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class="vector-toc-numb">2</span> <span>Salt bridge</span> </div> </a> <ul id="toc-Salt_bridge-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dipole–dipole_and_similar_interactions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dipole–dipole_and_similar_interactions"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Dipole–dipole and similar interactions</span> </div> </a> <button aria-controls="toc-Dipole–dipole_and_similar_interactions-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Dipole–dipole and similar interactions subsection</span> </button> <ul id="toc-Dipole–dipole_and_similar_interactions-sublist" class="vector-toc-list"> <li id="toc-Ion–dipole_and_ion–induced_dipole_forces" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ion–dipole_and_ion–induced_dipole_forces"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Ion–dipole and ion–induced dipole forces</span> </div> </a> <ul id="toc-Ion–dipole_and_ion–induced_dipole_forces-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Van_der_Waals_forces" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Van_der_Waals_forces"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Van der Waals forces</span> </div> </a> <button aria-controls="toc-Van_der_Waals_forces-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Van der Waals forces subsection</span> </button> <ul id="toc-Van_der_Waals_forces-sublist" class="vector-toc-list"> <li id="toc-Keesom_force_(permanent_dipole_–_permanent_dipole)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Keesom_force_(permanent_dipole_–_permanent_dipole)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Keesom force (permanent dipole – permanent dipole)</span> </div> </a> <ul id="toc-Keesom_force_(permanent_dipole_–_permanent_dipole)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Debye_force_(permanent_dipoles–induced_dipoles)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Debye_force_(permanent_dipoles–induced_dipoles)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Debye force (permanent dipoles–induced dipoles)</span> </div> </a> <ul id="toc-Debye_force_(permanent_dipoles–induced_dipoles)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-London_dispersion_force_(fluctuating_dipole–induced_dipole_interaction)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#London_dispersion_force_(fluctuating_dipole–induced_dipole_interaction)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>London dispersion force (fluctuating dipole–induced dipole interaction)</span> </div> </a> <ul id="toc-London_dispersion_force_(fluctuating_dipole–induced_dipole_interaction)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Relative_strength_of_forces" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relative_strength_of_forces"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Relative strength of forces</span> </div> </a> <ul id="toc-Relative_strength_of_forces-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Effect_on_the_behavior_of_gases" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Effect_on_the_behavior_of_gases"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Effect on the behavior of gases</span> </div> </a> <ul id="toc-Effect_on_the_behavior_of_gases-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantum_mechanical_theories" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Quantum_mechanical_theories"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Quantum mechanical theories</span> </div> </a> <ul id="toc-Quantum_mechanical_theories-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Intermolecular force</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 47 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-47" 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">47 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%D8%A9_%D8%A8%D9%8A%D9%86_%D8%AC%D8%B2%D9%8A%D8%A6%D9%8A%D8%A9" title="قوة بين جزيئية – Arabic" lang="ar" hreflang="ar" data-title="قوة بين جزيئية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Fuercia_intermolecular" title="Fuercia intermolecular – Asturian" lang="ast" hreflang="ast" data-title="Fuercia intermolecular" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%86%E0%A6%A8%E0%A7%8D%E0%A6%A4%E0%A6%83%E0%A6%86%E0%A6%A3%E0%A6%AC%E0%A6%BF%E0%A6%95_%E0%A6%AC%E0%A6%B2" title="আন্তঃআণবিক বল – Bangla" lang="bn" hreflang="bn" data-title="আন্তঃআণবিক বল" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D1%96%D0%B6%D0%BC%D0%B0%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D1%8F%D1%80%D0%BD%D0%B0%D0%B5_%D1%9E%D0%B7%D0%B0%D0%B5%D0%BC%D0%B0%D0%B4%D0%B7%D0%B5%D1%8F%D0%BD%D0%BD%D0%B5" title="Міжмалекулярнае ўзаемадзеянне – Belarusian" lang="be" hreflang="be" data-title="Міжмалекулярнае ўзаемадзеянне" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Me%C4%91umolekulska_sila" title="Međumolekulska sila – Bosnian" lang="bs" hreflang="bs" data-title="Međumolekulska 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/For%C3%A7a_intermolecular" title="Força intermolecular – Catalan" lang="ca" hreflang="ca" data-title="Força intermolecular" 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/Molekulov%C3%A1_interakce" title="Molekulová interakce – Czech" lang="cs" hreflang="cs" data-title="Molekulová interakce" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Grymoedd_rhyngfoleciwlaidd" title="Grymoedd rhyngfoleciwlaidd – Welsh" lang="cy" hreflang="cy" data-title="Grymoedd rhyngfoleciwlaidd" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Intermolekyl%C3%A6r_kraft" title="Intermolekylær kraft – Danish" lang="da" hreflang="da" data-title="Intermolekylær kraft" 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/Zwischenmolekulare_Kr%C3%A4fte" title="Zwischenmolekulare Kräfte – German" lang="de" hreflang="de" data-title="Zwischenmolekulare Kräfte" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%BD%CE%B4%CE%BF%CE%BC%CE%BF%CF%81%CE%B9%CE%B1%CE%BA%CE%AD%CF%82_%CE%B4%CF%85%CE%BD%CE%AC%CE%BC%CE%B5%CE%B9%CF%82" title="Ενδομοριακές δυνάμεις – Greek" lang="el" hreflang="el" data-title="Ενδομοριακές δυνάμεις" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Fuerza_intermolecular" title="Fuerza intermolecular – Spanish" lang="es" hreflang="es" data-title="Fuerza intermolecular" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Indar_intermolekular" title="Indar intermolekular – Basque" lang="eu" hreflang="eu" data-title="Indar intermolekular" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</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_%D8%A8%DB%8C%D9%86_%D9%85%D9%88%D9%84%DA%A9%D9%88%D9%84%DB%8C" title="نیروی بین مولکولی – Persian" lang="fa" hreflang="fa" data-title="نیروی بین مولکولی" 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/Force_intermol%C3%A9culaire" title="Force intermoléculaire – French" lang="fr" hreflang="fr" data-title="Force intermoléculaire" 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_idirmh%C3%B3il%C3%ADneach" title="Fórsa idirmhóilíneach – Irish" lang="ga" hreflang="ga" data-title="Fórsa idirmhóilíneach" 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%B6%84%EC%9E%90%EA%B0%84_%ED%9E%98" title="분자간 힘 – Korean" lang="ko" hreflang="ko" data-title="분자간 힘" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%82%E0%A4%A4%E0%A4%B0%E0%A4%BE%E0%A4%85%E0%A4%A3%E0%A5%81%E0%A4%95_%E0%A4%AC%E0%A4%B2" title="अंतराअणुक बल – Hindi" lang="hi" hreflang="hi" data-title="अंतराअणुक बल" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Me%C4%91umolekulske_sile" title="Međumolekulske sile – Croatian" lang="hr" hreflang="hr" data-title="Međumolekulske sile" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Intermolekulala_forco" title="Intermolekulala forco – Ido" lang="io" hreflang="io" data-title="Intermolekulala forco" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Gaya_antarmolekul" title="Gaya antarmolekul – Indonesian" lang="id" hreflang="id" data-title="Gaya antarmolekul" 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/Legami_intermolecolari" title="Legami intermolecolari – Italian" lang="it" hreflang="it" data-title="Legami intermolecolari" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D0%B0_%D0%B0%D1%80%D0%B0%D0%BB%D1%8B%D2%9B_%D3%A9%D0%B7%D0%B0%D1%80%D0%B0_%D3%99%D1%81%D0%B5%D1%80" title="Молекула аралық өзара әсер – Kazakh" lang="kk" hreflang="kk" data-title="Молекула аралық өзара әсер" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Molekul%C4%81rie_sp%C4%93ki" title="Molekulārie spēki – Latvian" lang="lv" hreflang="lv" data-title="Molekulārie spēki" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB_%D1%85%D0%BE%D0%BE%D1%80%D0%BE%D0%BD%D0%B4%D1%8B%D0%BD_%D1%85%D2%AF%D1%87" title="Молекул хоорондын хүч – Mongolian" lang="mn" hreflang="mn" data-title="Молекул хоорондын хүч" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Intermoleculaire_krachten" title="Intermoleculaire krachten – Dutch" lang="nl" hreflang="nl" data-title="Intermoleculaire krachten" 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/%E5%88%86%E5%AD%90%E9%96%93%E5%8A%9B" title="分子間力 – Japanese" lang="ja" hreflang="ja" data-title="分子間力" 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-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Intermolekyl%C3%A6r_binding" title="Intermolekylær binding – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Intermolekylær binding" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Humna_maddarroo_gidduu" title="Humna maddarroo gidduu – Oromo" lang="om" hreflang="om" data-title="Humna maddarroo gidduu" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Molekulyar_o%CA%BBzaro_ta%27sir_kuchlari" title="Molekulyar oʻzaro ta'sir kuchlari – Uzbek" lang="uz" hreflang="uz" data-title="Molekulyar oʻzaro ta'sir kuchlari" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Oddzia%C5%82ywania_mi%C4%99dzycz%C4%85steczkowe" title="Oddziaływania międzycząsteczkowe – Polish" lang="pl" hreflang="pl" data-title="Oddziaływania międzycząsteczkowe" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/For%C3%A7a_intermolecular" title="Força intermolecular – Portuguese" lang="pt" hreflang="pt" data-title="Força intermolecular" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/For%C8%9B%C4%83_intermolecular%C4%83" title="Forță intermoleculară – Romanian" lang="ro" hreflang="ro" data-title="Forță intermoleculară" 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%9C%D0%B5%D0%B6%D0%BC%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D1%8F%D1%80%D0%BD%D0%BE%D0%B5_%D0%B2%D0%B7%D0%B0%D0%B8%D0%BC%D0%BE%D0%B4%D0%B5%D0%B9%D1%81%D1%82%D0%B2%D0%B8%D0%B5" title="Межмолекулярное взаимодействие – Russian" lang="ru" hreflang="ru" data-title="Межмолекулярное взаимодействие" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Intermolecular_force" title="Intermolecular force – Simple English" lang="en-simple" hreflang="en-simple" data-title="Intermolecular force" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Medmolekulska_sila" title="Medmolekulska sila – Slovenian" lang="sl" hreflang="sl" data-title="Medmolekulska sila" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Me%C4%91umolekulska_sila" title="Međumolekulska sila – Serbian" lang="sr" hreflang="sr" data-title="Međumolekulska sila" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" 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id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=Intermolecular&redirect=no" class="mw-redirect" title="Intermolecular">Intermolecular</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Force of attraction or repulsion between molecules and neighboring particles</div> <p>An <b>intermolecular force</b> (<b>IMF</b>; also <b>secondary force</b>) is the force that mediates interaction between molecules, including the <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetic forces of attraction or repulsion</a> which act between atoms and other types of neighbouring particles, e.g. <a href="/wiki/Atom" title="Atom">atoms</a> or <a href="/wiki/Ion" title="Ion">ions</a>. Intermolecular forces are weak relative to <a href="/wiki/Intramolecular_force" title="Intramolecular force">intramolecular forces</a> – the forces which hold a molecule together. For example, the <a href="/wiki/Covalent_bond" title="Covalent bond">covalent bond</a>, involving sharing electron pairs between atoms, is much stronger than the forces present between neighboring molecules.<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> Both sets of forces are essential parts of <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force fields</a> frequently used in <a href="/wiki/Molecular_mechanics" title="Molecular mechanics">molecular mechanics</a>. </p><p>The first reference to the nature of microscopic forces is found in <a href="/wiki/Alexis_Clairaut" title="Alexis Clairaut">Alexis Clairaut</a>'s work <i>Théorie de la figure de la Terre,</i> published in Paris in 1743.<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> Other scientists who have contributed to the investigation of microscopic forces include: <a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Laplace</a>, <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a>, <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a>, <a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Boltzmann</a> and <a href="/wiki/Linus_Pauling" title="Linus Pauling">Pauling</a>. </p><p>Attractive intermolecular forces are categorized into the following types: </p> <ul><li><a href="/wiki/Hydrogen_bond" title="Hydrogen bond">Hydrogen bonding</a></li> <li>Ion–dipole forces and ion–induced dipole force</li> <li><a href="/wiki/Cation%E2%80%93%CF%80_interaction" title="Cation–π interaction">Cation–π</a>, σ–π and π–π bonding</li> <li><a href="/wiki/Van_der_Waals_force" title="Van der Waals force">Van der Waals forces</a> – <a href="/wiki/Keesom_force" class="mw-redirect" title="Keesom force">Keesom force</a>, <a href="/wiki/Debye_force" class="mw-redirect" title="Debye force">Debye force</a>, and <a href="/wiki/London_dispersion_force" title="London dispersion force">London dispersion force</a></li> <li><a href="/wiki/Cation%E2%80%93cation_bond" title="Cation–cation bond">Cation–cation bonding</a></li> <li><a href="/wiki/Salt_bridge_(protein_and_supramolecular)" title="Salt bridge (protein and supramolecular)">Salt bridge (protein and supramolecular)</a></li></ul> <p>Information on intermolecular forces is obtained by macroscopic measurements of properties like <a href="/wiki/Viscosity" title="Viscosity">viscosity</a>, <a href="/wiki/PVT_(physics)" class="mw-redirect" title="PVT (physics)">pressure, volume, temperature</a> (PVT) data. The link to microscopic aspects is given by <a href="/wiki/Virial_coefficient" title="Virial coefficient">virial coefficients</a> and intermolecular <a href="/wiki/Pair_potential" title="Pair potential">pair potentials</a>, such as the <a href="/wiki/Mie_potential" title="Mie potential">Mie potential</a>, <a href="/wiki/Buckingham_potential" title="Buckingham potential">Buckingham potential</a> or <a href="/wiki/Lennard-Jones_potential" title="Lennard-Jones potential">Lennard-Jones potential</a>. </p><p>In the broadest sense, it can be understood as such interactions between any particles (<a href="/wiki/Molecule" title="Molecule">molecules</a>, <a href="/wiki/Atom" title="Atom">atoms</a>, <a href="/wiki/Ion" title="Ion">ions</a> and <a href="/wiki/Molecular_ion" class="mw-redirect" title="Molecular ion">molecular ions</a>) in which the formation of chemical, that is, ionic, covalent or metallic bonds does not occur. In other words, these interactions are significantly weaker than <a href="/wiki/Covalent_bond" title="Covalent bond">covalent</a> ones and do not lead to a significant restructuring of the <a href="/wiki/Electronic_structure" class="mw-redirect" title="Electronic structure">electronic structure</a> of the interacting particles. (This is only partially true. For example, all <a href="/wiki/Enzyme" title="Enzyme">enzymatic</a> and <a href="/wiki/Catalysis" title="Catalysis">catalytic reactions</a> begin with a weak intermolecular interaction between a substrate and an <a href="/wiki/Enzyme" title="Enzyme">enzyme</a> or a molecule with a <a href="/wiki/Catalyst:_Agents_of_Change" title="Catalyst: Agents of Change">catalyst</a>, but several such weak interactions with the required spatial configuration of the active center of the enzyme lead to significant restructuring changes the energy state of molecules or substrate, which ultimately leads to the breaking of some and the formation of other covalent chemical bonds. Strictly speaking, all <a href="/wiki/Enzyme_catalysis" title="Enzyme catalysis">enzymatic reactions</a> begin with intermolecular interactions between the <a href="/wiki/Substrate_(chemistry)" title="Substrate (chemistry)">substrate</a> and the enzyme, therefore the importance of these interactions is especially great in <a href="/wiki/Biochemistry" title="Biochemistry">biochemistry</a> and <a href="/wiki/Molecular_biology" title="Molecular biology">molecular biology</a>,<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> and is the basis of <a href="/wiki/Enzyme" title="Enzyme">enzymology</a>). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Hydrogen_bonding">Hydrogen bonding</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intermolecular_force&action=edit&section=1" title="Edit section: Hydrogen bonding"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Hydrogen_bond" title="Hydrogen bond">Hydrogen bond</a></div> <p>A <i>hydrogen bond</i> is an extreme form of dipole-dipole bonding, referring to the attraction between a <a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a> atom that is bonded to an element with high <a href="/wiki/Electronegativity" title="Electronegativity">electronegativity</a>, usually <a href="/wiki/Nitrogen" title="Nitrogen">nitrogen</a>, <a href="/wiki/Oxygen" title="Oxygen">oxygen</a>, or <a href="/wiki/Fluorine" title="Fluorine">fluorine</a>.<sup id="cite_ref-GoldBook-H02899_4-0" class="reference"><a href="#cite_note-GoldBook-H02899-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The hydrogen bond is often described as a strong electrostatic dipole–dipole interaction. However, it also has some features of covalent bonding: it is directional, stronger than a <a href="/wiki/Van_der_Waals_force" title="Van der Waals force">van der Waals force</a> interaction, produces interatomic distances shorter than the sum of their <a href="/wiki/Van_der_Waals_radius" title="Van der Waals radius">van der Waals radii</a>, and usually involves a limited number of interaction partners, which can be interpreted as a kind of <a href="/wiki/Valence_(chemistry)" title="Valence (chemistry)">valence</a>. The number of Hydrogen bonds formed between molecules is equal to the number of active pairs. The molecule which donates its hydrogen is termed the donor molecule, while the molecule containing lone pair participating in H bonding is termed the acceptor molecule. The number of active pairs is equal to the common number between number of hydrogens the donor has and the number of lone pairs the acceptor has. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hydrogen-bonding-in-water-2D.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Hydrogen-bonding-in-water-2D.svg/220px-Hydrogen-bonding-in-water-2D.svg.png" decoding="async" width="220" height="134" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Hydrogen-bonding-in-water-2D.svg/330px-Hydrogen-bonding-in-water-2D.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/58/Hydrogen-bonding-in-water-2D.svg/440px-Hydrogen-bonding-in-water-2D.svg.png 2x" data-file-width="1173" data-file-height="716" /></a><figcaption>Hydrogen bonding in water</figcaption></figure> <p>Though both not depicted in the diagram, water molecules have four active bonds. The oxygen atom’s two lone pairs interact with a hydrogen each, forming two additional hydrogen bonds, and the second hydrogen atom also interacts with a neighbouring oxygen. Intermolecular hydrogen bonding is responsible for the high boiling point of <a href="/wiki/Water" title="Water">water</a> (100 °C) compared to the other <a href="/wiki/Hydrogen_chalcogenide" title="Hydrogen chalcogenide">group 16 hydrides</a>, which have little capability to hydrogen bond. Intramolecular hydrogen bonding is partly responsible for the <a href="/wiki/Secondary_structure" class="mw-redirect" title="Secondary structure">secondary</a>, <a href="/wiki/Tertiary_structure" class="mw-redirect" title="Tertiary structure">tertiary</a>, and <a href="/wiki/Quaternary_structure" class="mw-redirect" title="Quaternary structure">quaternary structures</a> of <a href="/wiki/Protein" title="Protein">proteins</a> and <a href="/wiki/Nucleic_acid" title="Nucleic acid">nucleic acids</a>. It also plays an important role in the structure of <a href="/wiki/Polymers" class="mw-redirect" title="Polymers">polymers</a>, both synthetic and natural.<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> <div class="mw-heading mw-heading2"><h2 id="Salt_bridge">Salt bridge</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intermolecular_force&action=edit&section=2" title="Edit section: Salt bridge"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Salt_bridge_(protein_and_supramolecular)" title="Salt bridge (protein and supramolecular)">Salt bridge (protein and supramolecular)</a></div> <p>The attraction between cationic and anionic sites is a noncovalent, or intermolecular interaction which is usually referred to as ion pairing or salt bridge.<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> It is essentially due to electrostatic forces, although in aqueous medium the association is driven by entropy and often even endothermic. Most salts form crystals with characteristic distances between the ions; in contrast to many other noncovalent interactions, salt bridges are not directional and show in the solid state usually contact determined only by the van der Waals radii of the ions. Inorganic as well as organic ions display in water at moderate ionic strength I similar salt bridge as association ΔG values around 5 to 6 kJ/mol for a 1:1 combination of anion and cation, almost independent of the nature (size, polarizability, etc.) of the ions.<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> The ΔG values are additive and approximately a linear function of the charges, the interaction of e.g. a doubly charged phosphate anion with a single charged ammonium cation accounts for about 2x5 = 10 kJ/mol. The ΔG values depend on the ionic strength I of the solution, as described by the Debye-Hückel equation, at zero ionic strength one observes ΔG = 8 kJ/mol. </p> <div class="mw-heading mw-heading2"><h2 id="Dipole–dipole_and_similar_interactions"><span id="Dipole.E2.80.93dipole_and_similar_interactions"></span>Dipole–dipole and similar interactions <span class="anchor" id="Dipole-dipole_interactions"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intermolecular_force&action=edit&section=3" title="Edit section: Dipole–dipole and similar interactions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dipole–dipole interactions (or Keesom interactions) are electrostatic interactions between molecules which have permanent dipoles. This interaction is stronger than the London forces but is weaker than ion-ion interaction because only partial charges are involved. These interactions tend to align the molecules to increase attraction (reducing <a href="/wiki/Potential_energy" title="Potential energy">potential energy</a>). An example of a dipole–dipole interaction can be seen in <a href="/wiki/Hydrogen_chloride" title="Hydrogen chloride">hydrogen chloride</a> (HCl): the positive end of a polar molecule will attract the negative end of the other molecule and influence its position. Polar molecules have a net attraction between them. Examples of polar molecules include <a href="/wiki/Hydrogen_chloride" title="Hydrogen chloride">hydrogen chloride</a> (HCl) and <a href="/wiki/Chloroform" title="Chloroform">chloroform</a> (CHCl<sub>3</sub>). </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 {\overset {\color {Red}\delta +}{{\ce {H}}}}-{\overset {\color {Red}\delta -}{{\ce {Cl}}}}\cdots {\overset {\color {Red}\delta +}{{\ce {H}}}}-{\overset {\color {Red}\delta -}{{\ce {Cl}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mtext>H</mtext> </mrow> <mstyle mathcolor="#ff5555"> <mi>δ</mi> <mo>+</mo> </mstyle> </mover> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mtext>Cl</mtext> </mrow> <mstyle mathcolor="#ff5555"> <mi>δ</mi> <mo>−</mo> </mstyle> </mover> </mrow> <mo>⋯</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mtext>H</mtext> </mrow> <mstyle mathcolor="#ff5555"> <mi>δ</mi> <mo>+</mo> </mstyle> </mover> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mtext>Cl</mtext> </mrow> <mstyle mathcolor="#ff5555"> <mi>δ</mi> <mo>−</mo> </mstyle> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overset {\color {Red}\delta +}{{\ce {H}}}}-{\overset {\color {Red}\delta -}{{\ce {Cl}}}}\cdots {\overset {\color {Red}\delta +}{{\ce {H}}}}-{\overset {\color {Red}\delta -}{{\ce {Cl}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e75de619876ab5f81675280fcaa98744742d331f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:17.868ex; height:4.343ex;" alt="{\displaystyle {\overset {\color {Red}\delta +}{{\ce {H}}}}-{\overset {\color {Red}\delta -}{{\ce {Cl}}}}\cdots {\overset {\color {Red}\delta +}{{\ce {H}}}}-{\overset {\color {Red}\delta -}{{\ce {Cl}}}}}"></span></dd></dl> <p>Often molecules contain dipolar groups of atoms, but have no overall <a href="/wiki/Electric_dipole_moment" title="Electric dipole moment">dipole moment</a> on the molecule as a whole. This occurs if there is symmetry within the molecule that causes the dipoles to cancel each other out. This occurs in molecules such as <a href="/wiki/Tetrachloromethane" class="mw-redirect" title="Tetrachloromethane">tetrachloromethane</a> and <a href="/wiki/Carbon_dioxide" title="Carbon dioxide">carbon dioxide</a>. The dipole–dipole interaction between two individual atoms is usually zero, since atoms rarely carry a permanent dipole. </p><p>The Keesom interaction is a van der Waals force. It is discussed further in the section "Van der Waals forces". </p> <div class="mw-heading mw-heading3"><h3 id="Ion–dipole_and_ion–induced_dipole_forces"><span id="Ion.E2.80.93dipole_and_ion.E2.80.93induced_dipole_forces"></span>Ion–dipole and ion–induced dipole forces</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intermolecular_force&action=edit&section=4" title="Edit section: Ion–dipole and ion–induced dipole forces"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ion–dipole and ion–induced dipole forces are similar to dipole–dipole and dipole–induced dipole interactions but involve ions, instead of only polar and non-polar molecules. Ion–dipole and ion–induced dipole forces are stronger than dipole–dipole interactions because the charge of any ion is much greater than the charge of a dipole moment. Ion–dipole bonding is stronger than hydrogen bonding.<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> </p><p>An ion–dipole force consists of an ion and a polar molecule interacting. They align so that the positive and negative groups are next to one another, allowing maximum attraction. An important example of this interaction is hydration of ions in water which give rise to <a href="/wiki/Hydration_energy" title="Hydration energy">hydration enthalpy</a>. The polar water molecules surround themselves around ions in water and the energy released during the process is known as hydration enthalpy. The interaction has its immense importance in justifying the stability of various ions (like Cu<sup>2+</sup>) in water. </p><p>An ion–induced dipole force consists of an ion and a non-polar molecule interacting. Like a dipole–induced dipole force, the charge of the ion causes distortion of the electron cloud on the non-polar molecule.<sup id="cite_ref-Michael-Blaber-1996_9-0" class="reference"><a href="#cite_note-Michael-Blaber-1996-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Van_der_Waals_forces">Van der Waals forces</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intermolecular_force&action=edit&section=5" title="Edit section: Van der Waals forces"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Van_der_Waals_force" title="Van der Waals force">van der Waals force</a></div> <p>The van der Waals forces arise from interaction between uncharged atoms or molecules, leading not only to such phenomena as the cohesion of condensed phases and physical absorption of gases, but also to a universal force of attraction between macroscopic bodies.<sup id="cite_ref-j1_10-0" class="reference"><a href="#cite_note-j1-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Keesom_force_(permanent_dipole_–_permanent_dipole)"><span id="Keesom_force_.28permanent_dipole_.E2.80.93_permanent_dipole.29"></span>Keesom force (permanent dipole – permanent dipole) <span class="anchor" id="Keesom_force"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intermolecular_force&action=edit&section=6" title="Edit section: Keesom force (permanent dipole – permanent dipole)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The first contribution to van der Waals forces is due to electrostatic interactions between rotating permanent dipoles, quadrupoles (all molecules with symmetry lower than cubic), and multipoles. It is termed the <i>Keesom interaction</i>, named after <a href="/wiki/Willem_Hendrik_Keesom" title="Willem Hendrik Keesom">Willem Hendrik Keesom</a>.<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> These forces originate from the attraction between permanent dipoles (dipolar molecules) and are temperature dependent.<sup id="cite_ref-j1_10-1" class="reference"><a href="#cite_note-j1-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>They consist of attractive interactions between dipoles that are <a href="/wiki/Canonical_ensemble" title="Canonical ensemble">ensemble</a> averaged over different rotational orientations of the dipoles. It is assumed that the molecules are constantly rotating and never get locked into place. This is a good assumption, but at some point molecules do get locked into place. The energy of a Keesom interaction depends on the inverse sixth power of the distance, unlike the interaction energy of two spatially fixed dipoles, which depends on the inverse third power of the distance. The Keesom interaction can only occur among molecules that possess permanent dipole moments, i.e., two polar molecules. Also Keesom interactions are very weak van der Waals interactions and do not occur in aqueous solutions that contain electrolytes. The angle averaged interaction is given by the following equation: </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 {\frac {-d_{1}^{2}d_{2}^{2}}{24\pi ^{2}\varepsilon _{0}^{2}\varepsilon _{r}^{2}k_{\text{B}}Tr^{6}}}=V,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <msubsup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msubsup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mrow> <mn>24</mn> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msubsup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>B</mtext> </mrow> </msub> <mi>T</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>V</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {-d_{1}^{2}d_{2}^{2}}{24\pi ^{2}\varepsilon _{0}^{2}\varepsilon _{r}^{2}k_{\text{B}}Tr^{6}}}=V,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23adbcb26cb29540b59d5c7b36dc2a9cc361c584" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:21.704ex; height:7.009ex;" alt="{\displaystyle {\frac {-d_{1}^{2}d_{2}^{2}}{24\pi ^{2}\varepsilon _{0}^{2}\varepsilon _{r}^{2}k_{\text{B}}Tr^{6}}}=V,}"></span></dd></dl> <p>where <i>d</i> = electric dipole moment, <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 \varepsilon _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/acb0a8377db20e42274444cb181d51b5532b5844" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.138ex; height:2.009ex;" alt="{\displaystyle \varepsilon _{0}}"></span> = permittivity of free space, <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 \varepsilon _{r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon _{r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/287bce0849b56661bbaebca9942dfe3a6cadc21c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.057ex; height:2.009ex;" alt="{\displaystyle \varepsilon _{r}}"></span> = dielectric constant of surrounding material, <i>T</i> = temperature, <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 k_{\text{B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>B</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{\text{B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9582c7c795d2def2c061f0dfa3a6f0fb3dd2de44" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.607ex; height:2.509ex;" alt="{\displaystyle k_{\text{B}}}"></span> = Boltzmann constant, and <i>r</i> = distance between molecules. </p> <div class="mw-heading mw-heading3"><h3 id="Debye_force_(permanent_dipoles–induced_dipoles)"><span id="Debye_force_.28permanent_dipoles.E2.80.93induced_dipoles.29"></span>Debye force (permanent dipoles–induced dipoles) <span class="anchor" id="Debye_force"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intermolecular_force&action=edit&section=7" title="Edit section: Debye force (permanent dipoles–induced dipoles)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The second contribution is the induction (also termed polarization) or Debye force, arising from interactions between rotating permanent dipoles and from the polarizability of atoms and molecules (induced dipoles). These induced dipoles occur when one molecule with a permanent dipole repels another molecule's electrons. A molecule with permanent dipole can induce a dipole in a similar neighboring molecule and cause mutual attraction. Debye forces cannot occur between atoms. The forces between induced and permanent dipoles are not as temperature dependent as Keesom interactions because the induced dipole is free to shift and rotate around the polar molecule. The Debye induction effects and Keesom orientation effects are termed polar interactions.<sup id="cite_ref-j1_10-2" class="reference"><a href="#cite_note-j1-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>The induced dipole forces appear from the induction (also termed <a href="/wiki/Dipolar_polarization" class="mw-redirect" title="Dipolar polarization">polarization</a>), which is the attractive interaction between a permanent multipole on one molecule with an induced (by the former di/multi-pole) 31 on another.<sup id="cite_ref-Blustin-1978_12-0" class="reference"><a href="#cite_note-Blustin-1978-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Roberts-Orr-1938_13-0" class="reference"><a href="#cite_note-Roberts-Orr-1938-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Sapse-et-al-1979_14-0" class="reference"><a href="#cite_note-Sapse-et-al-1979-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> This interaction is called the <i>Debye force</i>, named after <a href="/wiki/Peter_J._W._Debye" class="mw-redirect" title="Peter J. W. Debye">Peter J. W. Debye</a>. </p><p>One example of an induction interaction between permanent dipole and induced dipole is the interaction between HCl and Ar. In this system, Ar experiences a dipole as its electrons are attracted (to the H side of HCl) or repelled (from the Cl side) by HCl.<sup id="cite_ref-Blustin-1978_12-1" class="reference"><a href="#cite_note-Blustin-1978-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Roberts-Orr-1938_13-1" class="reference"><a href="#cite_note-Roberts-Orr-1938-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> The angle averaged interaction is given by the following equation: </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 {\frac {-d_{1}^{2}\alpha _{2}}{16\pi ^{2}\varepsilon _{0}^{2}\varepsilon _{r}^{2}r^{6}}}=V,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <msubsup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mn>16</mn> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msubsup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>V</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {-d_{1}^{2}\alpha _{2}}{16\pi ^{2}\varepsilon _{0}^{2}\varepsilon _{r}^{2}r^{6}}}=V,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9d6341951d0b89046be5f4ead24fa61e57d27f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:17.46ex; height:7.009ex;" alt="{\displaystyle {\frac {-d_{1}^{2}\alpha _{2}}{16\pi ^{2}\varepsilon _{0}^{2}\varepsilon _{r}^{2}r^{6}}}=V,}"></span></dd></dl> <p>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 \alpha _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aef5f08a56f51deb324e5eed2fb9b2e3c279889d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.542ex; height:2.009ex;" alt="{\displaystyle \alpha _{2}}"></span> = polarizability. </p><p>This kind of interaction can be expected between any polar molecule and non-polar/symmetrical molecule. The induction-interaction force is far weaker than dipole–dipole interaction, but stronger than the <a href="/wiki/London_dispersion_force" title="London dispersion force">London dispersion force</a>. </p> <div class="mw-heading mw-heading3"><h3 id="London_dispersion_force_(fluctuating_dipole–induced_dipole_interaction)"><span id="London_dispersion_force_.28fluctuating_dipole.E2.80.93induced_dipole_interaction.29"></span>London dispersion force (fluctuating dipole–induced dipole interaction)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intermolecular_force&action=edit&section=8" title="Edit section: London dispersion force (fluctuating dipole–induced dipole interaction)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/London_dispersion_force" title="London dispersion force">London dispersion force</a></div> <p>The third and dominant contribution is the dispersion or London force (fluctuating dipole–induced dipole), which arises due to the non-zero instantaneous dipole moments of all atoms and molecules. Such polarization can be induced either by a polar molecule or by the repulsion of negatively charged electron clouds in non-polar molecules. Thus, London interactions are caused by random fluctuations of electron density in an electron cloud. An atom with a large number of electrons will have a greater associated London force than an atom with fewer electrons. The dispersion (London) force is the most important component because all materials are polarizable, whereas Keesom and Debye forces require permanent dipoles. The London interaction is universal and is present in atom-atom interactions as well. For various reasons, London interactions (dispersion) have been considered relevant for interactions between macroscopic bodies in condensed systems. <a href="/wiki/Hamaker_theory" title="Hamaker theory">Hamaker</a> developed the theory of van der Waals between macroscopic bodies in 1937 and showed that the additivity of these interactions renders them considerably more long-range.<sup id="cite_ref-j1_10-3" class="reference"><a href="#cite_note-j1-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Relative_strength_of_forces">Relative strength of forces</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intermolecular_force&action=edit&section=9" title="Edit section: Relative strength of forces"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th>Bond type </th> <th>Dissociation energy<br />(kcal/mol)<sup id="cite_ref-Seyhan-Organic-Chemistry_15-0" class="reference"><a href="#cite_note-Seyhan-Organic-Chemistry-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </th> <th>Dissociation energy <p>(kJ/mol) </p> </th> <th>Note </th></tr> <tr> <td>Ionic lattice </td> <td>250–4000<sup id="cite_ref-Purdue-Lattice_16-0" class="reference"><a href="#cite_note-Purdue-Lattice-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </td> <td>1100–20000 </td> <td> </td></tr> <tr> <td>Covalent bond </td> <td>30–260 </td> <td>130–1100 </td> <td> </td></tr> <tr> <td><a href="/wiki/Hydrogen_bond" title="Hydrogen bond">Hydrogen bond</a> </td> <td>1–12 </td> <td>4–50 </td> <td>About 5 kcal/mol (21 kJ/mol) in water </td></tr> <tr> <td>Dipole–dipole </td> <td>0.5–2 </td> <td>2–8 </td> <td> </td></tr> <tr> <td>London dispersion forces </td> <td><1 to 15 </td> <td><4 to 63 </td> <td>Estimated from the enthalpies of vaporization of hydrocarbons<sup id="cite_ref-Majer-Svoboda-enthalpy-vap_17-0" class="reference"><a href="#cite_note-Majer-Svoboda-enthalpy-vap-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </td></tr></tbody></table> <p>This comparison is approximate. The actual relative strengths will vary depending on the molecules involved. For instance, the presence of water creates competing interactions that greatly weaken the strength of both ionic and hydrogen bonds.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> We may consider that for static systems, <a href="/wiki/Ionic_bonding" title="Ionic bonding">Ionic bonding</a> and <a href="/wiki/Covalent_bond" title="Covalent bond">covalent bonding</a> will always be stronger than intermolecular forces in any given substance. But it is not so for big moving systems like <a href="/wiki/Enzyme" title="Enzyme">enzyme</a> molecules interacting with <a href="/wiki/Substrate_(chemistry)" title="Substrate (chemistry)">substrate</a> molecules.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Here the numerous intramolecular (most often - <a href="/wiki/Hydrogen_bond" title="Hydrogen bond">hydrogen bonds</a>) bonds form an active intermediate state where the intermolecular bonds cause some of the <a href="/wiki/Covalent_bond" title="Covalent bond">covalent bond</a> to be broken, while the others are formed, in this way proceeding the thousands of <a href="/wiki/Enzyme_catalysis" title="Enzyme catalysis">enzymatic reactions</a>, so important for <a href="/wiki/Organism" title="Organism">living organisms</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Effect_on_the_behavior_of_gases">Effect on the behavior of gases</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intermolecular_force&action=edit&section=10" title="Edit section: Effect on the behavior of gases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Intermolecular forces are repulsive at short distances and attractive at long distances (see the <a href="/wiki/Lennard-Jones_potential" title="Lennard-Jones potential">Lennard-Jones potential</a>).<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> In a gas, the repulsive force chiefly has the effect of keeping two molecules from occupying the same volume. This gives a <a href="/wiki/Real_gas" title="Real gas">real gas</a> a tendency to occupy a larger volume than an <a href="/wiki/Ideal_gas" title="Ideal gas">ideal gas</a> at the same temperature and pressure. The attractive force draws molecules closer together and gives a real gas a tendency to occupy a smaller volume than an ideal gas. Which interaction is more important depends on temperature and pressure (see <a href="/wiki/Compressibility_factor" title="Compressibility factor">compressibility factor</a>). </p><p>In a gas, the distances between molecules are generally large, so intermolecular forces have only a small effect. The attractive force is not overcome by the repulsive force, but by the <a href="/wiki/Thermal_energy" title="Thermal energy">thermal energy</a> of the molecules. <a href="/wiki/Thermodynamic_temperature" title="Thermodynamic temperature">Temperature</a> is the measure of thermal energy, so increasing temperature reduces the influence of the attractive force. In contrast, the influence of the repulsive force is essentially unaffected by temperature. </p><p>When a gas is compressed to increase its density, the influence of the attractive force increases. If the gas is made sufficiently dense, the attractions can become large enough to overcome the tendency of thermal motion to cause the molecules to disperse. Then the gas can condense to form a solid or liquid, i.e., a condensed phase. Lower temperature favors the formation of a condensed phase. In a condensed phase, there is very nearly a balance between the attractive and repulsive forces. </p> <div class="mw-heading mw-heading2"><h2 id="Quantum_mechanical_theories">Quantum mechanical theories</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intermolecular_force&action=edit&section=11" title="Edit section: Quantum mechanical theories"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Covalent_bond#Quantum_mechanical_description" title="Covalent bond">Covalent bond § Quantum mechanical description</a></div> <p>Intermolecular forces observed between atoms and molecules can be described phenomenologically as occurring between permanent and instantaneous dipoles, as outlined above. Alternatively, one may seek a fundamental, unifying theory that is able to explain the various types of interactions such as <a href="/wiki/Hydrogen_bonding" class="mw-redirect" title="Hydrogen bonding">hydrogen bonding</a>,<sup id="cite_ref-:0_22-0" class="reference"><a href="#cite_note-:0-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Van_der_Waals_force" title="Van der Waals force">van der Waals force</a><sup id="cite_ref-LD_23-0" class="reference"><a href="#cite_note-LD-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> and dipole–dipole interactions. Typically, this is done by applying the ideas of <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> to molecules, and Rayleigh–Schrödinger <a href="/wiki/Perturbation_theory" title="Perturbation theory">perturbation theory</a> has been especially effective in this regard. When applied to existing <a href="/wiki/Quantum_chemistry" title="Quantum chemistry">quantum chemistry</a> methods, such a quantum mechanical explanation of intermolecular interactions provides an array of approximate methods that can be used to analyze intermolecular interactions.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> One of the most helpful methods to visualize this kind of intermolecular interactions, that we can find in quantum chemistry, is the <a href="/wiki/Non-covalent_interactions_index" title="Non-covalent interactions index">non-covalent interaction index</a>, which is based on the electron density of the system. London dispersion forces play a big role with this. </p><p>Concerning electron density topology, recent methods based on electron density gradient methods have emerged recently, notably with the development of IBSI (Intrinsic Bond Strength Index),<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> relying on the IGM (Independent Gradient Model) methodology.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p> <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=Intermolecular_force&action=edit&section=12" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 18em;"> <ul><li><a href="/wiki/Ionic_bonding" title="Ionic bonding">Ionic bonding</a></li> <li><a href="/wiki/Salt_bridge_(protein_and_supramolecular)" title="Salt bridge (protein and supramolecular)">Salt bridges</a></li> <li><a href="/wiki/Coomber%27s_relationship" title="Coomber's relationship">Coomber's relationship</a></li> <li><a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">Force field (chemistry)</a></li> <li><a href="/wiki/Hydrophobic_effect" title="Hydrophobic effect">Hydrophobic effect</a></li> <li><a href="/wiki/Intramolecular_force" title="Intramolecular force">Intramolecular force</a></li> <li><a href="/wiki/Molecular_solid" title="Molecular solid">Molecular solid</a></li> <li><a href="/wiki/Polymer" title="Polymer">Polymer</a></li> <li><a href="/wiki/Quantum_chemistry_computer_programs" class="mw-redirect" title="Quantum chemistry computer programs">Quantum chemistry computer programs</a></li> <li><a href="/wiki/Van_der_Waals_force" title="Van der Waals force">van der Waals force</a></li> <li><a href="/wiki/Comparison_of_software_for_molecular_mechanics_modeling" title="Comparison of software for molecular mechanics modeling">Comparison of software for molecular mechanics modeling</a></li> <li><a href="/wiki/Non-covalent_interactions" class="mw-redirect" title="Non-covalent interactions">Non-covalent interactions</a></li> <li><a href="/wiki/Solvation" title="Solvation">Solvation</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intermolecular_force&action=edit&section=13" title="Edit section: 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 reflist-columns references-column-width" style="column-width: 30em;"> <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="CITEREFFischerWendland2023" class="citation journal cs1">Fischer, Johann; Wendland, Martin (October 2023). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.fluid.2023.113876">"On the history of key empirical intermolecular potentials"</a>. <i>Fluid Phase Equilibria</i>. <b>573</b>: 113876. <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/2023FlPEq.57313876F">2023FlPEq.57313876F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.fluid.2023.113876">10.1016/j.fluid.2023.113876</a></span>.</cite><span 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title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Chemistry+Chemical+Physics&rft.atitle=Accurately+extracting+the+signature+of+intermolecular+interactions+present+in+the+NCI+plot+of+the+reduced+density+gradient+versus+electron+density&rft.volume=19&rft.issue=27&rft.pages=17928-17936&rft.date=2017-07&rft_id=info%3Apmid%2F28664951&rft_id=info%3Adoi%2F10.1039%2FC7CP02110K&rft_id=info%3Abibcode%2F2017PCCP...1917928L&rft.aulast=Lefebvre&rft.aufirst=C&rft.au=Rubez%2C+G&rft.au=Khartabil%2C+H&rft.au=Boisson%2C+JC&rft.au=Contreras-Garc%C3%ADa%2C+J&rft.au=H%C3%A9non%2C+E&rft_id=https%3A%2F%2Fhal.univ-reims.fr%2Fhal-02505160%2Ffile%2F2017_IGM_PROMOL%2520%25281%2529.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntermolecular+force" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLefebvreKhartabilBoissonContreras-García2018" class="citation journal cs1">Lefebvre C, Khartabil H, Boisson JC, Contreras-García J, Piquemal JP, Hénon E (March 2018). <a rel="nofollow" class="external text" href="https://hal.univ-reims.fr/hal-03377532/file/37_version.pdf">"The Independent Gradient Model: A New Approach for Probing Strong and Weak Interactions in Molecules from Wave Function Calculations"</a> <span class="cs1-format">(PDF)</span>. <i>ChemPhysChem</i>. <b>19</b> (6): 724–735. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fcphc.201701325">10.1002/cphc.201701325</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/29250908">29250908</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ChemPhysChem&rft.atitle=The+Independent+Gradient+Model%3A+A+New+Approach+for+Probing+Strong+and+Weak+Interactions+in+Molecules+from+Wave+Function+Calculations&rft.volume=19&rft.issue=6&rft.pages=724-735&rft.date=2018-03&rft_id=info%3Adoi%2F10.1002%2Fcphc.201701325&rft_id=info%3Apmid%2F29250908&rft.aulast=Lefebvre&rft.aufirst=C&rft.au=Khartabil%2C+H&rft.au=Boisson%2C+JC&rft.au=Contreras-Garc%C3%ADa%2C+J&rft.au=Piquemal%2C+JP&rft.au=H%C3%A9non%2C+E&rft_id=https%3A%2F%2Fhal.univ-reims.fr%2Fhal-03377532%2Ffile%2F37_version.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIntermolecular+force" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPonce-VargasLefebvreBoissonHénon2020" class="citation journal cs1">Ponce-Vargas M, Lefebvre C, Boisson JC, Hénon E (January 2020). "Atomic Decomposition Scheme of Noncovalent Interactions Applied to Host-Guest Assemblies". <i>Journal of Chemical Information and Modeling</i>. <b>60</b> (1): 268–278. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Facs.jcim.9b01016">10.1021/acs.jcim.9b01016</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/31877034">31877034</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:209488458">209488458</a>.</cite><span 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class="navbox-group" style="width:1%"><a href="/wiki/Covalent_bond" title="Covalent bond">Covalent</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/Electron_deficiency" title="Electron deficiency">Electron deficiency</a> <ul><li><a href="/wiki/Three-center_two-electron_bond" title="Three-center two-electron 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 class="mw-selflink selflink">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 href="/wiki/London_dispersion_force" title="London dispersion force">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 class="navbox-styles"><link rel="mw-deduplicated-inline-style" 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