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class="vector-toc-numb">2</span> <span>Types of covalent bonds</span> </div> </a> <ul id="toc-Types_of_covalent_bonds-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Covalent_structures" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Covalent_structures"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Covalent structures</span> </div> </a> <ul id="toc-Covalent_structures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-One-_and_three-electron_bonds" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#One-_and_three-electron_bonds"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>One- and three-electron bonds</span> </div> </a> <ul id="toc-One-_and_three-electron_bonds-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Resonance" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Resonance"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Resonance</span> </div> </a> <button aria-controls="toc-Resonance-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 Resonance subsection</span> </button> <ul id="toc-Resonance-sublist" class="vector-toc-list"> <li id="toc-Aromaticity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aromaticity"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Aromaticity</span> </div> </a> <ul id="toc-Aromaticity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hypervalence" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hypervalence"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Hypervalence</span> </div> </a> <ul id="toc-Hypervalence-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Electron_deficiency" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electron_deficiency"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Electron deficiency</span> </div> </a> <ul id="toc-Electron_deficiency-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Quantum_mechanical_description" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Quantum_mechanical_description"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Quantum mechanical description</span> </div> </a> <button aria-controls="toc-Quantum_mechanical_description-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 Quantum mechanical description subsection</span> </button> <ul id="toc-Quantum_mechanical_description-sublist" class="vector-toc-list"> <li id="toc-Comparison_of_VB_and_MO_theories" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Comparison_of_VB_and_MO_theories"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Comparison of VB and MO theories</span> </div> </a> <ul id="toc-Comparison_of_VB_and_MO_theories-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Covalency_from_atomic_contribution_to_the_electronic_density_of_states" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Covalency_from_atomic_contribution_to_the_electronic_density_of_states"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Covalency from atomic contribution to the electronic density of states</span> </div> </a> <ul id="toc-Covalency_from_atomic_contribution_to_the_electronic_density_of_states-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Analogous_effect_in_nuclear_systems" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Analogous_effect_in_nuclear_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Analogous effect in nuclear systems</span> </div> </a> <ul id="toc-Analogous_effect_in_nuclear_systems-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> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>External links</span> </div> </a> <ul id="toc-External_links-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">Covalent bond</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 93 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-93" 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">93 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Kovalente_binding" title="Kovalente binding – Afrikaans" lang="af" hreflang="af" data-title="Kovalente binding" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D8%A9_%D8%AA%D8%B3%D8%A7%D9%87%D9%85%D9%8A%D8%A9" title="رابطة تساهمية – Arabic" lang="ar" hreflang="ar" data-title="رابطة تساهمية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Enlace_covalent" title="Enlace covalent – Aragonese" lang="an" hreflang="an" data-title="Enlace covalent" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Enllaz_covalente" title="Enllaz covalente – Asturian" lang="ast" hreflang="ast" data-title="Enllaz covalente" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Kovalent_%C9%99laq%C9%99" title="Kovalent əlaqə – Azerbaijani" lang="az" hreflang="az" data-title="Kovalent əlaqə" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%AE%E0%A6%AF%E0%A7%8B%E0%A6%9C%E0%A7%80_%E0%A6%AC%E0%A6%A8%E0%A7%8D%E0%A6%A7%E0%A6%A8" title="সমযোজী বন্ধন – Bangla" lang="bn" hreflang="bn" data-title="সমযোজী বন্ধন" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ki%C5%8Dng-i%C3%BA_kiat-ha%CC%8Dp" title="Kiōng-iú kiat-ha̍p – Minnan" lang="nan" hreflang="nan" data-title="Kiōng-iú kiat-ha̍p" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9A%D0%B0%D0%B2%D0%B0%D0%BB%D0%B5%D0%BD%D1%82%D0%BD%D0%B0%D1%8F_%D1%81%D1%83%D0%B2%D1%8F%D0%B7%D1%8C" title="Кавалентная сувязь – Belarusian" lang="be" hreflang="be" data-title="Кавалентная сувязь" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%BE%D0%B2%D0%B0%D0%BB%D0%B5%D0%BD%D1%82%D0%BD%D0%B0_%D0%B2%D1%80%D1%8A%D0%B7%D0%BA%D0%B0" title="Ковалентна връзка – Bulgarian" lang="bg" hreflang="bg" data-title="Ковалентна връзка" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kovalentna_veza" title="Kovalentna veza – Bosnian" lang="bs" hreflang="bs" data-title="Kovalentna veza" 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/Enlla%C3%A7_covalent" title="Enllaç covalent – Catalan" lang="ca" hreflang="ca" data-title="Enllaç covalent" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9A%D0%BE%D0%B2%D0%B0%D0%BB%D0%B5%D0%BD%D1%82%D0%BB%D0%B0_%C3%A7%D1%8B%D1%85%C4%83%D0%BD%D1%83" title="Ковалентла çыхăну – Chuvash" lang="cv" hreflang="cv" data-title="Ковалентла çыхăну" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Kovalentn%C3%AD_vazba" title="Kovalentní vazba – Czech" lang="cs" hreflang="cs" data-title="Kovalentní vazba" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Bhondi_yeGombedzanwa" title="Bhondi yeGombedzanwa – Shona" lang="sn" hreflang="sn" data-title="Bhondi yeGombedzanwa" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Bond_cofalent" title="Bond cofalent – Welsh" lang="cy" hreflang="cy" data-title="Bond cofalent" 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/Kovalent_binding" title="Kovalent binding – Danish" lang="da" hreflang="da" data-title="Kovalent binding" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-se mw-list-item"><a href="https://se.wikipedia.org/wiki/Kovaleanta_%C4%8Danus" title="Kovaleanta čanus – Northern Sami" lang="se" hreflang="se" data-title="Kovaleanta čanus" data-language-autonym="Davvisámegiella" data-language-local-name="Northern Sami" class="interlanguage-link-target"><span>Davvisámegiella</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Kovalente_Bindung" title="Kovalente Bindung – German" lang="de" hreflang="de" data-title="Kovalente Bindung" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kovalentne_side" title="Kovalentne side – Estonian" lang="et" hreflang="et" data-title="Kovalentne side" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9F%CE%BC%CE%BF%CE%B9%CE%BF%CF%80%CE%BF%CE%BB%CE%B9%CE%BA%CF%8C%CF%82_%CE%B4%CE%B5%CF%83%CE%BC%CF%8C%CF%82" title="Ομοιοπολικός δεσμός – Greek" lang="el" hreflang="el" data-title="Ομοιοπολικός δεσμός" 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/Enlace_covalente" title="Enlace covalente – Spanish" lang="es" hreflang="es" data-title="Enlace covalente" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kovalenta_ligo" title="Kovalenta ligo – Esperanto" lang="eo" hreflang="eo" data-title="Kovalenta ligo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Lotura_kobalente" title="Lotura kobalente – Basque" lang="eu" hreflang="eu" data-title="Lotura kobalente" 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%BE%DB%8C%D9%88%D9%86%D8%AF_%DA%A9%D9%88%D9%88%D8%A7%D9%84%D8%A7%D9%86%D8%B3%DB%8C" title="پیوند کووالانسی – Persian" lang="fa" hreflang="fa" data-title="پیوند کووالانسی" 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/Liaison_covalente" title="Liaison covalente – French" lang="fr" hreflang="fr" data-title="Liaison covalente" 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/Nasc_comhfhi%C3%BAsach" title="Nasc comhfhiúsach – Irish" lang="ga" hreflang="ga" data-title="Nasc comhfhiúsach" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Kiangley_cofioosagh" title="Kiangley cofioosagh – Manx" lang="gv" hreflang="gv" data-title="Kiangley cofioosagh" data-language-autonym="Gaelg" data-language-local-name="Manx" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Enlace_covalente" title="Enlace covalente – Galician" lang="gl" hreflang="gl" data-title="Enlace covalente" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B3%B5%EC%9C%A0_%EA%B2%B0%ED%95%A9" title="공유 결합 – Korean" lang="ko" hreflang="ko" data-title="공유 결합" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%B8%D5%BE%D5%A1%D5%AC%D5%A5%D5%B6%D5%BF_%D5%AF%D5%A1%D5%BA" title="Կովալենտ կապ – Armenian" lang="hy" hreflang="hy" data-title="Կովալենտ կապ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%B9%E0%A4%B8%E0%A4%82%E0%A4%AF%E0%A5%8B%E0%A4%9C%E0%A5%80_%E0%A4%86%E0%A4%AC%E0%A4%82%E0%A4%A7" title="सहसंयोजी आबंध – Hindi" lang="hi" hreflang="hi" data-title="सहसंयोजी आबंध" 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/Kovalentna_veza" title="Kovalentna veza – Croatian" lang="hr" hreflang="hr" data-title="Kovalentna veza" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Ikatan_kovalen" title="Ikatan kovalen – Indonesian" lang="id" hreflang="id" data-title="Ikatan kovalen" 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/Legame_covalente" title="Legame covalente – Italian" lang="it" hreflang="it" data-title="Legame covalente" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%A9%D7%A8_%D7%A7%D7%95%D7%95%D7%9C%D7%A0%D7%98%D7%99" title="קשר קוולנטי – Hebrew" lang="he" hreflang="he" data-title="קשר קוולנטי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Ikatan_Kovalen" title="Ikatan Kovalen – Javanese" lang="jv" hreflang="jv" data-title="Ikatan Kovalen" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%99%E1%83%9D%E1%83%95%E1%83%90%E1%83%9A%E1%83%94%E1%83%9C%E1%83%A2%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%91%E1%83%9B%E1%83%90" title="კოვალენტური ბმა – Georgian" lang="ka" hreflang="ka" data-title="კოვალენტური ბმა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%B2%D0%B0%D0%BB%D0%B5%D0%BD%D1%82%D1%82%D1%96%D0%BA_%D0%B1%D0%B0%D0%B9%D0%BB%D0%B0%D0%BD%D1%8B%D1%81" title="Коваленттік байланыс – Kazakh" lang="kk" hreflang="kk" data-title="Коваленттік байланыс" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Lyezon_kovalan" title="Lyezon kovalan – Haitian Creole" lang="ht" hreflang="ht" data-title="Lyezon kovalan" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Kovalent%C4%81_saite" title="Kovalentā saite – Latvian" lang="lv" hreflang="lv" data-title="Kovalentā saite" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Kovalentinis_ry%C5%A1ys" title="Kovalentinis ryšys – Lithuanian" lang="lt" hreflang="lt" data-title="Kovalentinis ryšys" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Kovalens_k%C3%B6t%C3%A9s" title="Kovalens kötés – Hungarian" lang="hu" hreflang="hu" data-title="Kovalens kötés" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%B2%D0%B0%D0%BB%D0%B5%D0%BD%D1%82%D0%BD%D0%B0_%D0%B2%D1%80%D1%81%D0%BA%D0%B0" title="Ковалентна врска – Macedonian" lang="mk" hreflang="mk" data-title="Ковалентна врска" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B4%B9%E0%B4%B8%E0%B4%82%E0%B4%AF%E0%B5%8B%E0%B4%9C%E0%B4%95%E0%B4%AC%E0%B4%A8%E0%B5%8D%E0%B4%A7%E0%B4%A8%E0%B4%82" title="സഹസംയോജകബന്ധനം – Malayalam" lang="ml" hreflang="ml" data-title="സഹസംയോജകബന്ധനം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B8%E0%A4%B9%E0%A4%B8%E0%A4%82%E0%A4%AF%E0%A5%81%E0%A4%9C_%E0%A4%AC%E0%A4%82%E0%A4%A7" title="सहसंयुज बंध – Marathi" lang="mr" hreflang="mr" data-title="सहसंयुज बंध" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%99%E1%83%9D%E1%83%95%E1%83%90%E1%83%9A%E1%83%94%E1%83%9C%E1%83%A2%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%91%E1%83%A3%E1%83%9C%E1%83%90%E1%83%A4%E1%83%90" title="კოვალენტური ბუნაფა – Mingrelian" lang="xmf" hreflang="xmf" data-title="კოვალენტური ბუნაფა" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Ikatan_kovalen" title="Ikatan kovalen – Malay" lang="ms" hreflang="ms" data-title="Ikatan kovalen" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mni mw-list-item"><a href="https://mni.wikipedia.org/wiki/%EA%AF%80%EA%AF%A3%EA%AF%9A%EA%AF%A6%EA%AF%82%EA%AF%A6%EA%AF%9F%EA%AF%A0_%EA%AF%82%EA%AF%A4%EA%AF%84%EA%AF%A8%EA%AF%9F" title="ꯀꯣꯚꯦꯂꯦꯟꯠ ꯂꯤꯄꯨꯟ – Manipuri" lang="mni" hreflang="mni" data-title="ꯀꯣꯚꯦꯂꯦꯟꯠ ꯂꯤꯄꯨꯟ" data-language-autonym="ꯃꯤꯇꯩ ꯂꯣꯟ" data-language-local-name="Manipuri" class="interlanguage-link-target"><span>ꯃꯤꯇꯩ ꯂꯣꯟ</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/G%C3%AA%CC%A4%E1%B9%B3ng-g%C3%A1-gi%C3%B4ng" title="Gê̤ṳng-gá-giông – Mindong" lang="cdo" hreflang="cdo" data-title="Gê̤ṳng-gá-giông" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9A%D0%BE%D0%B2%D0%B0%D0%BB%D0%B5%D0%BD%D1%82_%D1%85%D0%BE%D0%BB%D0%B1%D0%BE%D0%BE" title="Ковалент холбоо – Mongolian" lang="mn" hreflang="mn" data-title="Ковалент холбоо" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%96%E1%80%80%E1%80%BA%E1%80%85%E1%80%95%E1%80%BA%E1%80%85%E1%80%8A%E1%80%BA%E1%80%B8" title="ဖက်စပ်စည်း – Burmese" lang="my" hreflang="my" data-title="ဖက်စပ်စည်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Covalente_binding" title="Covalente binding – Dutch" lang="nl" hreflang="nl" data-title="Covalente binding" 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%85%B1%E6%9C%89%E7%B5%90%E5%90%88" title="共有結合 – Japanese" lang="ja" hreflang="ja" data-title="共有結合" 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-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kovalent_binding" title="Kovalent binding – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Kovalent binding" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kovalent_binding" title="Kovalent binding – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Kovalent 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-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Ligam_covalent" title="Ligam covalent – Occitan" lang="oc" hreflang="oc" data-title="Ligam covalent" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Kovalent_va_ion_bog%CA%BBlanish" title="Kovalent va ion bogʻlanish – Uzbek" lang="uz" hreflang="uz" data-title="Kovalent va ion bogʻlanish" 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-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B8%E0%A8%B9%E0%A8%BF%E0%A8%AF%E0%A9%8B%E0%A8%9C%E0%A8%95%E0%A9%80_%E0%A8%9C%E0%A9%8B%E0%A9%9C" title="ਸਹਿਯੋਜਕੀ ਜੋੜ – Punjabi" lang="pa" hreflang="pa" data-title="ਸਹਿਯੋਜਕੀ ਜੋੜ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%DA%A9%D9%88%D9%88%DB%8C%D9%84%D9%86%D9%B9_%D8%AC%D9%88%DA%91" title="کوویلنٹ جوڑ – Western Punjabi" lang="pnb" hreflang="pnb" data-title="کوویلنٹ جوڑ" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%9F%E1%9E%98%E1%9F%92%E1%9E%96%E1%9F%90%E1%9E%93%E1%9F%92%E1%9E%92%E1%9E%80%E1%9E%BC%E1%9E%9C%E1%9F%89%E1%9E%B6%E1%9E%A1%E1%9E%84%E1%9F%8B" title="សម្ព័ន្ធកូវ៉ាឡង់ – Khmer" lang="km" hreflang="km" data-title="សម្ព័ន្ធកូវ៉ាឡង់" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Wi%C4%85zanie_kowalencyjne" title="Wiązanie kowalencyjne – Polish" lang="pl" hreflang="pl" data-title="Wiązanie kowalencyjne" 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/Liga%C3%A7%C3%A3o_covalente" title="Ligação covalente – Portuguese" lang="pt" hreflang="pt" data-title="Ligação covalente" 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/Leg%C4%83tur%C4%83_covalent%C4%83" title="Legătură covalentă – Romanian" lang="ro" hreflang="ro" data-title="Legătură covalentă" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%9A%D0%BE%D0%B2%D0%B0%D0%BB%D0%B5%D0%BD%D1%82%D0%BD%D0%B0_%D0%B2%D1%8F%D0%B7%D0%B1%D0%B0" title="Ковалентна вязба – Rusyn" lang="rue" hreflang="rue" data-title="Ковалентна вязба" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D0%B2%D0%B0%D0%BB%D0%B5%D0%BD%D1%82%D0%BD%D0%B0%D1%8F_%D1%81%D0%B2%D1%8F%D0%B7%D1%8C" title="Ковалентная связь – Russian" lang="ru" hreflang="ru" data-title="Ковалентная связь" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9A%D0%BE%D0%B2%D0%B0%D0%BB%D0%B5%D0%BD%D0%BD%D0%B0%D0%B0%D1%85_%D1%81%D0%B8%D1%82%D0%B8%D0%BC" title="Коваленнаах ситим – Yakut" lang="sah" hreflang="sah" data-title="Коваленнаах ситим" data-language-autonym="Саха тыла" data-language-local-name="Yakut" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-skr mw-list-item"><a href="https://skr.wikipedia.org/wiki/%D8%B4%D8%B1%DB%8C%DA%A9_%DA%AF%D8%B1%D9%81%D8%AA%DB%81_%D8%A8%D9%86%D8%AF" title="شریک گرفتہ بند – Saraiki" lang="skr" hreflang="skr" data-title="شریک گرفتہ بند" data-language-autonym="سرائیکی" data-language-local-name="Saraiki" class="interlanguage-link-target"><span>سرائیکی</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Covalent_bond" title="Covalent bond – Scots" lang="sco" hreflang="sco" data-title="Covalent bond" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Lidhja_kovalente" title="Lidhja kovalente – Albanian" lang="sq" hreflang="sq" data-title="Lidhja kovalente" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%83%E0%B7%84%E0%B7%83%E0%B6%82%E0%B6%BA%E0%B7%94%E0%B6%A2_%E0%B6%B6%E0%B6%B1%E0%B7%8A%E0%B6%B0%E0%B6%B1%E0%B6%BA" title="සහසංයුජ බන්ධනය – Sinhala" lang="si" hreflang="si" data-title="සහසංයුජ බන්ධනය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Covalent_bond" title="Covalent bond – Simple English" lang="en-simple" hreflang="en-simple" data-title="Covalent bond" 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-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Kovalentn%C3%A1_v%C3%A4zba" title="Kovalentná väzba – Slovak" lang="sk" hreflang="sk" data-title="Kovalentná väzba" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Kovalentna_vez" title="Kovalentna vez – Slovenian" lang="sl" hreflang="sl" data-title="Kovalentna vez" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%DB%95%D9%86%D8%AF%DB%8C_%DA%A9%D9%88%D8%A7%D9%84%D8%A7%D9%86%D8%B3%DB%8C" title="بەندی کوالانسی – Central Kurdish" lang="ckb" hreflang="ckb" data-title="بەندی کوالانسی" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%BE%D0%B2%D0%B0%D0%BB%D0%B5%D0%BD%D1%82%D0%BD%D0%B0_%D0%B2%D0%B5%D0%B7%D0%B0" title="Ковалентна веза – Serbian" lang="sr" hreflang="sr" data-title="Ковалентна веза" 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/Kovalentna_veza" title="Kovalentna veza – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Kovalentna veza" 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-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Beungkeut_koval%C3%A9n" title="Beungkeut kovalén – Sundanese" lang="su" hreflang="su" data-title="Beungkeut kovalén" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kovalenttinen_sidos" title="Kovalenttinen sidos – Finnish" lang="fi" hreflang="fi" data-title="Kovalenttinen sidos" data-language-autonym="Suomi" data-language-local-name="Finnish" 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<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">Chemical bond by sharing of electron pairs</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">"Covalent" redirects here. For other uses, see <a href="/wiki/Covalent_(disambiguation)" class="mw-disambig" title="Covalent (disambiguation)">Covalent (disambiguation)</a>.</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Covalent_bond_hydrogen.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Covalent_bond_hydrogen.svg/400px-Covalent_bond_hydrogen.svg.png" decoding="async" width="400" height="171" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Covalent_bond_hydrogen.svg/600px-Covalent_bond_hydrogen.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/19/Covalent_bond_hydrogen.svg/800px-Covalent_bond_hydrogen.svg.png 2x" data-file-width="700" data-file-height="300" /></a><figcaption>A covalent bond forming H<sub>2</sub> (right) where two <a href="/wiki/Hydrogen_atom" title="Hydrogen atom">hydrogen atoms</a> share the two <a href="/wiki/Electron" title="Electron">electrons</a></figcaption></figure> <p>A <b>covalent bond</b> is a <a href="/wiki/Chemical_bond" title="Chemical bond">chemical bond</a> that involves the sharing of <a href="/wiki/Electrons" class="mw-redirect" title="Electrons">electrons</a> to form <a href="/wiki/Electron_pair" title="Electron pair">electron pairs</a> between <a href="/wiki/Atom" title="Atom">atoms</a>. These electron pairs are known as <b>shared pairs</b> or <b>bonding pairs</b>. The stable balance of attractive and repulsive forces between atoms, when they share <a href="/wiki/Electron" title="Electron">electrons</a>, is known as covalent bonding.<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> For many <a href="/wiki/Molecule" title="Molecule">molecules</a>, the sharing of electrons allows each atom to attain the equivalent of a full valence shell, corresponding to a stable electronic configuration. In organic chemistry, covalent bonding is much more common than <a href="/wiki/Ionic_bonding" title="Ionic bonding">ionic bonding</a>. </p><p>Covalent bonding also includes many kinds of interactions, including <a href="/wiki/Sigma_bond" title="Sigma bond">σ-bonding</a>, <a href="/wiki/Pi_bond" title="Pi bond">π-bonding</a>, <a href="/wiki/Metallic_bonding" title="Metallic bonding">metal-to-metal bonding</a>, <a href="/wiki/Agostic_interaction" title="Agostic interaction">agostic interactions</a>, <a href="/wiki/Bent_bond" title="Bent bond">bent bonds</a>, <a href="/wiki/Three-center_two-electron_bond" title="Three-center two-electron bond">three-center two-electron bonds</a> and <a href="/wiki/Three-center_four-electron_bond" title="Three-center four-electron bond">three-center four-electron bonds</a>.<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><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> The term <i>covalent bond</i> dates from 1939.<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> The prefix <i>co-</i> means <i>jointly, associated in action, partnered to a lesser degree, </i> etc.; thus a "co-valent bond", in essence, means that the atoms share "<a href="/wiki/Valence_(chemistry)" title="Valence (chemistry)">valence</a>", such as is discussed in <a href="/wiki/Valence_bond_theory" title="Valence bond theory">valence bond theory</a>. </p><p>In the molecule <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span>, the <a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a> atoms share the two electrons via covalent bonding.<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> Covalency is greatest between atoms of similar <a href="/wiki/Electronegativity" title="Electronegativity">electronegativities</a>. Thus, covalent bonding does not necessarily require that the two atoms be of the same elements, only that they be of comparable electronegativity. Covalent bonding that entails the sharing of electrons over more than two atoms is said to be <a href="/wiki/Delocalized_electron" title="Delocalized electron">delocalized</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Covalent_bond&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Covalent.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Covalent.svg/200px-Covalent.svg.png" decoding="async" width="200" height="241" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Covalent.svg/300px-Covalent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/Covalent.svg/400px-Covalent.svg.png 2x" data-file-width="334" data-file-height="402" /></a><figcaption>Early concepts in covalent bonding arose from this kind of image of the molecule of <a href="/wiki/Methane" title="Methane">methane</a>. Covalent bonding is implied in the <a href="/wiki/Lewis_structure" title="Lewis structure">Lewis structure</a> by indicating electrons shared between atoms.</figcaption></figure> <p>The term <i>covalence</i> in regard to bonding was first used in 1919 by <a href="/wiki/Irving_Langmuir" title="Irving Langmuir">Irving Langmuir</a> in a <i><a href="/wiki/Journal_of_the_American_Chemical_Society" title="Journal of the American Chemical Society">Journal of the American Chemical Society</a></i> article entitled "The Arrangement of Electrons in Atoms and Molecules". Langmuir wrote that "we shall denote by the term <i>covalence</i> the number of pairs of electrons that a given atom shares with its neighbors."<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> </p><p>The idea of covalent bonding can be traced several years before 1919 to <a href="/wiki/Gilbert_N._Lewis" title="Gilbert N. Lewis">Gilbert N. Lewis</a>, who in 1916 described the sharing of electron pairs between atoms<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> (and in 1926 he also coined the term "<a href="/wiki/Photon" title="Photon">photon</a>" for the smallest unit of radiant energy). He introduced the <i><a href="/wiki/Lewis_Structure" class="mw-redirect" title="Lewis Structure">Lewis notation</a></i> or <i>electron dot notation</i> or <i>Lewis dot structure</i>, in which valence electrons (those in the outer shell) are represented as dots around the atomic symbols. Pairs of electrons located between atoms represent covalent bonds. Multiple pairs represent multiple bonds, such as <a href="/wiki/Double_bond" title="Double bond">double bonds</a> and <a href="/wiki/Triple_bond" title="Triple bond">triple bonds</a>. An alternative form of representation, not shown here, has bond-forming electron pairs represented as solid lines.<sup id="cite_ref-:0_8-0" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Lewis proposed that an atom forms enough covalent bonds to form a full (or closed) outer electron shell. In the diagram of methane shown here, the carbon atom has a valence of four and is, therefore, surrounded by eight electrons (the <a href="/wiki/Octet_rule" title="Octet rule">octet rule</a>), four from the carbon itself and four from the hydrogens bonded to it. Each hydrogen has a valence of one and is surrounded by two electrons (a duet rule) – its own one electron plus one from the carbon. The numbers of electrons correspond to full shells in the quantum theory of the atom; the outer shell of a carbon atom is the <i>n</i> = 2 shell, which can hold eight electrons, whereas the outer (and only) shell of a hydrogen atom is the <i>n</i> = 1 shell, which can hold only two.<sup id="cite_ref-:1_9-0" class="reference"><a href="#cite_note-:1-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>While the idea of shared electron pairs provides an effective qualitative picture of covalent bonding, <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> is needed to understand the nature of these bonds and predict the structures and properties of simple molecules. <a href="/wiki/Walter_Heitler" title="Walter Heitler">Walter Heitler</a> and <a href="/wiki/Fritz_London" title="Fritz London">Fritz London</a> are credited with the first successful quantum mechanical explanation of a chemical bond (<a href="/wiki/Molecular_hydrogen" class="mw-redirect" title="Molecular hydrogen">molecular hydrogen</a>) in 1927.<sup id="cite_ref-London_10-0" class="reference"><a href="#cite_note-London-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Their work was based on the valence bond model, which assumes that a chemical bond is formed when there is good overlap between the <a href="/wiki/Atomic_orbitals" class="mw-redirect" title="Atomic orbitals">atomic orbitals</a> of participating atoms. </p> <div class="mw-heading mw-heading2"><h2 id="Types_of_covalent_bonds">Types of covalent bonds</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Covalent_bond&action=edit&section=2" title="Edit section: Types of covalent bonds"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Atomic_orbitals" class="mw-redirect" title="Atomic orbitals">Atomic orbitals</a> (except for s orbitals) have specific directional properties leading to different types of covalent bonds. <a href="/wiki/Sigma_bond" title="Sigma bond">Sigma (σ) bonds</a> are the strongest covalent bonds and are due to head-on overlapping of orbitals on two different atoms. A <a href="/wiki/Single_bond" title="Single bond">single bond</a> is usually a σ bond. <a href="/wiki/Pi_bond" title="Pi bond">Pi (π) bonds</a> are weaker and are due to lateral overlap between p (or d) orbitals. A <a href="/wiki/Double_bond" title="Double bond">double bond</a> between two given atoms consists of one σ and one π bond, and a <a href="/wiki/Triple_bond" title="Triple bond">triple bond</a> is one σ and two π bonds.<sup id="cite_ref-:0_8-1" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Covalent bonds are also affected by the <a href="/wiki/Electronegativity" title="Electronegativity">electronegativity</a> of the connected atoms which determines the <a href="/wiki/Chemical_polarity" title="Chemical polarity">chemical polarity</a> of the bond. Two atoms with equal electronegativity will make nonpolar covalent bonds such as H–H. An unequal relationship creates a polar covalent bond such as with H−Cl. However polarity also requires <a href="/wiki/Geometry" title="Geometry">geometric</a> <a href="/wiki/Asymmetry" title="Asymmetry">asymmetry</a>, or else <a href="/wiki/Dipole" title="Dipole">dipoles</a> may cancel out, resulting in a non-polar molecule.<sup id="cite_ref-:0_8-2" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Covalent_structures">Covalent structures</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Covalent_bond&action=edit&section=3" title="Edit section: Covalent structures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are several types of structures for covalent substances, including individual molecules, <a href="/wiki/Molecular_structures" class="mw-redirect" title="Molecular structures">molecular structures</a>, <a href="/wiki/Macromolecular" class="mw-redirect" title="Macromolecular">macromolecular</a> structures and giant covalent structures. Individual molecules have strong bonds that hold the atoms together, but generally, there are negligible forces of attraction between molecules. Such covalent substances are usually gases, for example, <a href="/wiki/HCl" class="mw-redirect" title="HCl">HCl</a>, <a href="/wiki/Sulfur_dioxide" title="Sulfur dioxide">SO<sub>2</sub></a>, <a href="/wiki/Carbon_dioxide" title="Carbon dioxide">CO<sub>2</sub></a>, and <a href="/wiki/Methane" title="Methane">CH<sub>4</sub></a>. In molecular structures, there are weak forces of attraction. Such covalent substances are low-boiling-temperature liquids (such as <a href="/wiki/Ethanol" title="Ethanol">ethanol</a>), and low-melting-temperature solids (such as <a href="/wiki/Iodine" title="Iodine">iodine</a> and solid CO<sub>2</sub>). Macromolecular structures have large numbers of atoms linked by covalent bonds in chains, including synthetic polymers such as <a href="/wiki/Polyethylene" title="Polyethylene">polyethylene</a> and <a href="/wiki/Nylon" title="Nylon">nylon</a>, and biopolymers such as <a href="/wiki/Protein" title="Protein">proteins</a> and <a href="/wiki/Starch" title="Starch">starch</a>. <a href="/wiki/Network_covalent_bonding" title="Network covalent bonding">Network covalent structures</a> (or giant covalent structures) contain large numbers of atoms linked in sheets (such as <a href="/wiki/Graphite" title="Graphite">graphite</a>), or 3-dimensional structures (such as <a href="/wiki/Diamond" title="Diamond">diamond</a> and <a href="/wiki/Quartz" title="Quartz">quartz</a>). These substances have high melting and boiling points, are frequently brittle, and tend to have high electrical <a href="/wiki/Resistivity" class="mw-redirect" title="Resistivity">resistivity</a>. Elements that have high <a href="/wiki/Electronegativity" title="Electronegativity">electronegativity</a>, and the ability to form three or four electron pair bonds, often form such large macromolecular structures.<sup id="cite_ref-StranksEtAl1970_11-0" class="reference"><a href="#cite_note-StranksEtAl1970-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="One-_and_three-electron_bonds">One- and three-electron bonds</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Covalent_bond&action=edit&section=4" title="Edit section: One- and three-electron bonds"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Graphical_comparison_of_bonds.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Graphical_comparison_of_bonds.svg/200px-Graphical_comparison_of_bonds.svg.png" decoding="async" width="200" height="191" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Graphical_comparison_of_bonds.svg/300px-Graphical_comparison_of_bonds.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Graphical_comparison_of_bonds.svg/400px-Graphical_comparison_of_bonds.svg.png 2x" data-file-width="220" data-file-height="210" /></a><figcaption><a href="/wiki/Lewis_structure" title="Lewis structure">Lewis</a> and <a href="/wiki/MO_diagram" class="mw-redirect" title="MO diagram">MO diagrams</a> of an individual 2e<sup>-</sup> bond and 3e<sup>-</sup> bond</figcaption></figure> <p>Bonds with one or three electrons can be found in <a href="/wiki/Radical_(chemistry)" title="Radical (chemistry)">radical</a> species, which have an odd number of electrons. The simplest example of a 1-electron bond is found in the <a href="/wiki/Dihydrogen_cation" title="Dihydrogen cation">dihydrogen cation</a>, <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span>. One-electron bonds often have about half the bond energy of a 2-electron bond, and are therefore called "half bonds". However, there are exceptions: in the case of <a href="/wiki/Dilithium" title="Dilithium">dilithium</a>, the bond is actually stronger for the 1-electron <span class="chemf nowrap">Li<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> than for the 2-electron Li<sub>2</sub>. This exception can be explained in terms of <a href="/wiki/Orbital_hybridisation" title="Orbital hybridisation">hybridization</a> and inner-shell effects.<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> </p><p>The simplest example of three-electron bonding can be found in the <a href="/wiki/Helium_dimer" title="Helium dimer">helium dimer</a> cation, <span class="chemf nowrap">He<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span>. It is considered a "half bond" because it consists of only one shared electron (rather than two);<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> in molecular orbital terms, the third electron is in an anti-bonding orbital which cancels out half of the bond formed by the other two electrons. Another example of a molecule containing a 3-electron bond, in addition to two 2-electron bonds, is <a href="/wiki/Nitric_oxide" title="Nitric oxide">nitric oxide</a>, NO. The oxygen molecule, O<sub>2</sub> can also be regarded as having two 3-electron bonds and one 2-electron bond, which accounts for its <a href="/wiki/Paramagnetism" title="Paramagnetism">paramagnetism</a> and its formal bond order of 2.<sup id="cite_ref-pauling_14-0" class="reference"><a href="#cite_note-pauling-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Chlorine_dioxide" title="Chlorine dioxide">Chlorine dioxide</a> and its heavier analogues <a href="/wiki/Bromine_dioxide" title="Bromine dioxide">bromine dioxide</a> and <a href="/wiki/Iodine_oxide" title="Iodine oxide">iodine dioxide</a> also contain three-electron bonds. </p><p>Molecules with odd-electron bonds are usually highly reactive. These types of bond are only stable between atoms with similar electronegativities.<sup id="cite_ref-pauling_14-1" class="reference"><a href="#cite_note-pauling-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tnone center"><div class="thumbinner multiimageinner" style="width:308px;max-width:308px"><div class="trow"><div class="theader">Modified Lewis structures with 3e bonds</div></div><div class="trow"><div class="tsingle" style="width:152px;max-width:152px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Nitric_oxide.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Nitric_oxide.svg/150px-Nitric_oxide.svg.png" decoding="async" width="150" height="68" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Nitric_oxide.svg/225px-Nitric_oxide.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/Nitric_oxide.svg/300px-Nitric_oxide.svg.png 2x" data-file-width="320" data-file-height="145" /></a></span></div><div class="thumbcaption">Nitric oxide</div></div><div class="tsingle" style="width:152px;max-width:152px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Triplett-Sauerstoff.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Triplett-Sauerstoff.svg/150px-Triplett-Sauerstoff.svg.png" decoding="async" width="150" height="75" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Triplett-Sauerstoff.svg/225px-Triplett-Sauerstoff.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Triplett-Sauerstoff.svg/300px-Triplett-Sauerstoff.svg.png 2x" data-file-width="190" data-file-height="95" /></a></span></div><div class="thumbcaption">Dioxygen</div></div></div></div></div> <div class="mw-heading mw-heading2"><h2 id="Resonance">Resonance</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Covalent_bond&action=edit&section=5" title="Edit section: Resonance"><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/Resonance_(chemistry)" title="Resonance (chemistry)">Resonance (chemistry)</a></div> <p>There are situations whereby a single <a href="/wiki/Lewis_structure" title="Lewis structure">Lewis structure</a> is insufficient to explain the electron configuration in a molecule and its resulting experimentally-determined properties, hence a superposition of structures is needed. The same two atoms in such molecules can be bonded differently in different Lewis structures (a single bond in one, a double bond in another, or even none at all), resulting in a non-integer <a href="/wiki/Bond_order" title="Bond order">bond order</a>. The <a href="/wiki/Nitrate" title="Nitrate">nitrate</a> ion is one such example with three equivalent structures. The bond between the <a href="/wiki/Nitrogen" title="Nitrogen">nitrogen</a> and each oxygen is a double bond in one structure and a single bond in the other two, so that the average bond order for each N–O interaction is <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">2 + 1 + 1</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">4</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span>.<sup id="cite_ref-:0_8-3" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p><span typeof="mw:File"><a href="/wiki/File:Nitrate-ion-resonance-2D.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Nitrate-ion-resonance-2D.png/400px-Nitrate-ion-resonance-2D.png" decoding="async" width="400" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Nitrate-ion-resonance-2D.png/600px-Nitrate-ion-resonance-2D.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/Nitrate-ion-resonance-2D.png/800px-Nitrate-ion-resonance-2D.png 2x" data-file-width="1100" data-file-height="276" /></a></span> </p> <div class="mw-heading mw-heading3"><h3 id="Aromaticity">Aromaticity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Covalent_bond&action=edit&section=6" title="Edit section: Aromaticity"><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/Aromaticity" title="Aromaticity">Aromaticity</a></div> <p>In <a href="/wiki/Organic_chemistry" title="Organic chemistry">organic chemistry</a>, when a molecule with a planar ring obeys <a href="/wiki/H%C3%BCckel%27s_rule" title="Hückel's rule">Hückel's rule</a>, where the number of <a href="/wiki/Pi_bond" title="Pi bond">π electrons</a> fit the formula 4<i>n</i> + 2 (where <i>n</i> is an integer), it attains extra stability and symmetry. In <a href="/wiki/Benzene" title="Benzene">benzene</a>, the prototypical aromatic compound, there are 6 π bonding electrons (<i>n</i> = 1, 4<i>n</i> + 2 = 6). These occupy three delocalized π molecular orbitals (<a href="/wiki/Molecular_orbital_theory" title="Molecular orbital theory">molecular orbital theory</a>) or form conjugate π bonds in two resonance structures that linearly combine (<a href="/wiki/Valence_bond_theory" title="Valence bond theory">valence bond theory</a>), creating a regular <a href="/wiki/Hexagon" title="Hexagon">hexagon</a> exhibiting a greater stabilization than the hypothetical 1,3,5-cyclohexatriene.<sup id="cite_ref-:1_9-1" class="reference"><a href="#cite_note-:1-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>In the case of <a href="/wiki/Heterocyclic" class="mw-redirect" title="Heterocyclic">heterocyclic</a> aromatics and substituted <a href="/wiki/Benzene" title="Benzene">benzenes</a>, the electronegativity differences between different parts of the ring may dominate the chemical behavior of aromatic ring bonds, which otherwise are equivalent.<sup id="cite_ref-:1_9-2" class="reference"><a href="#cite_note-:1-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Hypervalence">Hypervalence</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Covalent_bond&action=edit&section=7" title="Edit section: Hypervalence"><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/Hypervalent_molecule" title="Hypervalent molecule">Hypervalent molecule</a></div> <p>Certain molecules such as <a href="/wiki/Xenon_difluoride" title="Xenon difluoride">xenon difluoride</a> and <a href="/wiki/Sulfur_hexafluoride" title="Sulfur hexafluoride">sulfur hexafluoride</a> have higher co-ordination numbers than would be possible due to strictly covalent bonding according to the <a href="/wiki/Octet_rule" title="Octet rule">octet rule</a>. This is explained by the <a href="/wiki/Three-center_four-electron_bond" title="Three-center four-electron bond">three-center four-electron bond</a> ("3c–4e") model which interprets the molecular wavefunction in terms of non-bonding <a href="/wiki/HOMO/LUMO" class="mw-redirect" title="HOMO/LUMO">highest occupied molecular orbitals</a> in <a href="/wiki/Molecular_orbital_theory" title="Molecular orbital theory">molecular orbital theory</a> and <a href="/wiki/Resonance_(chemistry)" title="Resonance (chemistry)">resonance</a> of sigma bonds in <a href="/wiki/Valence_bond_theory" title="Valence bond theory">valence bond theory</a>.<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> <div class="mw-heading mw-heading3"><h3 id="Electron_deficiency">Electron deficiency</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Covalent_bond&action=edit&section=8" title="Edit section: Electron deficiency"><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/Electron_deficiency" title="Electron deficiency">Electron deficiency</a></div> <p>In <a href="/wiki/Three-center_two-electron_bond" title="Three-center two-electron bond">three-center two-electron bonds</a> ("3c–2e") three atoms share two electrons in bonding. This type of bonding occurs in <a href="/wiki/Boron_hydrides" class="mw-redirect" title="Boron hydrides">boron hydrides</a> such as <a href="/wiki/Diborane" title="Diborane">diborane</a> (B<sub>2</sub>H<sub>6</sub>), which are often described as electron deficient because there are not enough valence electrons to form localized (2-centre 2-electron) bonds joining all the atoms. However the more modern description using 3c–2e bonds does provide enough bonding orbitals to connect all the atoms, so that the molecules can instead be classified as electron-precise. </p><p>Each such bond (2 per molecule in diborane) contains a pair of electrons which connect the <a href="/wiki/Boron" title="Boron">boron</a> atoms to each other in a banana shape, with a proton (the nucleus of a hydrogen atom) in the middle of the bond, sharing electrons with both boron atoms. In certain <a href="/wiki/Cluster_chemistry" class="mw-redirect" title="Cluster chemistry">cluster compounds</a>, so-called <a href="/wiki/Four-center_two-electron_bond" title="Four-center two-electron bond">four-center two-electron bonds</a> also have been postulated.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Quantum_mechanical_description">Quantum mechanical description</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Covalent_bond&action=edit&section=9" title="Edit section: Quantum mechanical description"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>After the development of quantum mechanics, two basic theories were proposed to provide a quantum description of chemical bonding: <a href="/wiki/Valence_bond_theory" title="Valence bond theory">valence bond (VB) theory</a> and <a href="/wiki/Molecular_orbital_theory" title="Molecular orbital theory">molecular orbital (MO) theory</a>. A more recent quantum description<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> is given in terms of atomic contributions to the electronic density of states. </p> <div class="mw-heading mw-heading3"><h3 id="Comparison_of_VB_and_MO_theories">Comparison of VB and MO theories</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Covalent_bond&action=edit&section=10" title="Edit section: Comparison of VB and MO theories"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The two theories represent two ways to build up the <a href="/wiki/Electron_configuration" title="Electron configuration">electron configuration</a> of the molecule.<sup id="cite_ref-Quanta_18-0" class="reference"><a href="#cite_note-Quanta-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> For valence bond theory, the atomic <a href="/wiki/Orbital_hybridisation" title="Orbital hybridisation">hybrid orbitals</a> are filled with electrons first to produce a fully bonded valence configuration, followed by performing a linear combination of contributing structures (<a href="/wiki/Resonance_(chemistry)" title="Resonance (chemistry)">resonance</a>) if there are several of them. In contrast, for molecular orbital theory a <a href="/wiki/Linear_combination_of_atomic_orbitals" title="Linear combination of atomic orbitals">linear combination of atomic orbitals</a> is performed first, followed by filling of the resulting <a href="/wiki/Molecular_orbital" title="Molecular orbital">molecular orbitals</a> with electrons.<sup id="cite_ref-:0_8-4" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>The two approaches are regarded as complementary, and each provides its own insights into the problem of chemical bonding. As valence bond theory builds the molecular wavefunction out of localized bonds, it is more suited for the calculation of <a href="/wiki/Bond_energy" title="Bond energy">bond energies</a> and the understanding of <a href="/wiki/Reaction_mechanism" title="Reaction mechanism">reaction mechanisms</a>. As molecular orbital theory builds the molecular wavefunction out of delocalized orbitals, it is more suited for the calculation of <a href="/wiki/Ionization_energy" title="Ionization energy">ionization energies</a> and the understanding of <a href="/wiki/Absorption_spectroscopy" title="Absorption spectroscopy">spectral absorption bands</a>.<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> </p><p>At the qualitative level, both theories contain incorrect predictions. Simple (Heitler–London) valence bond theory correctly predicts the dissociation of homonuclear diatomic molecules into separate atoms, while simple (Hartree–Fock) molecular orbital theory incorrectly predicts dissociation into a mixture of atoms and ions. On the other hand, simple molecular orbital theory correctly predicts <a href="/wiki/H%C3%BCckel%27s_rule" title="Hückel's rule">Hückel's rule</a> of aromaticity, while simple valence bond theory incorrectly predicts that cyclobutadiene has larger resonance energy than benzene.<sup id="cite_ref-Modern_Physical_Organic_Chemistry_20-0" class="reference"><a href="#cite_note-Modern_Physical_Organic_Chemistry-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>Although the wavefunctions generated by both theories at the qualitative level do not agree and do not match the stabilization energy by experiment, they can be corrected by <a href="/wiki/Configuration_interaction" title="Configuration interaction">configuration interaction</a>.<sup id="cite_ref-Quanta_18-1" class="reference"><a href="#cite_note-Quanta-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> This is done by combining the valence bond covalent function with the functions describing all possible ionic structures or by combining the molecular orbital ground state function with the functions describing all possible excited states using unoccupied orbitals. It can then be seen that the simple molecular orbital approach overestimates the weight of the ionic structures while the simple valence bond approach neglects them. This can also be described as saying that the simple molecular orbital approach neglects <a href="/wiki/Electron_correlation" class="mw-redirect" title="Electron correlation">electron correlation</a> while the simple valence bond approach overestimates it.<sup id="cite_ref-Quanta_18-2" class="reference"><a href="#cite_note-Quanta-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>Modern calculations in <a href="/wiki/Quantum_chemistry" title="Quantum chemistry">quantum chemistry</a> usually start from (but ultimately go far beyond) a molecular orbital rather than a valence bond approach, not because of any intrinsic superiority in the former but rather because the MO approach is more readily adapted to numerical computations. Molecular orbitals are orthogonal, which significantly increases the feasibility and speed of computer calculations compared to nonorthogonal valence bond orbitals. </p> <div class="mw-heading mw-heading3"><h3 id="Covalency_from_atomic_contribution_to_the_electronic_density_of_states">Covalency from atomic contribution to the electronic density of states</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Covalent_bond&action=edit&section=11" title="Edit section: Covalency from atomic contribution to the electronic density of states"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Evaluation of bond covalency is dependent on the <a href="/wiki/Basis_set_(chemistry)" title="Basis set (chemistry)">basis set</a> for approximate quantum-chemical methods such as COOP (crystal orbital overlap population),<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> COHP (Crystal orbital Hamilton population),<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> and BCOOP (Balanced crystal orbital overlap population).<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> To overcome this issue, an alternative formulation of the bond covalency can be provided in this way. </p><p>The <a href="/wiki/Center_of_mass" title="Center of mass">mass center</a> <span class="nowrap">⁠<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 cm(n,l,m_{l},m_{s})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mi>m</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mi>l</mi> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle cm(n,l,m_{l},m_{s})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e072189a11f250b39942c58de9df0ad208d52a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.853ex; height:2.843ex;" alt="{\displaystyle cm(n,l,m_{l},m_{s})}"></span>⁠</span> of an atomic orbital <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 |n,l,m_{l},m_{s}\rangle ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>n</mi> <mo>,</mo> <mi>l</mi> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |n,l,m_{l},m_{s}\rangle ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86b6e6052ba4aaee50c0f23e7b247fc218a252c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.195ex; height:2.843ex;" alt="{\displaystyle |n,l,m_{l},m_{s}\rangle ,}"></span> with <a href="/wiki/Quantum_number" title="Quantum number">quantum numbers</a> <span class="nowrap">⁠<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 n,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/397bfafc701afdf14c2743278a097f6f2957eabb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.042ex; height:2.009ex;" alt="{\displaystyle n,}"></span>⁠</span> <span class="nowrap">⁠<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 l,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a3cecfe01993ae24d62fc836c23e5fe226c18c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.34ex; height:2.509ex;" alt="{\displaystyle l,}"></span>⁠</span> <span class="nowrap">⁠<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 m_{l},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{l},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cbbf77c31595ed3233f82b5b3735d85671880d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.41ex; height:2.009ex;" alt="{\displaystyle m_{l},}"></span>⁠</span> <span class="nowrap">⁠<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 m_{s},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{s},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88bb2f200ccda66b4024a3f59ecb6198e6b55402" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.691ex; height:2.009ex;" alt="{\displaystyle m_{s},}"></span>⁠</span> for atom A is defined as </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 cm^{\mathrm {A} }(n,l,m_{l},m_{s})={\frac {\int \limits _{E_{0}}\limits ^{E_{1}}Eg_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)dE}{\int \limits _{E_{0}}\limits ^{E_{1}}g_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)dE}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msup> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mi>l</mi> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <munderover> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </munderover> <mi>E</mi> <msubsup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>n</mi> <mo>,</mo> <mi>l</mi> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msubsup> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>E</mi> </mrow> <mrow> <munderover> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </munderover> <msubsup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>n</mi> <mo>,</mo> <mi>l</mi> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msubsup> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>E</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle cm^{\mathrm {A} }(n,l,m_{l},m_{s})={\frac {\int \limits _{E_{0}}\limits ^{E_{1}}Eg_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)dE}{\int \limits _{E_{0}}\limits ^{E_{1}}g_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)dE}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18a99872af72dde179ccac61ba5bba2459ed563f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.838ex; width:41.769ex; height:14.843ex;" alt="{\displaystyle cm^{\mathrm {A} }(n,l,m_{l},m_{s})={\frac {\int \limits _{E_{0}}\limits ^{E_{1}}Eg_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)dE}{\int \limits _{E_{0}}\limits ^{E_{1}}g_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)dE}}}"></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 g_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>n</mi> <mo>,</mo> <mi>l</mi> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msubsup> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/125f22d442a29b81fe1d30adc60f18b9c427d435" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:13.11ex; height:3.676ex;" alt="{\displaystyle g_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)}"></span> is the contribution of the atomic orbital <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 |n,l,m_{l},m_{s}\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>n</mi> <mo>,</mo> <mi>l</mi> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |n,l,m_{l},m_{s}\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77d2c7da35e1fd409c95a4752646dc9cdd94c141" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.548ex; height:2.843ex;" alt="{\displaystyle |n,l,m_{l},m_{s}\rangle }"></span> of the atom A to the total electronic density of states <span class="nowrap">⁠<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 g(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cc6f6fcf06a7c595416e9f92905fa4936751fa3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.701ex; height:2.843ex;" alt="{\displaystyle g(E)}"></span>⁠</span> of the solid </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 g(E)=\sum _{\mathrm {A} }\sum _{n,l}\sum _{m_{l},m_{s}}{g_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </munder> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>l</mi> </mrow> </munder> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>n</mi> <mo>,</mo> <mi>l</mi> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msubsup> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g(E)=\sum _{\mathrm {A} }\sum _{n,l}\sum _{m_{l},m_{s}}{g_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92950987b0fa67534607a3c22f17bfe02ddda568" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:33.476ex; height:5.843ex;" alt="{\displaystyle g(E)=\sum _{\mathrm {A} }\sum _{n,l}\sum _{m_{l},m_{s}}{g_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)}}"></span></dd></dl> <p>where the outer sum runs over all atoms A of the unit cell. The energy window <span class="nowrap">⁠<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_{0},E_{1}]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [E_{0},E_{1}]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/972145e0fa9d0c7fe3d06950100d008bb94d3729" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.867ex; height:2.843ex;" alt="{\displaystyle [E_{0},E_{1}]}"></span>⁠</span> is chosen in such a way that it encompasses all of the relevant bands participating in the bond. If the range to select is unclear, it can be identified in practice by examining the molecular orbitals that describe the electron density along with the considered bond. </p><p>The relative position <span class="nowrap">⁠<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 C_{n_{\mathrm {A} }l_{\mathrm {A} },n_{\mathrm {B} }l_{\mathrm {B} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{n_{\mathrm {A} }l_{\mathrm {A} },n_{\mathrm {B} }l_{\mathrm {B} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c567fa564c80430be7c8508ae3b9439827473d87" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.852ex; height:2.843ex;" alt="{\displaystyle C_{n_{\mathrm {A} }l_{\mathrm {A} },n_{\mathrm {B} }l_{\mathrm {B} }}}"></span>⁠</span> of the mass center of <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 |n_{\mathrm {A} },l_{\mathrm {A} }\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |n_{\mathrm {A} },l_{\mathrm {A} }\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd4881c2f06937c30fa12fdbe45a3ddd343efa9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.603ex; height:2.843ex;" alt="{\displaystyle |n_{\mathrm {A} },l_{\mathrm {A} }\rangle }"></span> levels of atom A with respect to the mass center of <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 |n_{\mathrm {B} },l_{\mathrm {B} }\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |n_{\mathrm {B} },l_{\mathrm {B} }\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8411231b710406c4d7cfa00a85e2cdd5067132e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.465ex; height:2.843ex;" alt="{\displaystyle |n_{\mathrm {B} },l_{\mathrm {B} }\rangle }"></span> levels of atom B is given as </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 C_{n_{\mathrm {A} }l_{\mathrm {A} },n_{\mathrm {B} }l_{\mathrm {B} }}=-\left|cm^{\mathrm {A} }(n_{\mathrm {A} },l_{\mathrm {A} })-cm^{\mathrm {B} }(n_{\mathrm {B} },l_{\mathrm {B} })\right|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mo>|</mo> <mrow> <mi>c</mi> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msup> <mo stretchy="false">(</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> <mo>−</mo> <mi>c</mi> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msup> <mo stretchy="false">(</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mo>|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{n_{\mathrm {A} }l_{\mathrm {A} },n_{\mathrm {B} }l_{\mathrm {B} }}=-\left|cm^{\mathrm {A} }(n_{\mathrm {A} },l_{\mathrm {A} })-cm^{\mathrm {B} }(n_{\mathrm {B} },l_{\mathrm {B} })\right|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e3abd5f5dc0c871d96bd8417f1adef4c8de58823" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:43.819ex; height:3.509ex;" alt="{\displaystyle C_{n_{\mathrm {A} }l_{\mathrm {A} },n_{\mathrm {B} }l_{\mathrm {B} }}=-\left|cm^{\mathrm {A} }(n_{\mathrm {A} },l_{\mathrm {A} })-cm^{\mathrm {B} }(n_{\mathrm {B} },l_{\mathrm {B} })\right|}"></span></dd></dl> <p>where the contributions of the magnetic and spin quantum numbers are summed. According to this definition, the relative position of the A levels with respect to the B levels is </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 C_{\mathrm {A,B} }=-\left|cm^{\mathrm {A} }-cm^{\mathrm {B} }\right|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mo>,</mo> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mo>|</mo> <mrow> <mi>c</mi> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msup> <mo>−</mo> <mi>c</mi> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msup> </mrow> <mo>|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{\mathrm {A,B} }=-\left|cm^{\mathrm {A} }-cm^{\mathrm {B} }\right|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7da32345a82ffbf9d032e42a43b8d06a2083a654" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:23.131ex; height:3.509ex;" alt="{\displaystyle C_{\mathrm {A,B} }=-\left|cm^{\mathrm {A} }-cm^{\mathrm {B} }\right|}"></span></dd></dl> <p>where, for simplicity, we may omit the dependence from the principal quantum number <span class="nowrap">⁠<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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>⁠</span> in the notation referring to <span class="nowrap">⁠<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 C_{n_{\mathrm {A} }l_{\mathrm {A} },n_{\mathrm {B} }l_{\mathrm {B} }}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{n_{\mathrm {A} }l_{\mathrm {A} },n_{\mathrm {B} }l_{\mathrm {B} }}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5eddc08c2f99f001386fab7ef56fab172aac2ef7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.499ex; height:2.843ex;" alt="{\displaystyle C_{n_{\mathrm {A} }l_{\mathrm {A} },n_{\mathrm {B} }l_{\mathrm {B} }}.}"></span>⁠</span> </p><p>In this formalism, the greater the value of <span class="nowrap">⁠<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 C_{\mathrm {A,B} },}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mo>,</mo> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{\mathrm {A,B} },}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ffe4b657e51f760aebd1103d0b7215ff8afc16d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.394ex; height:2.843ex;" alt="{\displaystyle C_{\mathrm {A,B} },}"></span>⁠</span> the higher the overlap of the selected atomic bands, and thus the electron density described by those orbitals gives a more covalent <style data-mw-deduplicate="TemplateStyles:r1123817410">.mw-parser-output .template-chem2-su{display:inline-block;font-size:80%;line-height:1;vertical-align:-0.35em}.mw-parser-output .template-chem2-su>span{display:block;text-align:left}.mw-parser-output sub.template-chem2-sub{font-size:80%;vertical-align:-0.35em}.mw-parser-output sup.template-chem2-sup{font-size:80%;vertical-align:0.65em}</style><span class="chemf nowrap">A−B</span> bond. The quantity <span class="nowrap">⁠<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 C_{\mathrm {A,B} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mo>,</mo> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{\mathrm {A,B} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/020cde23f5f1dffb54a3fefe643d5c359d501af5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.748ex; height:2.843ex;" alt="{\displaystyle C_{\mathrm {A,B} }}"></span>⁠</span> is denoted as the <i>covalency</i> of the <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">A−B</span> bond, which is specified in the same units of the energy <span class="nowrap">⁠<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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span>⁠</span>. </p> <div class="mw-heading mw-heading2"><h2 id="Analogous_effect_in_nuclear_systems">Analogous effect in nuclear systems</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Covalent_bond&action=edit&section=12" title="Edit section: Analogous effect in nuclear systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An analogous effect to covalent binding is believed to occur in some nuclear systems, with the difference that the shared fermions are <a href="/wiki/Quarks" class="mw-redirect" title="Quarks">quarks</a> rather than electrons.<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> <a href="/wiki/Particle_physics" title="Particle physics">High energy</a> <a href="/wiki/Proton" title="Proton">proton</a>-proton <a href="/wiki/Scattering" title="Scattering">scattering</a> <a href="/wiki/Cross_section_(physics)" title="Cross section (physics)">cross-section</a> indicates that quark interchange of either u or d quarks is the dominant process of the <a href="/wiki/Nuclear_force" title="Nuclear force">nuclear force</a> at short distance. In particular, it dominates over the <a href="/wiki/Yukawa_interaction" title="Yukawa interaction">Yukawa interaction</a> where a <a href="/wiki/Meson" title="Meson">meson</a> is exchanged.<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> Therefore, covalent binding by quark interchange is expected to be the dominating mechanism of nuclear binding at small distance when the bound <a href="/wiki/Hadrons" class="mw-redirect" title="Hadrons">hadrons</a> have covalence quarks in common.<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> </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=Covalent_bond&action=edit&section=13" 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"> <ul><li><a href="/wiki/Bonding_in_solids" title="Bonding in solids">Bonding in solids</a></li> <li><a href="/wiki/Bond_order" title="Bond order">Bond order</a></li> <li><a href="/wiki/Coordinate_covalent_bond" title="Coordinate covalent bond">Coordinate covalent bond</a>, also known as a dipolar bond or a dative covalent bond</li> <li><a href="/wiki/Covalent_bond_classification" class="mw-redirect" title="Covalent bond classification">Covalent bond classification</a> (or LXZ notation)</li> <li><a href="/wiki/Covalent_radius" title="Covalent radius">Covalent radius</a></li> <li><a href="/wiki/Disulfide_bond" class="mw-redirect" title="Disulfide bond">Disulfide bond</a></li> <li><a href="/wiki/Orbital_hybridisation" title="Orbital hybridisation">Hybridization</a></li> <li><a href="/wiki/Hydrogen_bond" title="Hydrogen bond">Hydrogen bond</a></li> <li><a href="/wiki/Ionic_bond" class="mw-redirect" title="Ionic bond">Ionic bond</a></li> <li><a href="/wiki/Linear_combination_of_atomic_orbitals_molecular_orbital_method" class="mw-redirect" title="Linear combination of atomic orbitals molecular orbital method">Linear combination of atomic orbitals</a></li> <li><a href="/wiki/Metallic_bonding" title="Metallic bonding">Metallic bonding</a></li> <li><a href="/wiki/Noncovalent_bonding" class="mw-redirect" title="Noncovalent bonding">Noncovalent bonding</a></li> <li><a href="/wiki/Resonance_(chemistry)" title="Resonance (chemistry)">Resonance (chemistry)</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=Covalent_bond&action=edit&section=14" 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="CITEREFWhittenGaileyDavis1992" class="citation book cs1">Whitten, Kenneth W.; Gailey, Kenneth D.; Davis, Raymond E. (1992). "7-3 Formation of covalent bonds". <i>General Chemistry</i> (4th ed.). Saunders College Publishing. p. 264. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-03-072373-6" title="Special:BookSources/0-03-072373-6"><bdi>0-03-072373-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=7-3+Formation+of+covalent+bonds&rft.btitle=General+Chemistry&rft.pages=264&rft.edition=4th&rft.pub=Saunders+College+Publishing&rft.date=1992&rft.isbn=0-03-072373-6&rft.aulast=Whitten&rft.aufirst=Kenneth+W.&rft.au=Gailey%2C+Kenneth+D.&rft.au=Davis%2C+Raymond+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" 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="CITEREFMarch1992" class="citation book cs1">March, Jerry (1992). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/advancedorganicc04edmarc"><i>Advanced Organic Chemistry: Reactions, Mechanisms, and Structure</i></a></span>. John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-60180-2" title="Special:BookSources/0-471-60180-2"><bdi>0-471-60180-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Advanced+Organic+Chemistry%3A+Reactions%2C+Mechanisms%2C+and+Structure&rft.pub=John+Wiley+%26+Sons&rft.date=1992&rft.isbn=0-471-60180-2&rft.aulast=March&rft.aufirst=Jerry&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fadvancedorganicc04edmarc&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGary_L._MiesslerDonald_Arthur_Tarr2004" class="citation book cs1">Gary L. Miessler; Donald Arthur Tarr (2004). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/inorganicchemist03edmies"><i>Inorganic Chemistry</i></a></span>. Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-035471-6" title="Special:BookSources/0-13-035471-6"><bdi>0-13-035471-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Inorganic+Chemistry&rft.pub=Prentice+Hall&rft.date=2004&rft.isbn=0-13-035471-6&rft.au=Gary+L.+Miessler&rft.au=Donald+Arthur+Tarr&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Finorganicchemist03edmies&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a href="/wiki/Merriam-Webster" title="Merriam-Webster">Merriam-Webster</a> – Collegiate Dictionary (2000).</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html">"Chemical Bonds"</a>. Hyperphysics.phy-astr.gsu.edu<span class="reference-accessdate">. Retrieved <span class="nowrap">2013-06-09</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Chemical+Bonds&rft.pub=Hyperphysics.phy-astr.gsu.edu&rft_id=http%3A%2F%2Fhyperphysics.phy-astr.gsu.edu%2Fhbase%2Fchemical%2Fbond.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLangmuir1919" class="citation journal cs1">Langmuir, Irving (1919-06-01). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1429026">"The Arrangement of Electrons in Atoms and Molecules"</a>. <i>Journal of the American Chemical Society</i>. <b>41</b> (6): 868–934. <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%2Fja02227a002">10.1021/ja02227a002</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+American+Chemical+Society&rft.atitle=The+Arrangement+of+Electrons+in+Atoms+and+Molecules&rft.volume=41&rft.issue=6&rft.pages=868-934&rft.date=1919-06-01&rft_id=info%3Adoi%2F10.1021%2Fja02227a002&rft.aulast=Langmuir&rft.aufirst=Irving&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1429026&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLewis1916" class="citation journal cs1">Lewis, Gilbert N. (1916-04-01). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1429068">"The atom and the molecule"</a>. <i>Journal of the American Chemical Society</i>. <b>38</b> (4): 762–785. <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%2Fja02261a002">10.1021/ja02261a002</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:95865413">95865413</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+American+Chemical+Society&rft.atitle=The+atom+and+the+molecule&rft.volume=38&rft.issue=4&rft.pages=762-785&rft.date=1916-04-01&rft_id=info%3Adoi%2F10.1021%2Fja02261a002&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A95865413%23id-name%3DS2CID&rft.aulast=Lewis&rft.aufirst=Gilbert+N.&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1429068&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span></span> </li> <li id="cite_note-:0-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_8-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:0_8-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:0_8-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:0_8-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcMurry2016" class="citation book cs1">McMurry, John (2016). <i>Chemistry</i> (7 ed.). Pearson. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-321-94317-0" title="Special:BookSources/978-0-321-94317-0"><bdi>978-0-321-94317-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemistry&rft.edition=7&rft.pub=Pearson&rft.date=2016&rft.isbn=978-0-321-94317-0&rft.aulast=McMurry&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span></span> </li> <li id="cite_note-:1-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_9-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:1_9-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBruice2016" class="citation book cs1">Bruice, Paula (2016). <i>Organic Chemistry</i> (8 ed.). Pearson. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-404228-2" title="Special:BookSources/978-0-13-404228-2"><bdi>978-0-13-404228-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Organic+Chemistry&rft.edition=8&rft.pub=Pearson&rft.date=2016&rft.isbn=978-0-13-404228-2&rft.aulast=Bruice&rft.aufirst=Paula&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span></span> </li> <li id="cite_note-London-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-London_10-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeitlerLondon1927" class="citation journal cs1">Heitler, W.; London, F. (1927). "Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik" [Interaction of neutral atoms and homeopolar bonds according to quantum mechanics]. <i>Zeitschrift für Physik</i>. <b>44</b> (6–7): 455–472. <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/1927ZPhy...44..455H">1927ZPhy...44..455H</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%2Fbf01397394">10.1007/bf01397394</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:119739102">119739102</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=Wechselwirkung+neutraler+Atome+und+hom%C3%B6opolare+Bindung+nach+der+Quantenmechanik&rft.volume=44&rft.issue=6%E2%80%937&rft.pages=455-472&rft.date=1927&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119739102%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2Fbf01397394&rft_id=info%3Abibcode%2F1927ZPhy...44..455H&rft.aulast=Heitler&rft.aufirst=W.&rft.au=London%2C+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span> English translation in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHettema2000" class="citation book cs1">Hettema, H. (2000). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=qsidHRJmUoIC"><i>Quantum Chemistry: Classic Scientific Papers</i></a>. World Scientific. p. 140. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-02-2771-5" title="Special:BookSources/978-981-02-2771-5"><bdi>978-981-02-2771-5</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2012-02-05</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Chemistry%3A+Classic+Scientific+Papers&rft.pages=140&rft.pub=World+Scientific&rft.date=2000&rft.isbn=978-981-02-2771-5&rft.aulast=Hettema&rft.aufirst=H.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DqsidHRJmUoIC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span></span> </li> <li id="cite_note-StranksEtAl1970-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-StranksEtAl1970_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStranksHeffernanLee_DowMcTigue1970" class="citation book cs1">Stranks, D. R.; Heffernan, M. L.; Lee Dow, K. C.; McTigue, P. T.; Withers, G. R. A. (1970). <i>Chemistry: A structural view</i>. <a href="/wiki/Carlton,_Victoria" title="Carlton, Victoria">Carlton, Vic.</a>: Melbourne University Press. p. 184. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-522-83988-6" title="Special:BookSources/0-522-83988-6"><bdi>0-522-83988-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemistry%3A+A+structural+view&rft.place=Carlton%2C+Vic.&rft.pages=184&rft.pub=Melbourne+University+Press&rft.date=1970&rft.isbn=0-522-83988-6&rft.aulast=Stranks&rft.aufirst=D.+R.&rft.au=Heffernan%2C+M.+L.&rft.au=Lee+Dow%2C+K.+C.&rft.au=McTigue%2C+P.+T.&rft.au=Withers%2C+G.+R.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeinholdLandis2005" class="citation book cs1">Weinhold, F.; Landis, C. (2005). <i>Valency and Bonding</i>. Cambridge. pp. 96–100. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-83128-8" title="Special:BookSources/0-521-83128-8"><bdi>0-521-83128-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Valency+and+Bonding&rft.pages=96-100&rft.pub=Cambridge&rft.date=2005&rft.isbn=0-521-83128-8&rft.aulast=Weinhold&rft.aufirst=F.&rft.au=Landis%2C+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarcourt2015" class="citation book cs1">Harcourt, Richard D., ed. (2015). "Chapter 2: Pauling "3-Electron Bonds", 4-Electron 3-Centre Bonding, and the Need for an "Increased-Valence" Theory". <i>Bonding in Electron-Rich Molecules: Qualitative Valence-Bond Approach via Increased-Valence Structures</i>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783319166766" title="Special:BookSources/9783319166766"><bdi>9783319166766</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+2%3A+Pauling+%223-Electron+Bonds%22%2C+4-Electron+3-Centre+Bonding%2C+and+the+Need+for+an+%22Increased-Valence%22+Theory&rft.btitle=Bonding+in+Electron-Rich+Molecules%3A+Qualitative+Valence-Bond+Approach+via+Increased-Valence+Structures&rft.pub=Springer&rft.date=2015&rft.isbn=9783319166766&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span></span> </li> <li id="cite_note-pauling-14"><span class="mw-cite-backlink">^ <a href="#cite_ref-pauling_14-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-pauling_14-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPauling1960" class="citation book cs1">Pauling, L. (1960). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/natureofchemical00paul"><i>The Nature of the Chemical Bond</i></a></span>. 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"Novel Six-Quark Hidden-Color Dibaryon States in QCD". <i>Physics Letters B</i>. <b>727</b> (4–5): 438. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1308.6404">1308.6404</a></span>. <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/2013PhLB..727..438B">2013PhLB..727..438B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.physletb.2013.10.059">10.1016/j.physletb.2013.10.059</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:30153514">30153514</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Letters+B&rft.atitle=Novel+Six-Quark+Hidden-Color+Dibaryon+States+in+QCD&rft.volume=727&rft.issue=4%E2%80%935&rft.pages=438&rft.date=2013&rft_id=info%3Aarxiv%2F1308.6404&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A30153514%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.physletb.2013.10.059&rft_id=info%3Abibcode%2F2013PhLB..727..438B&rft.aulast=Bashkanova&rft.aufirst=M.&rft.au=Brodsky%2C+S.+J.&rft.au=Clement%2C+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Sources">Sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Covalent_bond&action=edit&section=15" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.chemguide.co.uk/atoms/bonding/covalent.html">"Covalent bonding – Single bonds"</a>. chemguide. 2000<span class="reference-accessdate">. Retrieved <span class="nowrap">2012-02-05</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Covalent+bonding+%E2%80%93+Single+bonds&rft.pub=chemguide&rft.date=2000&rft_id=http%3A%2F%2Fwww.chemguide.co.uk%2Fatoms%2Fbonding%2Fcovalent.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.chem.ox.ac.uk/vrchemistry/electronsandbonds/intro1.htm">"Electron Sharing and Covalent Bonds"</a>. Department of Chemistry University of Oxford<span class="reference-accessdate">. Retrieved <span class="nowrap">2012-02-05</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Electron+Sharing+and+Covalent+Bonds&rft.pub=Department+of+Chemistry+University+of+Oxford&rft_id=http%3A%2F%2Fwww.chem.ox.ac.uk%2Fvrchemistry%2Felectronsandbonds%2Fintro1.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html#c5">"Chemical Bonds"</a>. Department of Physics and Astronomy, Georgia State University<span class="reference-accessdate">. Retrieved <span class="nowrap">2012-02-05</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Chemical+Bonds&rft.pub=Department+of+Physics+and+Astronomy%2C+Georgia+State+University&rft_id=http%3A%2F%2Fhyperphysics.phy-astr.gsu.edu%2Fhbase%2Fchemical%2Fbond.html%23c5&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACovalent+bond" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Covalent_bond&action=edit&section=16" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_07.html">Covalent Bonds and Molecular Structure</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090210183035/http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_07.html">Archived</a> 2009-02-10 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090430011156/http://www.chm.bris.ac.uk/pt/harvey/gcse/covalent.html">Structure and Bonding in Chemistry—Covalent Bonds</a></li></ul> <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 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href="/wiki/Special:EditPage/Template:Chemical_bonds" title="Special:EditPage/Template:Chemical bonds"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Chemical_bonds" style="font-size:114%;margin:0 4em"><a href="/wiki/Chemical_bond" title="Chemical bond">Chemical bonds</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Intramolecular_force" title="Intramolecular force">Intramolecular</a><br />(strong)</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 class="mw-selflink selflink">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 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 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" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Chemical_bonding_theory" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Chemical_bonding_theory" title="Template:Chemical bonding theory"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Chemical_bonding_theory" title="Template talk:Chemical bonding theory"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Chemical_bonding_theory" title="Special:EditPage/Template:Chemical bonding theory"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Chemical_bonding_theory" style="font-size:114%;margin:0 4em"><a href="/wiki/Chemical_bond" title="Chemical bond">Chemical bonding</a> theory</div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Atomic_orbital" title="Atomic orbital">Atomic orbital</a></li> <li><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a> <ul><li><a href="/wiki/Introduction_to_quantum_mechanics" title="Introduction to quantum mechanics">Introduction to quantum mechanics</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types of bonds</th><td class="navbox-list-with-group navbox-list navbox-odd" 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%">By symmetry</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/Sigma_bond" title="Sigma bond">Sigma (σ)</a></li> <li><a href="/wiki/Pi_bond" title="Pi bond">Pi (π)</a></li> <li><a href="/wiki/Delta_bond" title="Delta bond">Delta (δ)</a></li> <li><a href="/wiki/Phi_bond" title="Phi bond">Phi (φ)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By <a href="/wiki/Bond_order" title="Bond order">multiplicity</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/Single_bond" title="Single bond">1 (single)</a></li> <li><a href="/wiki/Double_bond" title="Double bond">2 (double)</a></li> <li><a href="/wiki/Triple_bond" title="Triple bond">3 (triple)</a></li> <li><a href="/wiki/Quadruple_bond" title="Quadruple bond">4 (quadruple)</a></li> <li><a href="/wiki/Quintuple_bond" title="Quintuple bond">5 (quintuple)</a></li> <li><a href="/wiki/Sextuple_bond" title="Sextuple bond">6 (sextuple)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</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/Triplet_state" title="Triplet state">Triplet</a></li> <li><a href="/wiki/Singlet_state" title="Singlet state">Singlet</a></li> <li><a href="/wiki/Exchange_interaction" title="Exchange interaction">Exchange-coupled</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/Valence_bond_theory" title="Valence bond theory">Valence bond theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd" 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%">Concepts</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/Orbital_hybridisation" title="Orbital hybridisation">Hybrid orbital</a></li> <li><a href="/wiki/Resonance_(chemistry)" title="Resonance (chemistry)">Resonance</a></li> <li><a href="/wiki/Lewis_structure" title="Lewis structure">Lewis structure</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Constituent units</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 class="mw-selflink selflink">Covalent bond</a></li> <li><a href="/wiki/Lone_pair" title="Lone pair">Lone pair</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/Molecular_orbital_theory" title="Molecular orbital theory">Molecular orbital theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd" 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%">Concepts</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/Molecular_orbital" title="Molecular orbital">Molecular orbital</a></li> <li><a href="/wiki/Linear_combination_of_atomic_orbitals" title="Linear combination of atomic orbitals">LCAO</a></li> <li><a href="/wiki/Molecular_orbital_diagram" title="Molecular orbital diagram">MO diagram</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Constituent units</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/Bonding_molecular_orbital" title="Bonding molecular orbital">Bonding MO</a></li> <li><a href="/wiki/Non-bonding_orbital" title="Non-bonding orbital">Non-bonding MO</a></li> <li><a href="/wiki/Antibonding_molecular_orbital" title="Antibonding molecular orbital">Antibonding MO</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Concepts_in_organic_chemistry" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Organic_chemistry" title="Template:Organic chemistry"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Organic_chemistry" title="Template talk:Organic chemistry"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Organic_chemistry" title="Special:EditPage/Template:Organic chemistry"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Concepts_in_organic_chemistry" style="font-size:114%;margin:0 4em">Concepts in <a href="/wiki/Organic_chemistry" title="Organic chemistry">organic chemistry</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aromaticity" title="Aromaticity">Aromaticity</a></li> <li><a class="mw-selflink selflink">Covalent bonding</a></li> <li><a href="/wiki/Functional_group" title="Functional group">Functional groups</a></li> <li><a href="/wiki/IUPAC_nomenclature_of_organic_chemistry" title="IUPAC nomenclature of organic chemistry">Nomenclature</a></li> <li><a href="/wiki/Organic_compound" title="Organic compound">Organic compounds</a></li> <li><a href="/wiki/Organic_reaction" title="Organic reaction">Organic reactions</a></li> <li><a href="/wiki/Organic_synthesis" title="Organic synthesis">Organic synthesis</a></li> <li><a href="/wiki/List_of_important_publications_in_chemistry#Organic_chemistry" title="List of important publications in chemistry">Publications</a></li> <li><a href="/wiki/Spectroscopy" title="Spectroscopy">Spectroscopy</a></li> <li><a href="/wiki/Stereochemistry" title="Stereochemistry">Stereochemistry</a></li> <li><a href="/wiki/List_of_organic_compounds" class="mw-redirect" title="List of organic compounds">List of organic compounds</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img 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