Physics:Quantum Molecular orbital diagram - Revision history

WikiHarold: Restore missing Quantum reference definitions

2026-05-24T00:31:16Z

Restore missing Quantum reference definitions

← Older revision		Revision as of 00:31, 24 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;">
	A '''molecular orbital diagram''', or '''MO diagram''', is a qualitative descriptive tool explaining chemical bonding in molecules in terms of molecular orbital theory in general and the linear combination of atomic orbitals (LCAO) method in particular.<ref></ref><ref>''Organic Chemistry'', Third Edition, Marye Anne Fox, James K. Whitesell, '''2003''', {{ISBN\|978-0-7637-3586-9}}</ref><ref>''Organic Chemistry'' 3rd Ed. '''2001''', Paula Yurkanis Bruice, {{ISBN\|0-13-017858-6}}</ref> A fundamental principle of these theories is that as atoms bond to form molecules, a certain number of atomic orbitals combine to form the same number of molecular orbitals, although the electrons involved may be redistributed among the orbitals. This tool is very well suited for simple diatomic molecules such as dihydrogen, dioxygen, and carbon monoxide but becomes more complex when discussing even comparatively simple polyatomic molecules, such as methane. MO diagrams can explain why some molecules exist and others do not. They can also predict bond strength, as well as the electronic transitions that can take place.		A '''molecular orbital diagram''', or '''MO diagram''', is a qualitative descriptive tool explaining chemical bonding in molecules in terms of molecular orbital theory in general and the linear combination of atomic orbitals (LCAO) method in particular.<ref>{{cite book \|last1=Clayden \|first1=Jonathan \|last2=Greeves \|first2=Nick \|last3=Warren \|first3=Stuart \|title=Organic Chemistry \|edition=2nd \|publisher=Oxford University Press \|date=2012 \|isbn=978-0-19-927029-3 \|pages=96–103}}</ref><ref>''Organic Chemistry'', Third Edition, Marye Anne Fox, James K. Whitesell, '''2003''', {{ISBN\|978-0-7637-3586-9}}</ref><ref>''Organic Chemistry'' 3rd Ed. '''2001''', Paula Yurkanis Bruice, {{ISBN\|0-13-017858-6}}</ref> A fundamental principle of these theories is that as atoms bond to form molecules, a certain number of atomic orbitals combine to form the same number of molecular orbitals, although the electrons involved may be redistributed among the orbitals. This tool is very well suited for simple diatomic molecules such as dihydrogen, dioxygen, and carbon monoxide but becomes more complex when discussing even comparatively simple polyatomic molecules, such as methane. MO diagrams can explain why some molecules exist and others do not. They can also predict bond strength, as well as the electronic transitions that can take place.
	</div>		</div>

Line 185:		Line 185:
	===Carbon dioxide===		===Carbon dioxide===
	Carbon dioxide, {{chem\|CO\|2}}, is a linear molecule with a total of sixteen bonding electrons in its valence shell. Carbon is the central atom of the molecule and a principal axis, the z-axis, is visualized as a single axis that goes through the center of carbon and the two oxygens atoms.		Carbon dioxide, {{chem\|CO\|2}}, is a linear molecule with a total of sixteen bonding electrons in its valence shell. Carbon is the central atom of the molecule and a principal axis, the z-axis, is visualized as a single axis that goes through the center of carbon and the two oxygens atoms.
	For convention, blue atomic orbital lobes are positive phases, red atomic orbitals are negative phases, with respect to the wave function from the solution of the Schrödinger equation.<ref></ref> In carbon dioxide the carbon 2s (−19.4 eV), carbon 2p (−10.7 eV), and oxygen 2p (−15.9 eV)) energies associated with the atomic orbitals are in proximity whereas the oxygen 2s energy (−32.4 eV) is different.<ref>"An Introduction to Molecular Orbitals". Jean & volatron. ""1993"" {{ISBN\|0-19-506918-8}}. p.192</ref>		For convention, blue atomic orbital lobes are positive phases, red atomic orbitals are negative phases, with respect to the wave function from the solution of the Schrödinger equation.<ref>{{cite book \|last1=Housecroft \|first1=Catherine E. \|last2=Sharpe \|first2=Alan G. \|title=Inorganic Chemistry \|edition=3rd \|publisher=Pearson Prentice Hall \|date=2008 \|isbn=978-0-13-175553-6 \|page=9}}</ref> In carbon dioxide the carbon 2s (−19.4 eV), carbon 2p (−10.7 eV), and oxygen 2p (−15.9 eV)) energies associated with the atomic orbitals are in proximity whereas the oxygen 2s energy (−32.4 eV) is different.<ref>"An Introduction to Molecular Orbitals". Jean & volatron. ""1993"" {{ISBN\|0-19-506918-8}}. p.192</ref>

	Carbon and each oxygen atom will have a 2s atomic orbital and a 2p atomic orbital, where the p orbital is divided into p<sub>x</sub>, p<sub>y</sub>, and p<sub>z</sub>. With these derived atomic orbitals, symmetry labels are deduced with respect to rotation about the principal axis which generates a phase change, pi bond (''π'')<ref></ref> or generates no phase change, known as a sigma bond (''σ'').<ref></ref> Symmetry labels are further defined by whether the atomic orbital maintains its original character after an inversion about its center atom; if the atomic orbital does retain its original character it is defined gerade, ''g'', or if the atomic orbital does not maintain its original character, ungerade, ''u''. The final symmetry-labeled atomic orbital is now known as an irreducible representation.		Carbon and each oxygen atom will have a 2s atomic orbital and a 2p atomic orbital, where the p orbital is divided into p<sub>x</sub>, p<sub>y</sub>, and p<sub>z</sub>. With these derived atomic orbitals, symmetry labels are deduced with respect to rotation about the principal axis which generates a phase change, pi bond (''π'')<ref>{{cite book \|last1=Housecroft \|first1=Catherine E. \|last2=Sharpe \|first2=Alan G. \|title=Inorganic Chemistry \|edition=3rd \|publisher=Pearson Prentice Hall \|date=2008 \|isbn=978-0-13-175553-6 \|page=38}}</ref> or generates no phase change, known as a sigma bond (''σ'').<ref>{{cite book \|last1=Housecroft \|first1=Catherine E. \|last2=Sharpe \|first2=Alan G. \|title=Inorganic Chemistry \|edition=3rd \|publisher=Pearson Prentice Hall \|date=2008 \|isbn=978-0-13-175553-6 \|page=34}}</ref> Symmetry labels are further defined by whether the atomic orbital maintains its original character after an inversion about its center atom; if the atomic orbital does retain its original character it is defined gerade, ''g'', or if the atomic orbital does not maintain its original character, ungerade, ''u''. The final symmetry-labeled atomic orbital is now known as an irreducible representation.

	Carbon dioxide’s molecular orbitals are made by the linear combination of atomic orbitals of the same irreducible representation that are also similar in atomic orbital energy. Significant atomic orbital overlap explains why sp bonding may occur.<ref></ref> Strong mixing of the oxygen 2s atomic orbital is not to be expected and are non-bonding degenerate molecular orbitals. The combination of similar atomic orbital/wave functions and the combinations of atomic orbital/wave function inverses create particular energies associated with the nonbonding (no change), bonding (lower than either parent orbital energy) and antibonding (higher energy than either parent atomic orbital energy) molecular orbitals.		Carbon dioxide’s molecular orbitals are made by the linear combination of atomic orbitals of the same irreducible representation that are also similar in atomic orbital energy. Significant atomic orbital overlap explains why sp bonding may occur.<ref>{{cite book \|last1=Housecroft \|first1=Catherine E. \|last2=Sharpe \|first2=Alan G. \|title=Inorganic Chemistry \|edition=3rd \|publisher=Pearson Prentice Hall \|date=2008 \|isbn=978-0-13-175553-6 \|page=33}}</ref> Strong mixing of the oxygen 2s atomic orbital is not to be expected and are non-bonding degenerate molecular orbitals. The combination of similar atomic orbital/wave functions and the combinations of atomic orbital/wave function inverses create particular energies associated with the nonbonding (no change), bonding (lower than either parent orbital energy) and antibonding (higher energy than either parent atomic orbital energy) molecular orbitals.

	<gallery caption="MO model carbon dioxide" class="skin-invert-image" widths="250px" heights="300px" perrow="3">		<gallery caption="MO model carbon dioxide" class="skin-invert-image" widths="250px" heights="300px" perrow="3">
Line 228:		Line 228:
	Hydrogen sulfide (H<sub>2</sub>S) too has a C<sub>2v</sub> symmetry with 8 valence electrons but the bending angle is only 92°. As reflected in its photoelectron spectrum as compared to water the 5a<sub>1</sub> MO (corresponding to the 3a<sub>1</sub> MO in water) is stabilised (improved overlap) and the 2b<sub>2</sub> MO (corresponding to the 1b<sub>2</sub> MO in water) is destabilized (poorer overlap).		Hydrogen sulfide (H<sub>2</sub>S) too has a C<sub>2v</sub> symmetry with 8 valence electrons but the bending angle is only 92°. As reflected in its photoelectron spectrum as compared to water the 5a<sub>1</sub> MO (corresponding to the 3a<sub>1</sub> MO in water) is stabilised (improved overlap) and the 2b<sub>2</sub> MO (corresponding to the 1b<sub>2</sub> MO in water) is destabilized (poorer overlap).

	==References==		= References =
	{{Reflist\|2}}		{{Reflist\|2}}

WikiHarold: Remove imported red links from Quantum page

2026-05-23T23:46:28Z

Remove imported red links from Quantum page

← Older revision		Revision as of 23:46, 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;">
	A '''molecular orbital diagram''', or '''MO diagram''', is a qualitative descriptive tool explaining chemical bonding in molecules in terms of molecular orbital theory in general and the linear combination of atomic orbitals (LCAO) method in particular.<ref>~~{{Clayden\|pages=96–103}}~~</ref><ref>''Organic Chemistry'', Third Edition, Marye Anne Fox, James K. Whitesell, '''2003''', {{ISBN\|978-0-7637-3586-9}}</ref><ref>''Organic Chemistry'' 3rd Ed. '''2001''', Paula Yurkanis Bruice, {{ISBN\|0-13-017858-6}}</ref> A fundamental principle of these theories is that as atoms bond to form molecules, a certain number of atomic orbitals combine to form the same number of molecular orbitals, although the electrons involved may be redistributed among the orbitals. This tool is very well suited for simple diatomic molecules such as dihydrogen, dioxygen, and carbon monoxide but becomes more complex when discussing even comparatively simple polyatomic molecules, such as methane. MO diagrams can explain why some molecules exist and others do not. They can also predict bond strength, as well as the electronic transitions that can take place.		A '''molecular orbital diagram''', or '''MO diagram''', is a qualitative descriptive tool explaining chemical bonding in molecules in terms of molecular orbital theory in general and the linear combination of atomic orbitals (LCAO) method in particular.<ref></ref><ref>''Organic Chemistry'', Third Edition, Marye Anne Fox, James K. Whitesell, '''2003''', {{ISBN\|978-0-7637-3586-9}}</ref><ref>''Organic Chemistry'' 3rd Ed. '''2001''', Paula Yurkanis Bruice, {{ISBN\|0-13-017858-6}}</ref> A fundamental principle of these theories is that as atoms bond to form molecules, a certain number of atomic orbitals combine to form the same number of molecular orbitals, although the electrons involved may be redistributed among the orbitals. This tool is very well suited for simple diatomic molecules such as dihydrogen, dioxygen, and carbon monoxide but becomes more complex when discussing even comparatively simple polyatomic molecules, such as methane. MO diagrams can explain why some molecules exist and others do not. They can also predict bond strength, as well as the electronic transitions that can take place.
	</div>		</div>

Line 91:		Line 91:

	===Dilithium===		===Dilithium===
	MO theory correctly predicts that dilithium is a stable~~{{huh\|date=September 2024}}~~<!-- what sort of lifespan counts as "stable"? --> molecule with bond order 1 (configuration 1σ<sub>''g''</sub><sup>2</sup>1σ<sub>''u''</sub><sup>2</sup>2σ<sub>''g''</sub><sup>2</sup>). The 1s MOs are completely filled and do not participate in bonding.		MO theory correctly predicts that dilithium is a stable<!-- what sort of lifespan counts as "stable"? --> molecule with bond order 1 (configuration 1σ<sub>''g''</sub><sup>2</sup>1σ<sub>''u''</sub><sup>2</sup>2σ<sub>''g''</sub><sup>2</sup>). The 1s MOs are completely filled and do not participate in bonding.

	[[Image:MO diagram dilithium molecule.png\|class=skin-invert-image\|thumb\|center\|300px\|MO diagram of dilithium]]		[[Image:MO diagram dilithium molecule.png\|class=skin-invert-image\|thumb\|center\|300px\|MO diagram of dilithium]]
Line 185:		Line 185:
	===Carbon dioxide===		===Carbon dioxide===
	Carbon dioxide, {{chem\|CO\|2}}, is a linear molecule with a total of sixteen bonding electrons in its valence shell. Carbon is the central atom of the molecule and a principal axis, the z-axis, is visualized as a single axis that goes through the center of carbon and the two oxygens atoms.		Carbon dioxide, {{chem\|CO\|2}}, is a linear molecule with a total of sixteen bonding electrons in its valence shell. Carbon is the central atom of the molecule and a principal axis, the z-axis, is visualized as a single axis that goes through the center of carbon and the two oxygens atoms.
	For convention, blue atomic orbital lobes are positive phases, red atomic orbitals are negative phases, with respect to the wave function from the solution of the Schrödinger equation.<ref>~~{{Housecroft3rd\|page=9}}~~</ref> In carbon dioxide the carbon 2s (−19.4 eV), carbon 2p (−10.7 eV), and oxygen 2p (−15.9 eV)) energies associated with the atomic orbitals are in proximity whereas the oxygen 2s energy (−32.4 eV) is different.<ref>"An Introduction to Molecular Orbitals". Jean & volatron. ""1993"" {{ISBN\|0-19-506918-8}}. p.192</ref>		For convention, blue atomic orbital lobes are positive phases, red atomic orbitals are negative phases, with respect to the wave function from the solution of the Schrödinger equation.<ref></ref> In carbon dioxide the carbon 2s (−19.4 eV), carbon 2p (−10.7 eV), and oxygen 2p (−15.9 eV)) energies associated with the atomic orbitals are in proximity whereas the oxygen 2s energy (−32.4 eV) is different.<ref>"An Introduction to Molecular Orbitals". Jean & volatron. ""1993"" {{ISBN\|0-19-506918-8}}. p.192</ref>

	Carbon and each oxygen atom will have a 2s atomic orbital and a 2p atomic orbital, where the p orbital is divided into p<sub>x</sub>, p<sub>y</sub>, and p<sub>z</sub>. With these derived atomic orbitals, symmetry labels are deduced with respect to rotation about the principal axis which generates a phase change, pi bond (''π'')<ref>~~{{Housecroft3rd\|page=38}}~~</ref> or generates no phase change, known as a sigma bond (''σ'').<ref>~~{{Housecroft3rd\|page=34}}~~</ref> Symmetry labels are further defined by whether the atomic orbital maintains its original character after an inversion about its center atom; if the atomic orbital does retain its original character it is defined gerade, ''g'', or if the atomic orbital does not maintain its original character, ungerade, ''u''. The final symmetry-labeled atomic orbital is now known as an irreducible representation.		Carbon and each oxygen atom will have a 2s atomic orbital and a 2p atomic orbital, where the p orbital is divided into p<sub>x</sub>, p<sub>y</sub>, and p<sub>z</sub>. With these derived atomic orbitals, symmetry labels are deduced with respect to rotation about the principal axis which generates a phase change, pi bond (''π'')<ref></ref> or generates no phase change, known as a sigma bond (''σ'').<ref></ref> Symmetry labels are further defined by whether the atomic orbital maintains its original character after an inversion about its center atom; if the atomic orbital does retain its original character it is defined gerade, ''g'', or if the atomic orbital does not maintain its original character, ungerade, ''u''. The final symmetry-labeled atomic orbital is now known as an irreducible representation.

	Carbon dioxide’s molecular orbitals are made by the linear combination of atomic orbitals of the same irreducible representation that are also similar in atomic orbital energy. Significant atomic orbital overlap explains why sp bonding may occur.<ref>~~{{Housecroft3rd\|page=33}}~~</ref> Strong mixing of the oxygen 2s atomic orbital is not to be expected and are non-bonding degenerate molecular orbitals. The combination of similar atomic orbital/wave functions and the combinations of atomic orbital/wave function inverses create particular energies associated with the nonbonding (no change), bonding (lower than either parent orbital energy) and antibonding (higher energy than either parent atomic orbital energy) molecular orbitals.		Carbon dioxide’s molecular orbitals are made by the linear combination of atomic orbitals of the same irreducible representation that are also similar in atomic orbital energy. Significant atomic orbital overlap explains why sp bonding may occur.<ref></ref> Strong mixing of the oxygen 2s atomic orbital is not to be expected and are non-bonding degenerate molecular orbitals. The combination of similar atomic orbital/wave functions and the combinations of atomic orbital/wave function inverses create particular energies associated with the nonbonding (no change), bonding (lower than either parent orbital energy) and antibonding (higher energy than either parent atomic orbital energy) molecular orbitals.

	<gallery caption="MO model carbon dioxide" class="skin-invert-image" widths="250px" heights="300px" perrow="3">		<gallery caption="MO model carbon dioxide" class="skin-invert-image" widths="250px" heights="300px" perrow="3">
Line 235:		Line 235:
	*MO diagrams at chem1.com [http://www.chem1.com/acad/webtext/chembond/cb08.html Link]		*MO diagrams at chem1.com [http://www.chem1.com/acad/webtext/chembond/cb08.html Link]
	*Molecular orbitals at winter.group.shef.ac.uk [http://www.winter.group.shef.ac.uk/orbitron/MOs/N2/2px2px-pi/index.html Link]		*Molecular orbitals at winter.group.shef.ac.uk [http://www.winter.group.shef.ac.uk/orbitron/MOs/N2/2px2px-pi/index.html Link]

	~~{{Chemical bonding theory}}~~

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

	{{Sourceattribution\|Molecular orbital diagram}}		{{Sourceattribution\|Molecular orbital diagram}}

WikiHarold: Clean Quantum page image and red links

2026-05-23T23:33:02Z

Clean Quantum page image and red links

Show changes

Harold: Add missing image fallback to Quantum header

2026-05-17T22:32:44Z

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

2026-05-17T21:51:08Z

Restore Quantum article header template

@@ Line 1: / Line 1: @@
 {{Short description|Visual tool in quantum chemistry}}
 A '''molecular orbital diagram''', or '''MO diagram''', is a qualitative descriptive tool explaining chemical bonding in [[Physics:Molecule|molecule]]s in terms of [[Chemistry:Molecular orbital theory|molecular orbital theory]] in general and the [[Physics:Linear combination of atomic orbitals|linear combination of atomic orbitals]] (LCAO) method in particular.<ref>{{Clayden|pages=96–103}}</ref><ref>''Organic Chemistry'', Third Edition, Marye Anne Fox, James K. Whitesell, '''2003''', {{ISBN|978-0-7637-3586-9}}</ref><ref>''Organic Chemistry'' 3rd Ed. '''2001''', Paula Yurkanis Bruice, {{ISBN|0-13-017858-6}}</ref>   A fundamental principle of these theories is that as atoms bond to form molecules, a certain number of [[Physics:Atomic orbital|atomic orbital]]s combine to form the same number of [[Chemistry:Molecular orbital|molecular orbital]]s, although the [[Physics:Electron|electron]]s involved may be redistributed among the orbitals.  This tool is very well suited for simple [[Chemistry:Diatomic molecule|diatomic molecule]]s such as dihydrogen, [[Chemistry:Dioxygen|dioxygen]], and [[Chemistry:Carbon monoxide|carbon monoxide]] but becomes more complex when discussing even comparatively simple polyatomic molecules, such as [[Chemistry:Methane|methane]].  MO diagrams can explain why some molecules exist and others do not. They can also predict bond strength, as well as the electronic transitions that can take place.
 ==History==

imported>WikiHarold: WikiHarold moved page Physics:Molecular orbital diagram to Physics:Quantum Molecular orbital diagram without leaving a redirect

2026-05-04T13:42:35Z

WikiHarold moved page Physics:Molecular orbital diagram to Physics:Quantum Molecular orbital diagram without leaving a redirect

← Older revision	Revision as of 13:42, 4 May 2026
(No difference)

imported>WikiHarold: WikiHarold moved page Physics:Molecular orbital diagram to Physics:Quantum Molecular orbital diagram without leaving a redirect

2026-05-04T13:42:35Z

WikiHarold moved page Physics:Molecular orbital diagram to Physics:Quantum Molecular orbital diagram without leaving a redirect

Show changes