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Available in 27 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-27" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">27 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D9%88%D9%89_%D8%AA%D8%B4%D8%AA%D8%AA_%D9%84%D9%86%D8%AF%D9%86" title="قوى تشتت لندن – Arabic" lang="ar" hreflang="ar" data-title="قوى تشتت لندن" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Dispers_q%C3%BCvv%C9%99l%C9%99r" title="Dispers qüvvələr – Azerbaijani" lang="az" hreflang="az" data-title="Dispers qüvvələr" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Londonova_disperzijska_sila" title="Londonova disperzijska sila – Bosnian" lang="bs" hreflang="bs" data-title="Londonova disperzijska sila" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Forces_de_dispersi%C3%B3_de_London" title="Forces de dispersió de London – Catalan" lang="ca" hreflang="ca" data-title="Forces de dispersió de London" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Disperzn%C3%AD_s%C3%ADla" title="Disperzní síla – Czech" lang="cs" hreflang="cs" data-title="Disperzní síla" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Londonbinding" title="Londonbinding – Danish" lang="da" hreflang="da" data-title="Londonbinding" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/London-Kraft" title="London-Kraft – German" lang="de" hreflang="de" data-title="London-Kraft" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Fuerzas_de_dispersi%C3%B3n_de_London" title="Fuerzas de dispersión de London – Spanish" lang="es" hreflang="es" data-title="Fuerzas de dispersión de London" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%86%DB%8C%D8%B1%D9%88%DB%8C_%D9%BE%D8%B1%D8%A7%DA%A9%D9%86%D8%AF%DA%AF%DB%8C_%D9%84%D8%A7%D9%86%D8%AF%D9%86" title="نیروی پراکندگی لاندن – Persian" lang="fa" hreflang="fa" data-title="نیروی پراکندگی لاندن" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Forces_de_London" title="Forces de London – French" lang="fr" hreflang="fr" data-title="Forces de London" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/F%C3%B3rsa_easraithe_London" title="Fórsa easraithe London – Irish" lang="ga" hreflang="ga" data-title="Fórsa easraithe London" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%9F%B0%EB%8D%98_%EB%B6%84%EC%82%B0%EB%A0%A5" title="런던 분산력 – Korean" lang="ko" hreflang="ko" data-title="런던 분산력" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Gaya_London" title="Gaya London – Indonesian" lang="id" hreflang="id" data-title="Gaya London" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Forza_di_London" title="Forza di London – Italian" lang="it" hreflang="it" data-title="Forza di London" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Diszperzi%C3%B3s_k%C3%B6lcs%C3%B6nhat%C3%A1s" title="Diszperziós kölcsönhatás – Hungarian" lang="hu" hreflang="hu" data-title="Diszperziós kölcsönhatás" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Londonkracht" title="Londonkracht – Dutch" lang="nl" hreflang="nl" data-title="Londonkracht" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%AD%E3%83%B3%E3%83%89%E3%83%B3%E5%88%86%E6%95%A3%E5%8A%9B" title="ロンドン分散力 – Japanese" lang="ja" hreflang="ja" data-title="ロンドン分散力" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Si%C5%82y_Londona" title="Siły Londona – Polish" lang="pl" hreflang="pl" data-title="Siły Londona" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/For%C8%9B%C4%83_de_dispersie_London" title="Forță de dispersie London – Romanian" lang="ro" hreflang="ro" data-title="Forță de dispersie London" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%94%D0%B8%D1%81%D0%BF%D0%B5%D1%80%D1%81%D0%B8%D0%BE%D0%BD%D0%BD%D1%8B%D0%B5_%D1%81%D0%B8%D0%BB%D1%8B" title="Дисперсионные силы – Russian" lang="ru" hreflang="ru" data-title="Дисперсионные силы" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Londonova_disperziona_sila" title="Londonova disperziona sila – Serbian" lang="sr" hreflang="sr" data-title="Londonova disperziona sila" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Londonova_disperziona_sila" title="Londonova disperziona sila – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Londonova disperziona sila" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Londonin_voima" title="Londonin voima – Finnish" lang="fi" hreflang="fi" data-title="Londonin voima" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Dispersionkraft" title="Dispersionkraft – Swedish" lang="sv" hreflang="sv" data-title="Dispersionkraft" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%87%E0%AE%B2%E0%AE%A3%E0%AF%8D%E0%AE%9F%E0%AE%A9%E0%AF%8D_%E0%AE%95%E0%AE%B2%E0%AF%88%E0%AE%B5%E0%AF%81_%E0%AE%B5%E0%AE%BF%E0%AE%9A%E0%AF%88" title="இலண்டன் கலைவு விசை – Tamil" lang="ta" hreflang="ta" data-title="இலண்டன் கலைவு விசை" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D0%B8%D1%81%D0%BF%D0%B5%D1%80%D1%81%D1%96%D0%B9%D0%BD%D1%96_%D1%81%D0%B8%D0%BB%D0%B8" title="Дисперсійні сили – 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src="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Argon_dimer_potential.png/300px-Argon_dimer_potential.png" decoding="async" width="300" height="210" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Argon_dimer_potential.png/450px-Argon_dimer_potential.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/04/Argon_dimer_potential.png/600px-Argon_dimer_potential.png 2x" data-file-width="1500" data-file-height="1050" /></a><figcaption>Interaction energy of an <a href="/wiki/Argon" title="Argon">argon</a> <a href="/wiki/Dimer_(chemistry)" class="mw-redirect" title="Dimer (chemistry)">dimer</a>. The long-range section is due to London dispersion forces.</figcaption></figure> <p><b>London dispersion forces</b> (<b>LDF</b>, also known as <b>dispersion forces</b>, <b>London forces</b>, <b>instantaneous dipole–induced dipole forces, fluctuating induced dipole bonds</b><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> or loosely as <b>van der Waals forces</b>) are a type of <a href="/wiki/Intermolecular_force" title="Intermolecular force">intermolecular force</a> acting between <a href="/wiki/Atom" title="Atom">atoms</a> and <a href="/wiki/Molecule" title="Molecule">molecules</a> that are normally electrically symmetric; that is, the electrons are symmetrically distributed with respect to the nucleus.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> They are part of the <a href="/wiki/Van_der_Waals_force" title="Van der Waals force">van der Waals forces</a>. The LDF is named after the German physicist <a href="/wiki/Fritz_London" title="Fritz London">Fritz London</a>. They are the weakest intermolecular force. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Introduction">Introduction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=London_dispersion_force&action=edit&section=1" title="Edit section: Introduction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The electron distribution around an atom or molecule undergoes fluctuations in time. These fluctuations create instantaneous electric fields which are felt by other nearby atoms and molecules, which in turn adjust the spatial distribution of their own electrons. The net effect is that the fluctuations in electron positions in one atom induce a corresponding redistribution of electrons in other atoms, such that the electron motions become correlated. While the detailed theory requires a quantum-mechanical explanation <i>(see <a href="#Quantum_mechanical_theory">quantum mechanical theory of dispersion forces</a>)</i>, the effect is frequently described as the formation of <i><a href="/wiki/Dipole#Molecular_dipoles" title="Dipole">instantaneous dipoles</a></i> that (when separated by <a href="/wiki/Vacuum" title="Vacuum">vacuum</a>) attract each other. The magnitude of the London dispersion force is frequently described in terms of a single parameter called the <a href="/wiki/Hamaker_constant" title="Hamaker constant">Hamaker constant</a>, typically symbolized <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>. For atoms that are located closer together than the <a href="/wiki/Light#Electromagnetic_spectrum_and_visible_light" title="Light">wavelength of light</a>, the interaction is essentially instantaneous and is described in terms of a "non-retarded" Hamaker constant. For entities that are farther apart, the finite time required for the fluctuation at one atom to be felt at a second atom ("retardation") requires use of a "retarded" Hamaker constant.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>While the London dispersion force between individual atoms and molecules is quite weak and decreases quickly with separation <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> like <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{R^{6}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{R^{6}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e72eec49e71b43d30564883794079db2eb38dd11" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:3.654ex; height:5.509ex;" alt="{\displaystyle {\frac {1}{R^{6}}}}"></span>, in condensed matter (liquids and solids), the effect is cumulative over the volume of materials,<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> or within and between organic molecules, such that London dispersion forces can be quite strong in bulk solid and liquids and decay much more slowly with distance. For example, the total force per unit area between two bulk solids decreases by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{R^{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{R^{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25e802421844f17e4f8cebd76271dc47930fa1cd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:3.654ex; height:5.509ex;" alt="{\displaystyle {\frac {1}{R^{3}}}}"></span><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> is the separation between them. The effects of London dispersion forces are most obvious in systems that are very non-polar (e.g., that lack <a href="/wiki/Ionic_bonds" class="mw-redirect" title="Ionic bonds">ionic bonds</a>), such as <a href="/wiki/Hydrocarbon" title="Hydrocarbon">hydrocarbons</a> and highly symmetric molecules like <a href="/wiki/Bromine" title="Bromine">bromine</a> (Br<sub>2, </sub>a liquid at room temperature) or <a href="/wiki/Iodine" title="Iodine">iodine</a> (I<sub>2,</sub> a solid at room temperature). In hydrocarbons and <a href="/wiki/Wax" title="Wax">waxes</a>, the dispersion forces are sufficient to cause <a href="/wiki/Condensation" title="Condensation">condensation</a> from the gas phase into the liquid or solid phase. Sublimation heats of e.g. hydrocarbon crystals reflect the dispersion interaction. Liquification of oxygen and nitrogen gases into liquid phases is also dominated by attractive London dispersion forces. </p><p>When atoms/molecules are separated by a third medium (rather than vacuum), the situation becomes more complex. In <a href="/wiki/Aqueous_solution" title="Aqueous solution">aqueous solutions</a>, the effects of dispersion forces between atoms or molecules are frequently less pronounced due to competition with polarizable <a href="/wiki/Solvent" title="Solvent">solvent</a> molecules. That is, the instantaneous fluctuations in one atom or molecule are felt both by the solvent (water) and by other molecules. </p><p>Larger and heavier atoms and molecules exhibit stronger dispersion forces than smaller and lighter ones.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> This is due to the increased <a href="/wiki/Polarizability" title="Polarizability">polarizability</a> of molecules with larger, more dispersed <a href="/wiki/Electron_clouds" class="mw-redirect" title="Electron clouds">electron clouds</a>. The polarizability is a measure of how easily electrons can be redistributed; a large polarizability implies that the electrons are more easily redistributed. This trend is exemplified by the <a href="/wiki/Halogen" title="Halogen">halogens</a> (from smallest to largest: F<sub>2</sub>, Cl<sub>2</sub>, Br<sub>2</sub>, I<sub>2</sub>). The same increase of dispersive attraction occurs within and between organic molecules in the order RF, RCl, RBr, RI (from smallest to largest) or with other more polarizable <a href="/wiki/Heteroatom" title="Heteroatom">heteroatoms</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Fluorine" title="Fluorine">Fluorine</a> and <a href="/wiki/Chlorine" title="Chlorine">chlorine</a> are <a href="/wiki/Gas" title="Gas">gases</a> at room temperature, bromine is a liquid, and iodine is a solid. The London forces are thought to arise from the motion of electrons. </p> <div class="mw-heading mw-heading2"><h2 id="Quantum_mechanical_theory">Quantum mechanical theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=London_dispersion_force&action=edit&section=2" title="Edit section: Quantum mechanical theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The first explanation of the attraction between noble gas atoms was given by <a href="/wiki/Fritz_London" title="Fritz London">Fritz London</a> in 1930.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> He used a quantum-mechanical theory based on <a href="/wiki/Perturbation_theory_(quantum_mechanics)" title="Perturbation theory (quantum mechanics)">second-order perturbation theory</a>. The perturbation is because of the <a href="/wiki/Coulomb_interaction" class="mw-redirect" title="Coulomb interaction">Coulomb interaction</a> between the electrons and nuclei of the two moieties (atoms or molecules). The second-order perturbation expression of the interaction energy contains a sum over states. The states appearing in this sum are simple products of the stimulated electronic states of the <a href="/wiki/Monomer" title="Monomer">monomers</a>. Thus, no intermolecular antisymmetrization of the electronic states is included, and the <a href="/wiki/Pauli_exclusion_principle" title="Pauli exclusion principle">Pauli exclusion principle</a> is only partially satisfied. </p><p>London wrote a <a href="/wiki/Taylor_series" title="Taylor series">Taylor series</a> expansion of the perturbation in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{R}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>R</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{R}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52f112a30dcebb32b7520e1a5491a8033ac212a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:2.6ex; height:5.343ex;" alt="{\displaystyle {\frac {1}{R}}}"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> is the distance between the <a href="/wiki/Center_of_mass" title="Center of mass">nuclear centers of mass</a> of the moieties. </p><p>This expansion is known as the <a href="/wiki/Multipole_expansion" title="Multipole expansion">multipole expansion</a> because the terms in this series can be regarded as energies of two interacting multipoles, one on each monomer. Substitution of the multipole-expanded form of V into the second-order energy yields an expression that resembles an expression describing the interaction between instantaneous multipoles (see the qualitative description above). Additionally, an approximation, named after <a href="/wiki/Albrecht_Uns%C3%B6ld" title="Albrecht Unsöld">Albrecht Unsöld</a>, must be introduced in order to obtain a description of London dispersion in terms of <a href="/wiki/Polarizability" title="Polarizability">polarizability volumes</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha '}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>α</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha '}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cb0468d39268c4405a9286d2cba77c2e4631fed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.172ex; height:2.509ex;" alt="{\displaystyle \alpha '}"></span>, and <a href="/wiki/Ionization_energy" title="Ionization energy">ionization energies</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span>, (ancient term: <a href="/wiki/Ionization_potential" class="mw-redirect" title="Ionization potential">ionization potentials</a>). </p><p>In this manner, the following approximation is obtained for the dispersion interaction <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{AB}^{\rm {disp}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">p</mi> </mrow> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{AB}^{\rm {disp}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/286e747b52bbd31e263933cc1c6b65a48062e2d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.959ex; height:3.509ex;" alt="{\displaystyle E_{AB}^{\rm {disp}}}"></span> between two atoms <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>. Here <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha '_{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mo>′</mo> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha '_{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b864a12b4ab4a49560e5771fa0b37fa7527a3a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.952ex; height:2.843ex;" alt="{\displaystyle \alpha '_{A}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha '_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> <mo>′</mo> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha '_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8534884a90758134c70de4fc4a8e548f77624eb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.967ex; height:2.843ex;" alt="{\displaystyle \alpha '_{B}}"></span> are the polarizability volumes of the respective atoms. The quantities <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fad11afeef762471a89c8a258282a40af27d6516" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.488ex; height:2.509ex;" alt="{\displaystyle I_{A}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d40597cfee42fba5f2d94723c8332dbc4b3f1c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.503ex; height:2.509ex;" alt="{\displaystyle I_{B}}"></span> are the first ionization energies of the atoms, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> is the intermolecular distance. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{AB}^{\rm {disp}}\approx -{3 \over 2}{I_{A}I_{B} \over I_{A}+I_{B}}{\alpha '_{A}\alpha '_{B} \over {R^{6}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">p</mi> </mrow> </mrow> </msubsup> <mo>≈</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mo>′</mo> </msubsup> <msubsup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> <mo>′</mo> </msubsup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{AB}^{\rm {disp}}\approx -{3 \over 2}{I_{A}I_{B} \over I_{A}+I_{B}}{\alpha '_{A}\alpha '_{B} \over {R^{6}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8886514b10ab7cdccc74c7db94bda05084891f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:27.287ex; height:6.176ex;" alt="{\displaystyle E_{AB}^{\rm {disp}}\approx -{3 \over 2}{I_{A}I_{B} \over I_{A}+I_{B}}{\alpha '_{A}\alpha '_{B} \over {R^{6}}}}"></span></dd></dl> <p>Note that this final London equation does not contain instantaneous dipoles (see <a href="/wiki/Molecular_dipole_moment" class="mw-redirect" title="Molecular dipole moment">molecular dipoles</a>). The "explanation" of the dispersion force as the interaction between two such dipoles was invented after London arrived at the proper quantum mechanical theory. The authoritative work<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> contains a criticism of the instantaneous dipole model<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> and a modern and thorough exposition of the theory of intermolecular forces. </p><p>The London theory has much similarity to the quantum mechanical theory of <a href="/wiki/Dispersion_(optics)" title="Dispersion (optics)">light dispersion</a>, which is why London coined the phrase "dispersion effect". In physics, the term "dispersion" describes the variation of a quantity with frequency, which is the fluctuation of the electrons in the case of the London dispersion. </p> <div class="mw-heading mw-heading2"><h2 id="Relative_magnitude">Relative magnitude</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=London_dispersion_force&action=edit&section=3" title="Edit section: Relative magnitude"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dispersion forces are usually dominant over the three van der Waals forces (orientation, induction, dispersion) between atoms and molecules, with the exception of molecules that are small and highly polar, such as water. The following contribution of the dispersion to the total intermolecular interaction energy has been given:<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable sortable"> <caption>Contribution of the dispersion to the total intermolecular interaction energy </caption> <tbody><tr> <th>Molecule pair</th> <th>% of the total energy of interaction </th></tr> <tr> <td><a href="/wiki/Neon" title="Neon">Ne</a>-Ne</td> <td>100 </td></tr> <tr> <td><a href="/wiki/Methane" title="Methane">CH<sub>4</sub></a>-CH<sub>4</sub></td> <td>100 </td></tr> <tr> <td><a href="/wiki/Hydrogen_chloride" title="Hydrogen chloride">HCl</a>-HCl</td> <td>86 </td></tr> <tr> <td><a href="/wiki/Hydrogen_bromide" title="Hydrogen bromide">HBr</a>-HBr</td> <td>96 </td></tr> <tr> <td><a href="/wiki/Hydrogen_iodide" title="Hydrogen iodide">HI</a>-HI</td> <td>99 </td></tr> <tr> <td><a href="/wiki/Chloromethane" title="Chloromethane">CH<sub>3</sub>Cl</a>-CH<sub>3</sub>Cl</td> <td>68 </td></tr> <tr> <td><a href="/wiki/Ammonia" title="Ammonia">NH<sub>3</sub></a>-NH<sub>3</sub></td> <td>57 </td></tr> <tr> <td><a href="/wiki/Water" title="Water">H<sub>2</sub>O</a>-H<sub>2</sub>O</td> <td>24 </td></tr> <tr> <td>HCl-HI</td> <td>96 </td></tr> <tr> <td>H<sub>2</sub>O-CH<sub>4</sub></td> <td>87 </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=London_dispersion_force&action=edit&section=4" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid 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References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFCallister2000" class="citation book cs1">Callister, William (December 5, 2000). <i>Fundamentals of Materials Science and Engineering: An Interactive e . Text</i>. John Wiley & Sons, Inc. p. 25. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-39551-X" title="Special:BookSources/0-471-39551-X"><bdi>0-471-39551-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Materials+Science+and+Engineering%3A+An+Interactive+e+.+Text&rft.pages=25&rft.pub=John+Wiley+%26+Sons%2C+Inc.&rft.date=2000-12-05&rft.isbn=0-471-39551-X&rft.aulast=Callister&rft.aufirst=William&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALondon+dispersion+force" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCallister,_William_D._Jr.Callister,_William_D._Jr.2001" class="citation book cs1">Callister, William D. Jr.; Callister, William D. Jr. (2001). <i>Fundamentals of materials science and engineering : an interactive etext</i>. 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London (1930), "Über das Verhältnis der van der Waalsschen Kräfte zu den homöopolaren Bindungskräften", <i>Zeitschrift für Physik</i>, <b>60</b> (7–8): 491–527, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1930ZPhy...60..491E">1930ZPhy...60..491E</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01341258">10.1007/BF01341258</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:125644826">125644826</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Zeitschrift+f%C3%BCr+Physik&rft.atitle=%C3%9Cber+das+Verh%C3%A4ltnis+der+van+der+Waalsschen+Kr%C3%A4fte+zu+den+hom%C3%B6opolaren+Bindungskr%C3%A4ften&rft.volume=60&rft.issue=7%E2%80%938&rft.pages=491-527&rft.date=1930&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A125644826%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF01341258&rft_id=info%3Abibcode%2F1930ZPhy...60..491E&rft.au=R.+Eisenschitz&rft.au=F.+London&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALondon+dispersion+force" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLondon1930" class="citation cs2">London, F. 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title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Intermolecular+and+Surface+Forces&rft.edition=2nd&rft.pub=Academic+Press&rft.date=1992&rft.au=Jacob+Israelachvili&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALondon+dispersion+force" class="Z3988"></span></span> </li> </ol></div></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output 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bond">3c–2e</a></li> <li><a href="/wiki/Four-center_two-electron_bond" title="Four-center two-electron bond">4c–2e</a></li> <li><a href="/wiki/Eight-center_two-electron_bond" class="mw-redirect" title="Eight-center two-electron bond">8c–2e</a></li></ul></li> <li><a href="/wiki/Hypervalent_molecule" title="Hypervalent molecule">Hypervalence</a> <ul><li><a href="/wiki/Three-center_four-electron_bond" title="Three-center four-electron bond">3c–4e</a></li></ul></li> <li><a href="/wiki/Agostic_interaction" title="Agostic interaction">Agostic</a></li> <li><a href="/wiki/Bent_bond" title="Bent bond">Bent</a></li> <li><a href="/wiki/Coordinate_covalent_bond" title="Coordinate covalent bond">Coordinate (dipolar)</a></li> <li><a href="/wiki/Pi_backbonding" title="Pi backbonding">Pi backbond</a></li> <li><a href="/wiki/Metal%E2%80%93ligand_multiple_bond" title="Metal–ligand multiple bond">Metal–ligand multiple bond</a></li> <li><a href="/wiki/Charge-shift_bond" title="Charge-shift bond">Charge-shift</a></li> <li><a href="/wiki/Hapticity" title="Hapticity">Hapticity</a></li> <li><a href="/wiki/Conjugated_system" title="Conjugated system">Conjugation</a></li> <li><a href="/wiki/Hyperconjugation" title="Hyperconjugation">Hyperconjugation</a></li> <li><a href="/wiki/Aromaticity" title="Aromaticity">Aromaticity</a> <ul><li><a href="/wiki/Homoaromaticity" title="Homoaromaticity">homo</a></li> <li><a href="/wiki/Bicycloaromaticity" title="Bicycloaromaticity">bicyclo</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Metallic_bonding" title="Metallic bonding">Metallic</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Metal_aromaticity" title="Metal aromaticity">Metal aromaticity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ionic_bonding" title="Ionic bonding">Ionic</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li class="mw-empty-elt"></li></ul> </div></td></tr></tbody></table><div></div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Ligatio-covalens.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Ligatio-covalens.svg/200px-Ligatio-covalens.svg.png" decoding="async" width="200" height="89" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Ligatio-covalens.svg/300px-Ligatio-covalens.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/Ligatio-covalens.svg/400px-Ligatio-covalens.svg.png 2x" data-file-width="597" data-file-height="265" /></a></span><br /><span typeof="mw:File"><a href="/wiki/File:Chemfm_carbon_monoxide_3_1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Chemfm_carbon_monoxide_3_1.svg/200px-Chemfm_carbon_monoxide_3_1.svg.png" decoding="async" width="200" height="113" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Chemfm_carbon_monoxide_3_1.svg/300px-Chemfm_carbon_monoxide_3_1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/Chemfm_carbon_monoxide_3_1.svg/400px-Chemfm_carbon_monoxide_3_1.svg.png 2x" data-file-width="99" data-file-height="56" /></a></span><br /><span typeof="mw:File"><a href="/wiki/File:Pi-Bond.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Pi-Bond.svg/200px-Pi-Bond.svg.png" decoding="async" width="200" height="113" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Pi-Bond.svg/300px-Pi-Bond.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/70/Pi-Bond.svg/400px-Pi-Bond.svg.png 2x" data-file-width="1920" data-file-height="1080" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Intermolecular_force" title="Intermolecular force">Intermolecular</a><br />(weak)</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Van_der_Waals_force" title="Van der Waals force">Van der Waals<br />forces</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">London dispersion</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Hydrogen_bond" title="Hydrogen bond">Hydrogen</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Low-barrier_hydrogen_bond" title="Low-barrier hydrogen bond">Low-barrier</a></li> <li><a href="/wiki/Resonance-assisted_hydrogen_bond" class="mw-redirect" title="Resonance-assisted hydrogen bond">Resonance-assisted</a></li> <li><a href="/wiki/Symmetric_hydrogen_bond" title="Symmetric hydrogen bond">Symmetric</a></li> <li><a href="/wiki/Dihydrogen_bond" title="Dihydrogen bond">Dihydrogen bonds</a></li> <li><a href="/wiki/C%E2%80%93H%C2%B7%C2%B7%C2%B7O_interaction" title="C–H···O interaction">C–H···O interaction</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Non-covalent_interactions" class="mw-redirect" title="Non-covalent interactions">Noncovalent</a><br />other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mechanically_interlocked_molecular_architectures" title="Mechanically interlocked molecular architectures">Mechanical</a></li> <li><a href="/wiki/Halogen_bond" title="Halogen bond">Halogen</a></li> <li><a href="/wiki/Chalcogen_bond" title="Chalcogen bond">Chalcogen</a></li> <li><a href="/wiki/Metallophilic_interaction" title="Metallophilic interaction">Metallophilic</a> (<a href="/wiki/Aurophilicity" title="Aurophilicity">aurophilic</a>)</li> <li><a href="/wiki/Intercalation_(chemistry)" title="Intercalation (chemistry)">Intercalation</a></li> <li><a href="/wiki/Stacking_(chemistry)" title="Stacking (chemistry)">Stacking</a></li> <li><a href="/wiki/Cation%E2%80%93pi_interaction" class="mw-redirect" title="Cation–pi interaction">Cation–pi</a></li> <li><a href="/wiki/Cation%E2%80%93pi_interaction#Anion–π_interaction" class="mw-redirect" title="Cation–pi interaction">Anion–pi</a></li> <li><a href="/wiki/Salt_bridge_(protein_and_supramolecular)" title="Salt bridge (protein and supramolecular)">Salt bridge</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Bond_cleavage" title="Bond cleavage">Bond cleavage</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Heterolysis_(chemistry)" title="Heterolysis (chemistry)">Heterolysis</a></li> <li><a href="/wiki/Homolysis_(chemistry)" title="Homolysis (chemistry)">Homolysis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Electron_counting" title="Electron counting">Electron counting</a> rules</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aromaticity" title="Aromaticity">Aromaticity</a> <ul><li><a href="/wiki/H%C3%BCckel%27s_rule" title="Hückel's rule">Hückel's rule</a></li> <li><a href="/wiki/Baird%27s_rule" title="Baird's rule">Baird's rule</a></li> <li><a href="/wiki/M%C3%B6bius_aromaticity" title="Möbius aromaticity">Möbius</a></li> <li><a href="/wiki/Spherical_aromaticity" title="Spherical aromaticity">spherical</a></li></ul></li> <li><a href="/wiki/Polyhedral_skeletal_electron_pair_theory" title="Polyhedral skeletal electron pair theory">Polyhedral skeletal electron pair theory</a></li> <li><a href="/wiki/Jemmis_mno_rules" title="Jemmis mno rules">Jemmis mno rules</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=London_dispersion_force&oldid=1229270220">https://en.wikipedia.org/w/index.php?title=London_dispersion_force&oldid=1229270220</a>"</div></div> <div id="catlinks" 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