals have no directionality in space and ''px'', ''py'', and ''pz'' orbitals are all 90o with respect to each other. Therefore, in order to obtain orbitals corresponding to [[Chemistry:Chemical bond|chemical bond]]s to describe chemical reactions, Edmiston and Ruedenberg pioneered the development of localization procedures.<ref name="Cohen 1969">{{Cite journal|last1=Cohen|first1=Irwin|last2=Del Bene|first2=Janet|date=1969-08-01|title=Hybrid orbitals in molecular orbital theory|journal=Journal of Chemical Education|volume=46|issue=8|page=487|doi=10.1021/ed046p487|bibcode=1969JChEd..46..487C|issn=0021-9584}}</ref><ref>{{Cite journal|last=Edmiston|first=Clyde|date=1963|title=Localized Atomic and Molecular Orbitals|journal=Reviews of Modern Physics|volume=35|issue=3|pages=457–464|doi=10.1103/revmodphys.35.457|bibcode=1963RvMP...35..457E}}</ref> For example, in CH4, the four electrons from the 1''s'' orbitals of the hydrogen atoms and the [[Physics:Valence electron|valence electron]]s from the carbon atom (2 in ''s'' and 2 in ''p'') occupy the bonding molecular orbitals, σ and π.<ref name="Cohen 1969"/> The delocalized MOs of the carbon atom in the molecule of methane can then be [[Chemistry:Localized molecular orbitals|localized]] to give four ''sp''3 [[Physics:Orbital hybridisation|hybrid orbitals]].

== Applications ==

Molecular orbitals and, more specifically, the bonding orbital is a theory that is taught in all different areas of chemistry, from organic to physical and even analytical, because it is widely applicable. Organic chemists use molecular orbital theory in their thought rationale for reactions;<ref name="Dannenberg 1999">{{Cite journal|last=Dannenberg|first=J. J.|date=1999-05-12|title=Using Perturbation and Frontier Molecular Orbital Theory To Predict Diastereofacial Selectivity|journal=Chemical Reviews|volume=99|issue=5|pages=1225–1242|doi=10.1021/cr980382f|pmid=11749445|issn=0009-2665}}</ref><ref>{{Cite journal|last1=Li|first1=Yongjun|last2=Jia|first2=Zhiyu|last3=Xiao|first3=Shengqiang|last4=Liu|first4=Huibiao|last5=Li|first5=Yuliang|date=2016-05-16|title=A method for controlling the synthesis of stable twisted two-dimensional conjugated molecules|journal=Nature Communications|language=En|volume=7|page=11637|doi=10.1038/ncomms11637|pmid=27181692|pmc=4873669|bibcode=2016NatCo...711637L}}</ref> analytical chemists use it in different spectroscopy methods;<ref>{{Cite journal|last=Smith|first=Wendell F.|title=Application of molecular orbital theory to the electronic absorption spectra of schiff bases|journal=Tetrahedron|volume=19|issue=3|pages=445–454|doi=10.1016/s0040-4020(01)99192-6|year=1963}}</ref><ref>{{Cite journal|last=Mulliken|first=Robert S.|date=1967-07-07|title=Spectroscopy, Molecular Orbitals, and Chemical Bonding|journal=Science|language=en|volume=157|issue=3784|pages=13–24|doi=10.1126/science.157.3784.13|issn=0036-8075|pmid=5338306|bibcode=1967Sci...157...13M}}</ref> physical chemists use it in calculations;<ref name="Dannenberg 1999" /><ref>{{Cite journal|last=Gimarc|first=Benjamin M.|date=1974|title=Applications of qualitative molecular orbital theory|journal=Accounts of Chemical Research|volume=7|issue=11|pages=384–392|doi=10.1021/ar50083a004}}</ref> it is even seen in materials chemistry through [[Physics:Electronic band structure|band theory]]—an extension of molecular orbital theory.<ref>{{Cite journal|last1=Brédas|first1=J. L.|last2=Calbert|first2=J. P.|last3=da Silva Filho|first3=D. A.|last4=Cornil|first4=J.|date=2002-04-30|title=Organic semiconductors: A theoretical characterization of the basic parameters governing charge transport|journal=Proceedings of the National Academy of Sciences|volume=99|issue=9|pages=5804–5809|doi=10.1073/pnas.092143399|pmid=11972059|pmc=122857|bibcode=2002PNAS...99.5804B|doi-access=free}}</ref>

== References ==
<references />

{{Chemical bonding theory}}

[[Category:Chemical bonding]]

{{Sourceattribution|Bonding molecular orbital}}