View source for Physics:Quantum chemical bond

{{Short description|Quantum-mechanical association of atoms into molecules and matter}}

{{Quantum book backlink|Molecules}}
{{Quantum matter backlink|Molecules}}

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'''Chemical bond''' is the association of [[Physics:Quantum atoms|atoms]] or [[Physics:Quantum atoms/ion|ions]] into [[Physics:Quantum molecular structure|molecules]], crystals, metals, and other forms of matter. In quantum physics, bonding is explained by the behavior of [[Physics:Quantum atoms/electron|electrons]], their [[Physics:Quantum wavefunction|wavefunctions]], and the allowed [[Physics:Quantum atoms/orbital|atomic orbitals]] and [[Physics:Quantum atoms/orbital|molecular orbitals]].

A chemical bond may result from electrostatic attraction between oppositely charged ions, as in ionic bonding, or from the sharing and delocalization of electrons, as in covalent and metallic bonding. In a quantum description, constructive wavefunction interference can stabilize two nuclei by forming a lower-energy electronic state.<ref name="Levine Head-Gordon 2020 p. ">{{cite journal | last1=Levine | first1=Daniel S. | last2=Head-Gordon | first2=Martin | title=Clarifying the quantum mechanical origin of the covalent chemical bond | journal=Nature Communications | publisher=Springer Science and Business Media LLC | volume=11 | issue=1 | date=2020-09-29 | issn=2041-1723 | doi=10.1038/s41467-020-18670-8 | page=4893| pmid=32994392 | pmc=7524788 | bibcode=2020NatCo..11.4893L | s2cid=222157102 }}</ref> The equilibrium bond distance reflects a balance between attractive and repulsive interactions that can be treated quantitatively by quantum theory.<ref>{{citation | last=Pauling | first=L. | year=1931 | title=The nature of the chemical bond. Application of results obtained from the quantum mechanics and from a theory of paramagnetic susceptibility to the structure of molecules | journal=[[Journal of the American Chemical Society]] | volume=53 | issue=4 | pages=1367–1400 | doi=10.1021/ja01355a027 | bibcode=1931JAChS..53.1367P }}</ref><ref>{{Cite journal |last=Hund |first=F. |date=1928 |title=Zur Deutung der Molekelspektren. IV |url=http://link.springer.com/10.1007/BF01400239 |journal=Zeitschrift für Physik |language=de |volume=51 |issue=11–12 |pages=759–795 |doi=10.1007/BF01400239 |bibcode=1928ZPhy...51..759H |s2cid=121366097 |issn=1434-6001|url-access=subscription }}</ref>
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<div style="font-size:90%;">Covalent bonding in hydrogen can be described by electron sharing in a bonding orbital.</div>
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[[File:Dihydrogen-phase-3D-balls.png|thumb|280px|Quantum chemical bond.]]
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== Quantum description ==

All chemical bonds can be described by [[Physics:Quantum mechanics|quantum mechanics]], although simplified models remain useful in chemistry. The [[Physics:Quantum atoms/electron|electron]] density in a bond is not simply assigned to one atom; it may be shared, polarized, or delocalized across several atoms. Models such as the octet rule and VSEPR are useful approximations, while more advanced descriptions include valence bond theory, molecular orbital theory, orbital hybridization, resonance, and ligand field theory.<ref>{{Cite journal |last1=Frenking |first1=Gernot |last2=Krapp |first2=Andreas |date=2007-01-15 |title=Unicorns in the world of chemical bonding models |doi-access=free|s2cid-access=free |journal=Journal of Computational Chemistry |language=en |volume=28 |issue=1 |pages=15–24 |doi=10.1002/jcc.20543|pmid=17109434 |bibcode=2007JCoCh..28...15F |s2cid=7504671 }}</ref><ref name="Frank">{{cite book |first=Frank |last=Jensen |title=Introduction to Computational Chemistry |publisher=John Wiley and Sons |year=1999 |isbn=978-0-471-98425-2}}</ref><ref name="Pauling">{{cite book|first=Linus|last=Pauling|chapter-url=https://books.google.com/books?id=L-1K9HmKmUUC&pg=PA10|title=The Nature of the Chemical Bond – An Introduction to Modern Structural Chemistry|publisher=Cornell University Press|edition=3rd|date=1960|chapter=The Concept of Resonance|pages=10–13|isbn=978-0801403330}}</ref><ref>{{citation | last=Gillespie | first=R.J. | year=2004 | title=Teaching molecular geometry with the VSEPR model | journal=Journal of Chemical Education | volume=81 | issue=3 | pages=298–304 | doi=10.1021/ed081p298 | bibcode=2004JChEd..81..298G | doi-access=free }}</ref>

== Main types of chemical bonds ==

=== Covalent bond ===

In a covalent bond, two or more atoms share valence electrons. A single bond shares one electron pair, while double and triple bonds share two and three electron pairs. In quantum terms, the shared electrons occupy bonding states whose spatial distribution lowers the energy of the combined system. The stability of the hydrogen molecule, for example, can be understood in terms of electron delocalization and the resulting change in kinetic and potential energy.<ref>{{cite book |last1=Housecroft |first1=Catherine E. |last2=Sharpe |first2=Alan G. |title=Inorganic Chemistry |date=2005 |publisher=Pearson Prentice-Hal |isbn=0130-39913-2 |page=100 |edition=2nd}}</ref><ref>{{cite journal|doi=10.1007/s00897010509a|author=Rioux, F. |title=The Covalent Bond in H<sub>2</sub> |journal=The Chemical Educator |volume=6 |issue=5 |pages=288–290 |year=2001 |s2cid=97871973 }}</ref>

Covalent bonding is central to molecules, polymers, organic compounds, and network solids such as diamond and quartz. Non-polar covalent bonds have small electronegativity differences, while polar covalent bonds have unequal electron sharing and partial charge separation.<ref>{{Cite book|title=Introduction to organic chemistry.|last1=Streitwieser|first1=Andrew|last2=Heathcock|first2=Clayton H.|last3=Kosower|first3=Edward M.|publisher=Macmillan|others=Heathcock, Clayton H., Kosower, Edward M.|year=1992|isbn=978-0024181701|edition=4th|location=New York|pages=[https://archive.org/details/introductiontoor00stre_0/page/250 250]|oclc=24501305|url-access=registration|url=https://archive.org/details/introductiontoor00stre_0/page/250}}</ref>

=== Ionic bond ===

In an ionic bond, electrons are transferred so that one atom becomes a positive ion and another becomes a negative ion. The attraction is mainly electrostatic. Ionic bonding is common in salts such as sodium chloride. An electronegativity difference above about 1.7 is often treated as strongly ionic, while smaller differences are more covalent in character.<ref>{{cite book | last=Atkins | first=Peter | author-link=Peter Atkins |author2=Loretta Jones | title=Chemistry: Molecules, Matter and Change | publisher=W.H. Freeman & Co. | year=1997 | location=New York | pages=294–295 | isbn=978-0-7167-3107-8 }}</ref>

=== Metallic bonding ===

In metallic bonding, electrons are delocalized over a lattice of metal atoms. This collective electron behavior explains metallic properties such as electrical conductivity, thermal conductivity, ductility, tensile strength, and luster.

=== Coordinate covalent bond ===

A coordinate covalent bond is a covalent bond in which both shared electrons originate from the same atom. Such bonds occur in Lewis acid-base adducts and transition-metal complexes.

== History ==

Early chemical theory developed before atoms were fully understood. Robert Boyle, Antoine Lavoisier, Joseph Proust, Humphry Davy, Jöns Jakob Berzelius, Edward Frankland, August Kekulé, A. S. Couper, Alexander Butlerov, Hermann Kolbe, and Richard Abegg contributed to ideas about elements, compounds, valency, and chemical combination.<ref name="Whittaker">{{Cite book |last=Whittaker |first=Edmund T. |title=A history of the theories of aether & electricity. 1: The classical theories |date=1989 |publisher=Dover Publ |isbn=978-0-486-26126-3 |edition=Repr |location=New York}}</ref><ref name=Pullman-1998>{{cite book|last1=Pullman|first1=Bernard|title=The Atom in the History of Human Thought|date=1998|publisher=Oxford University Press|location=Oxford, England|isbn=978-0-19-515040-7|pages=31–33|url=https://books.google.com/books?id=IQs5hur-BpgC&|access-date=25 October 2020|archive-date=5 February 2021|archive-url=https://web.archive.org/web/20210205165029/https://books.google.com/books?id=IQs5hur-BpgC&q=Leucippus+Democritus+atom&pg=PA56|url-status=live}}</ref><ref>{{Cite web|title=Law of definite proportions {{!}} chemistry|url=https://www.britannica.com/science/law-of-definite-proportions|access-date=2020-09-03|website=Encyclopedia Britannica|language=en}}</ref><ref name=Hudson-1992>{{Cite book |last=Hudson |first=John |url=http://link.springer.com/10.1007/978-1-4684-6441-2 |title=The History of Chemistry |date=1992 |publisher=Springer US |isbn=978-1-4684-6443-6 |location=Boston, MA |language=en |doi=10.1007/978-1-4684-6441-2}}</ref><ref>{{cite journal |last1=Frankland |first1=E. |year=1852 |title=On a New Series of Organic Bodies Containing Metals |journal=Philosophical Transactions of the Royal Society of London |volume=142 |pages=417–444 |doi=10.1098/rstl.1852.0020 |s2cid=186210604}}</ref><ref>{{Cite journal |last=Abegg |first=R. |year=1904 |title=Die Valenz und das periodische System. Versuch einer Theorie der Molekularverbindungen |trans-title=Valency and the periodic table. Attempt at a theory of molecular compounds |url=https://babel.hathitrust.org/cgi/pt?id=uc1.b3959087;view=1up;seq=344 |journal=Zeitschrift für anorganische Chemie |language=German |volume=39 |issue=1 |pages=330–380 |doi=10.1002/zaac.19040390125}}</ref>

The nuclear atom and the role of electrons became clearer through the work of Hantaro Nagaoka, Ernest Rutherford, Max Planck, and Niels Bohr.<ref>The Genesis of the Bohr Atom, John L. Heilbron and Thomas S. Kuhn, Historical Studies in the Physical Sciences, Vol. 1 (1969), pp. vi, 211-290 (81 pages), University of California Press.</ref><ref>{{cite book |author=B. Bryson |title=A Short History of Nearly Everything |title-link=A Short History of Nearly Everything |publisher=[[Broadway Books]] |year=2003 |isbn=0-7679-0817-1 |author-link=Bill Bryson }}</ref><ref>Original Proceedings of the 1911 Solvay Conference published 1912. THÉORIE DU RAYONNEMENT ET LES QUANTA. RAPPORTS ET DISCUSSIONS DELA Réunion tenue à Bruxelles, du 30 octobre au 3 novembre 1911, Sous les Auspices dk M. E. SOLVAY. Publiés par MM. P. LANGEVIN et M. de BROGLIE. Translated from the French, p. 127.</ref>

In 1916 Gilbert N. Lewis introduced the electron-pair bond model, while Walther Kossel developed an ionic bonding model. Bohr also proposed an early model of chemical bonding.<ref>{{cite journal|last=Lewis|first=Gilbert N.|author-link=Gilbert N. Lewis|year=1916|title=The Atom and the Molecule|journal=[[Journal of the American Chemical Society]]|volume=38|page=772|url=http://osulibrary.oregonstate.edu/specialcollections/coll/pauling/bond/papers/corr216.3-lewispub-19160400.html|doi=10.1021/ja02261a002|issue=4|bibcode=1916JAChS..38..762L |s2cid=95865413|url-access=subscription}} [http://www.itis.arezzo.it/index.php?option=com_content&view=article&id=221%3Athe-atom-and-the-molecule-&catid=106%3Apagine-html&Itemid=98 a copy] {{Webarchive|url=https://web.archive.org/web/20210418014936/http://www.itis.arezzo.it/index.php?option=com_content&view=article&id=221%3Athe-atom-and-the-molecule-&catid=106%3Apagine-html&Itemid=98 |date=2021-04-18 }}</ref><ref name="Pais">{{Cite book|last=Pais|first=Abraham |year=1986|location=New York|title=Inward Bound: Of Matter and Forces in the Physical World|publisher=Oxford University Press|isbn=978-0-19-851971-3|pages=[https://archive.org/details/inwardboundofmat00pais_0/page/228 228–230]|url=https://archive.org/details/inwardboundofmat00pais_0/page/228}}</ref><ref>{{cite journal|last=Svidzinsky|first=Anatoly A. |author2=Marlan O. Scully |author3-link=Dudley R. Herschbach |author3=Dudley R. Herschbach|year=2005|title=Bohr's 1913 molecular model revisited |journal=Proceedings of the National Academy of Sciences |volume=102|pages=11985–11988|doi=10.1073/pnas.0505778102 |pmid=16103360 |pmc=1186029 |issue=34|arxiv=physics/0508161|bibcode=2005PNAS..10211985S|doi-access=free |url=http://www.pnas.org/content/102/34/11985.full.pdf |archive-url=https://web.archive.org/web/20180718233029/http://www.pnas.org/content/102/34/11985.full.pdf |archive-date=2018-07-18 |url-status=live}}</ref>

In 1927 Øyvind Burrau gave a quantum treatment of the hydrogen molecular ion, and Walter Heitler and Fritz London developed the approach that became valence bond theory.<ref>{{cite book| author=Laidler, K. J. |year=1993|title=The World of Physical Chemistry| url=https://archive.org/details/worldofphysicalc0000laid | url-access=registration |publisher=Oxford University Press | page=[https://archive.org/details/worldofphysicalc0000laid/page/346 346]|isbn=978-0-19-855919-1}}</ref><ref name="London">{{cite journal|first1=W. |last1=Heitler |first2=F. |last2=London |title=Wechselwirkung neutraler Atome und homoopolare Bindung nach der Quantenmechanik |trans-title=Interaction of neutral atoms and homeopolar bonds according to quantum mechanics |journal=Zeitschrift für Physik |volume=44 |issue=6–7 |pages=455–472 |date=1927 |doi=10.1007/bf01397394 |bibcode=1927ZPhy...44..455H |s2cid=119739102}} English translation in {{cite book| last=Hettema| first=H.| title=Quantum Chemistry: Classic Scientific Papers| url=https://books.google.com/books?id=qsidHRJmUoIC| access-date=2012-02-05| year=2000| publisher=World Scientific| isbn=978-981-02-2771-5| pages=140}}</ref> Molecular orbital theory, LCAO methods, and later density functional theory became major tools in quantum chemistry.<ref>{{cite journal | last=James | first=H.H. |author2=Coolidge, A S. | title=The Ground State of the Hydrogen Molecule | journal=[[Journal of Chemical Physics]] | volume=1 | issue=12 | pages=825–835 | year=1933 | doi=10.1063/1.1749252 | bibcode=1933JChPh...1..825J }}</ref>

== Bond energies and lengths ==

Strong chemical bonds are intramolecular forces that hold atoms together in molecules and solids. Their lengths and energies vary by element, bond order, and chemical environment. Typical bond energy tables are useful approximations for comparing bond strengths.<ref>{{cite web|url=https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Chemical_Bonding/Fundamentals_of_Chemical_Bonding/Bond_Energies |title=Bond Energies |date=2 October 2013 |publisher=Chemistry Libre Texts |access-date=2019-02-25}}</ref>

== Intermolecular bonding ==

Chemical bonding also includes weaker interactions between molecules. Van der Waals forces include interactions between partial charges and repulsions between closed electron shells.<ref name="Atkins">{{cite book |last1=Atkins |first1=Peter |last2=de Paula |first2=Julio |title=Physical Chemistry |date=2002 |publisher=W.H.Freeman |isbn=0-7167-3539-3 |pages=696–706 |edition=7th}}</ref> Keesom forces act between permanent dipoles, London dispersion forces arise from induced dipoles, and hydrogen bonds occur when a hydrogen atom bound to an electronegative atom interacts with a lone pair on another electronegative atom.{{r|Atkins|p=701}}{{r|Atkins|p=702}}{{r|Atkins|p=703}}{{r|Atkins|p=705-6}}

== Theories of chemical bonding ==

In pure ionic bonding, the force between atoms can be approximated by electrostatic attraction between ions. Covalent bonds require quantum-mechanical descriptions such as valence bond theory and molecular orbital theory. Valence bond theory emphasizes localized electron pairs and orbital overlap, while molecular orbital theory treats electrons as occupying orbitals delocalized over the molecule. These approaches are complementary and are both used in modern quantum chemistry. Polar covalent bonds form an intermediate case between covalent and ionic bonding.<ref>{{cite web |last1=Ouellette |first1=Robert J. |last2=Rawn |first2=J. David |title=Polar Covalent Bond |url=https://www.sciencedirect.com/topics/chemistry/polar-covalent-bond |publisher=Science Direct |access-date=14 September 2023 |date=2015 |quote=A polar covalent bond exists when atoms with different electronegativities share electrons in a covalent bond.}}</ref>

=See also=
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also/Matter}}

=References=
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Chemical bond|1}}