Molecuulfysica - Wikipedia

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class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Inhoud</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">verbergen</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Top</div> </a> </li> <li id="toc-Molecuulspectra" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Molecuulspectra"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Molecuulspectra</span> </div> </a> <button aria-controls="toc-Molecuulspectra-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>Molecuulspectra-subkopje inklappen</span> </button> <ul id="toc-Molecuulspectra-sublist" class="vector-toc-list"> <li id="toc-Rotatie_van_een_tweeatomig_molecuul" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rotatie_van_een_tweeatomig_molecuul"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Rotatie van een tweeatomig molecuul</span> </div> </a> <ul id="toc-Rotatie_van_een_tweeatomig_molecuul-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Trillingen_van_een_tweeatomig_molecuul" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Trillingen_van_een_tweeatomig_molecuul"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Trillingen van een tweeatomig molecuul</span> </div> </a> <ul id="toc-Trillingen_van_een_tweeatomig_molecuul-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rotatie-trillingswisselwerking" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rotatie-trillingswisselwerking"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Rotatie-trillingswisselwerking</span> </div> </a> <ul id="toc-Rotatie-trillingswisselwerking-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Elektronentoestanden_van_tweeatomige_moleculen" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Elektronentoestanden_van_tweeatomige_moleculen"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Elektronentoestanden van tweeatomige moleculen</span> </div> </a> <ul id="toc-Elektronentoestanden_van_tweeatomige_moleculen-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-De_totale_energie_van_een_molecuul" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#De_totale_energie_van_een_molecuul"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>De totale energie van een molecuul</span> </div> </a> <ul id="toc-De_totale_energie_van_een_molecuul-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zie_ook" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Zie_ook"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Zie ook</span> </div> </a> <ul id="toc-Zie_ook-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Literatuur" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Literatuur"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Literatuur</span> </div> </a> <ul id="toc-Literatuur-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="Inhoud" 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="Inhoudsopgave omschakelen" > <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">Inhoudsopgave omschakelen</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">Molecuulfysica</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="Ga naar een artikel in een andere taal. Beschikbaar in 50 talen" > <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-50" 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">50 talen</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%81%D9%8A%D8%B2%D9%8A%D8%A7%D8%A1_%D8%AC%D8%B2%D9%8A%D8%A6%D9%8A%D8%A9" title="فيزياء جزيئية – Arabisch" lang="ar" hreflang="ar" data-title="فيزياء جزيئية" data-language-autonym="العربية" data-language-local-name="Arabisch" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Molekulyar_fizika" title="Molekulyar fizika – Azerbeidzjaans" lang="az" hreflang="az" data-title="Molekulyar fizika" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbeidzjaans" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D0%B0%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D1%8F%D1%80%D0%BD%D0%B0%D1%8F_%D1%84%D1%96%D0%B7%D1%96%D0%BA%D0%B0" title="Малекулярная фізіка – Belarussisch" lang="be" hreflang="be" data-title="Малекулярная фізіка" data-language-autonym="Беларуская" data-language-local-name="Belarussisch" 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%9C%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D0%BD%D0%B0_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0" title="Молекулна физика – Bulgaars" lang="bg" hreflang="bg" data-title="Молекулна физика" data-language-autonym="Български" data-language-local-name="Bulgaars" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%86%E0%A6%A3%E0%A6%AC%E0%A6%BF%E0%A6%95_%E0%A6%AA%E0%A6%A6%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%A5%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8" title="আণবিক পদার্থবিজ্ঞান – Bengaals" lang="bn" hreflang="bn" data-title="আণবিক পদার্থবিজ্ঞান" data-language-autonym="বাংলা" data-language-local-name="Bengaals" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/F%C3%ADsica_molecular" title="Física molecular – Catalaans" lang="ca" hreflang="ca" data-title="Física molecular" data-language-autonym="Català" data-language-local-name="Catalaans" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Molekulov%C3%A1_fyzika" title="Molekulová fyzika – Tsjechisch" lang="cs" hreflang="cs" data-title="Molekulová fyzika" data-language-autonym="Čeština" data-language-local-name="Tsjechisch" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%C4%83%D1%81%D0%B5%D0%BD_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B8" title="Молекулăсен физики – Tsjoevasjisch" lang="cv" hreflang="cv" data-title="Молекулăсен физики" data-language-autonym="Чӑвашла" data-language-local-name="Tsjoevasjisch" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Ffiseg_foleciwlaidd" title="Ffiseg foleciwlaidd – Welsh" lang="cy" hreflang="cy" data-title="Ffiseg foleciwlaidd" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Molek%C3%BClphysik" title="Molekülphysik – Duits" lang="de" hreflang="de" data-title="Molekülphysik" data-language-autonym="Deutsch" data-language-local-name="Duits" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Molecular_physics" title="Molecular physics – Engels" lang="en" hreflang="en" data-title="Molecular physics" data-language-autonym="English" data-language-local-name="Engels" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/F%C3%ADsica_molecular" title="Física molecular – Spaans" lang="es" hreflang="es" data-title="Física molecular" data-language-autonym="Español" data-language-local-name="Spaans" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Molekulaarf%C3%BC%C3%BCsika" title="Molekulaarfüüsika – Estisch" lang="et" hreflang="et" data-title="Molekulaarfüüsika" data-language-autonym="Eesti" data-language-local-name="Estisch" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Fisika_molekular" title="Fisika molekular – Baskisch" lang="eu" hreflang="eu" data-title="Fisika molekular" data-language-autonym="Euskara" data-language-local-name="Baskisch" 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%81%DB%8C%D8%B2%DB%8C%DA%A9_%D9%85%D9%88%D9%84%DA%A9%D9%88%D9%84%DB%8C" title="فیزیک مولکولی – Perzisch" lang="fa" hreflang="fa" data-title="فیزیک مولکولی" data-language-autonym="فارسی" data-language-local-name="Perzisch" 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/Physique_mol%C3%A9culaire" title="Physique moléculaire – Frans" lang="fr" hreflang="fr" data-title="Physique moléculaire" data-language-autonym="Français" data-language-local-name="Frans" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/F%C3%ADsica_molecular" title="Física molecular – Galicisch" lang="gl" hreflang="gl" data-title="Física molecular" data-language-autonym="Galego" data-language-local-name="Galicisch" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A4%D7%99%D7%96%D7%99%D7%A7%D7%94_%D7%9E%D7%95%D7%9C%D7%A7%D7%95%D7%9C%D7%A8%D7%99%D7%AA" title="פיזיקה מולקולרית – Hebreeuws" lang="he" hreflang="he" data-title="פיזיקה מולקולרית" data-language-autonym="עברית" data-language-local-name="Hebreeuws" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Molekularna_fizika" title="Molekularna fizika – Kroatisch" lang="hr" hreflang="hr" data-title="Molekularna fizika" data-language-autonym="Hrvatski" data-language-local-name="Kroatisch" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%B8%D5%AC%D5%A5%D5%AF%D5%B8%D6%82%D5%AC%D5%A1%D5%B5%D5%AB%D5%B6_%D6%86%D5%AB%D5%A6%D5%AB%D5%AF%D5%A1" title="Մոլեկուլային ֆիզիկա – Armeens" lang="hy" hreflang="hy" data-title="Մոլեկուլային ֆիզիկա" data-language-autonym="Հայերեն" data-language-local-name="Armeens" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Fisika_molekuler" title="Fisika molekuler – Indonesisch" lang="id" hreflang="id" data-title="Fisika molekuler" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesisch" 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/Fisica_molecolare" title="Fisica molecolare – Italiaans" lang="it" hreflang="it" data-title="Fisica molecolare" data-language-autonym="Italiano" data-language-local-name="Italiaans" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%88%86%E5%AD%90%E7%89%A9%E7%90%86%E5%AD%A6" title="分子物理学 – Japans" lang="ja" hreflang="ja" data-title="分子物理学" data-language-autonym="日本語" data-language-local-name="Japans" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%9D%E1%83%9A%E1%83%94%E1%83%99%E1%83%A3%E1%83%9A%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%A4%E1%83%98%E1%83%96%E1%83%98%E1%83%99%E1%83%90" title="მოლეკულური ფიზიკა – Georgisch" lang="ka" hreflang="ka" data-title="მოლეკულური ფიზიკა" data-language-autonym="ქართული" data-language-local-name="Georgisch" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Molekulyar_fizika" title="Molekulyar fizika – Karakalpaks" lang="kaa" hreflang="kaa" data-title="Molekulyar fizika" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Karakalpaks" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D0%B0%D0%BB%D1%8B%D2%9B_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0" title="Молекулалық физика – Kazachs" lang="kk" hreflang="kk" data-title="Молекулалық физика" data-language-autonym="Қазақша" data-language-local-name="Kazachs" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B6%84%EC%9E%90%EB%AC%BC%EB%A6%AC%ED%95%99" title="분자물리학 – Koreaans" lang="ko" hreflang="ko" data-title="분자물리학" data-language-autonym="한국어" data-language-local-name="Koreaans" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D0%B0%D0%BB%D1%8B%D0%BA_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0" title="Молекулалык физика – Kirgizisch" lang="ky" hreflang="ky" data-title="Молекулалык физика" data-language-autonym="Кыргызча" data-language-local-name="Kirgizisch" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Molekulin%C4%97_fizika" title="Molekulinė fizika – Litouws" lang="lt" hreflang="lt" data-title="Molekulinė fizika" data-language-autonym="Lietuvių" data-language-local-name="Litouws" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Molekul%C4%81rfizika" title="Molekulārfizika – Lets" lang="lv" hreflang="lv" data-title="Molekulārfizika" data-language-autonym="Latviešu" data-language-local-name="Lets" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D0%B0%D1%80%D0%BD%D0%B0_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0" title="Молекуларна физика – Macedonisch" lang="mk" hreflang="mk" data-title="Молекуларна физика" data-language-autonym="Македонски" data-language-local-name="Macedonisch" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D1%8B%D0%BD_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA" title="Молекулын физик – Mongools" lang="mn" hreflang="mn" data-title="Молекулын физик" data-language-autonym="Монгол" data-language-local-name="Mongools" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Fizik_molekul" title="Fizik molekul – Maleis" lang="ms" hreflang="ms" data-title="Fizik molekul" data-language-autonym="Bahasa Melayu" data-language-local-name="Maleis" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Molekylfysikk" title="Molekylfysikk – Noors - Nynorsk" lang="nn" hreflang="nn" data-title="Molekylfysikk" data-language-autonym="Norsk nynorsk" data-language-local-name="Noors - Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Molekylfysikk" title="Molekylfysikk – Noors - Bokmål" lang="nb" hreflang="nb" data-title="Molekylfysikk" data-language-autonym="Norsk bokmål" data-language-local-name="Noors - Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Fizyka_molekularna" title="Fizyka molekularna – Pools" lang="pl" hreflang="pl" data-title="Fizyka molekularna" data-language-autonym="Polski" data-language-local-name="Pools" 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/F%C3%ADsica_molecular" title="Física molecular – Portugees" lang="pt" hreflang="pt" data-title="Física molecular" data-language-autonym="Português" data-language-local-name="Portugees" 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/Fizica_molecular%C4%83" title="Fizica moleculară – Roemeens" lang="ro" hreflang="ro" data-title="Fizica moleculară" data-language-autonym="Română" data-language-local-name="Roemeens" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D1%8F%D1%80%D0%BD%D0%B0%D1%8F_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0" title="Молекулярная физика – Russisch" lang="ru" hreflang="ru" data-title="Молекулярная физика" data-language-autonym="Русский" data-language-local-name="Russisch" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D0%B0%D1%80%D0%BD%D0%B0_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0" title="Молекуларна физика – Servisch" lang="sr" hreflang="sr" data-title="Молекуларна физика" data-language-autonym="Српски / srpski" data-language-local-name="Servisch" class="interlanguage-link-target"><span>Српски / 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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">verbergen</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Uit Wikipedia, de vrije encyclopedie</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="nl" dir="ltr"><p>De <b>molecuulfysica</b> is dat deelgebied van de <a href="/wiki/Natuurkunde" title="Natuurkunde">natuurkunde</a> dat de structuur en het gedrag van <a href="/wiki/Molecuul" title="Molecuul">moleculen</a> onderzoekt. Zij is gebaseerd op de inzichten uit de <a href="/wiki/Atoomfysica" title="Atoomfysica">atoomfysica</a> en de <a href="/wiki/Kwantummechanica" title="Kwantummechanica">kwantummechanica</a>. Een belangrijk model voor de berekening van molecuuleigenschappen is de <a href="/wiki/Born-Oppenheimerbenadering" title="Born-Oppenheimerbenadering">Born-Oppenheimerbenadering</a>. </p><p>Een belangrijke methode in de molecuulfysica is de <a href="/wiki/Spectroscopie" title="Spectroscopie">spectroscopie</a>, waarin niet alleen de <a href="/wiki/Energieniveau" title="Energieniveau">energieniveaus</a> van de <a href="/wiki/Elektron" title="Elektron">elektronen</a>, maar ook de <a href="/wiki/Trilling" title="Trilling">trillings</a>- en <a href="/wiki/Rotatie_(natuurkunde)" title="Rotatie (natuurkunde)">rotatietoestanden</a> worden beschreven. Het in de atoomfysica belangrijke <a href="/wiki/Orbitaal" title="Orbitaal">orbitaalmodel</a> wordt in de molecuulfysica uitgebreid met molecuulorbitalen. </p><p>De molecuulfysica kan worden gezien als een grensgebied tussen natuurkunde en <a href="/wiki/Scheikunde" title="Scheikunde">scheikunde</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Molecuulspectra">Molecuulspectra</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecuulfysica&veaction=edit&section=1" title="Bewerk dit kopje: Molecuulspectra" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Molecuulfysica&action=edit&section=1" title="De broncode bewerken van de sectie: Molecuulspectra"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In moleculen worden de (van <a href="/wiki/Atoom" title="Atoom">atomen</a> bekende) energieniveaus van de elektronen onderverdeeld in trillingstoestanden, en deze laatste verder in rotatietoestanden. De energieverschillen tussen de elektronentoestanden zijn het grootst en liggen bij enkele <a href="/wiki/Elektronvolt" title="Elektronvolt">elektronvolts</a>, en de bijbehorende straling ligt ongeveer in het zichtbare gebied. De straling van trillingsovergangen ligt in het midden-<a href="/wiki/Infrarood" title="Infrarood">infrarood</a> (ongeveer tussen 3 en 10 <a href="/wiki/Meter#Micrometer" title="Meter">µm</a>); die van rotatieovergangen liggen in het ver-infrarood (ongeveer tussen 30 en 150 µm). Het spectrum van een molecuul bestaat in het algemeen uit veel meer lijnen dan dat van een atoom. Bij de verandering van de toestand van een elektron behoort een zogenaamd <i>bandensysteem</i>, waarbij elke afzonderlijke band overeenkomt met een gelijktijdige trillingsovergang bij een elektronenovergang. Elke band bestaat weer uit afzonderlijke spectraallijnen, waar steeds een tegelijk met de elektronenovergang en de trillingsovergang plaatsvindende rotatieovergang bijhoort. </p><p>We bekijken hier vooral tweeatomige moleculen, waarbij de toestanden eenvoudiger kunnen worden weergegeven. </p> <div class="mw-heading mw-heading3"><h3 id="Rotatie_van_een_tweeatomig_molecuul">Rotatie van een tweeatomig molecuul</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecuulfysica&veaction=edit&section=2" title="Bewerk dit kopje: Rotatie van een tweeatomig molecuul" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Molecuulfysica&action=edit&section=2" title="De broncode bewerken van de sectie: Rotatie van een tweeatomig molecuul"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Bestand:Rotational_spectrum_example.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Rotational_spectrum_example.png/260px-Rotational_spectrum_example.png" decoding="async" width="260" height="319" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Rotational_spectrum_example.png/390px-Rotational_spectrum_example.png 1.5x, //upload.wikimedia.org/wikipedia/commons/3/35/Rotational_spectrum_example.png 2x" data-file-width="409" data-file-height="502" /></a><figcaption>Voorbeeld van een rotatiespectrum.</figcaption></figure> <p>Voor lage rotatiekwantumgetallen, dat wil zeggen wanneer het molecuul niet zo snel draait dat de afstand tot de kern merkbaar toeneemt, kan men bij benadering het molecuul als star beschouwen. Dat betekent dat de afstand tussen de atoomkernen constant is. Het impulsmoment (<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 {\vec {L}}_{N}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {L}}_{N}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74061485ff6fb028bf9130d93d8a61cd23426296" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.274ex; height:3.176ex;" alt="{\displaystyle {\vec {L}}_{N}}"></span> genaamd, hoewel het bijbehorende kwantumgetal <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 J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/359e4f407b49910e02c27c2f52e87a36cd74c053" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.471ex; height:2.176ex;" alt="{\displaystyle J}"></span> wordt genoemd) wordt gekwantiseerd: </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 |{\vec {L}}_{N}|={\sqrt {J\cdot (J+1)}}\cdot \hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>J</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>J</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </msqrt> </mrow> <mo>⋅</mo> <mi class="MJX-variant">ℏ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |{\vec {L}}_{N}|={\sqrt {J\cdot (J+1)}}\cdot \hbar }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbe0160dcb592f032406d863aa22c4ca6000e43e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:23.41ex; height:4.843ex;" alt="{\displaystyle |{\vec {L}}_{N}|={\sqrt {J\cdot (J+1)}}\cdot \hbar }"></span></dd></dl> <p>waarin <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 J=0,1,2,\ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J=0,1,2,\ldots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc83d911b21544fbb781ed64b171ba767f7468bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.882ex; height:2.509ex;" alt="{\displaystyle J=0,1,2,\ldots }"></span> de rotatiekwantumgetallen en <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 \hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">ℏ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hbar }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de68de3a92517953436c93b5a76461d49160cc41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.306ex; height:2.176ex;" alt="{\displaystyle \hbar }"></span> de <a href="/wiki/Constante_van_Dirac" title="Constante van Dirac">constante van Dirac</a> is. De rotatie-energie bedraagt </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E={\frac {|{\vec {L}}_{N}|^{2}}{2\cdot I}}={\frac {J\cdot (J+1)\cdot \hbar ^{2}}{2\cdot I}}=h\cdot c\cdot B\cdot J\cdot (J+1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <mo>⋅</mo> <mi>I</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>J</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>J</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>⋅</mo> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <mo>⋅</mo> <mi>I</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>h</mi> <mo>⋅</mo> <mi>c</mi> <mo>⋅</mo> <mi>B</mi> <mo>⋅</mo> <mi>J</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>J</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E={\frac {|{\vec {L}}_{N}|^{2}}{2\cdot I}}={\frac {J\cdot (J+1)\cdot \hbar ^{2}}{2\cdot I}}=h\cdot c\cdot B\cdot J\cdot (J+1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84db89fcae6d9064a563c38c6dd51906fd8a06eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:52.436ex; height:6.176ex;" alt="{\displaystyle E={\frac {|{\vec {L}}_{N}|^{2}}{2\cdot I}}={\frac {J\cdot (J+1)\cdot \hbar ^{2}}{2\cdot I}}=h\cdot c\cdot B\cdot J\cdot (J+1)}"></span></dd></dl> <p>waarin <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> het <a href="/wiki/Traagheidsmoment" title="Traagheidsmoment">traagheidsmoment</a> is en </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 B={\frac {h}{8\cdot \pi ^{2}\cdot c\cdot I}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mrow> <mn>8</mn> <mo>⋅</mo> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⋅</mo> <mi>c</mi> <mo>⋅</mo> <mi>I</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B={\frac {h}{8\cdot \pi ^{2}\cdot c\cdot I}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ff1ca10c2967ba5242522becede91eb0d0e1642" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:16.465ex; height:5.676ex;" alt="{\displaystyle B={\frac {h}{8\cdot \pi ^{2}\cdot c\cdot I}}}"></span></dd></dl> <p>de zogenaamde rotatieconstante van het molecuul is. Door spectroscopische metingen kan men de rotatieconstante bepalen en daaruit het traagheidsmoment berekenen. </p><p>De afstand tussen de energieniveaus <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 J=n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> <mo>=</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J=n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b62b3b18819d64341c38e4963254e2c81bf60c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.965ex; height:2.176ex;" alt="{\displaystyle J=n}"></span> en <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 J=n+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> <mo>=</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J=n+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd9ff310e434b41aaffc4ec41a15b6e7d341e88d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.967ex; height:2.343ex;" alt="{\displaystyle J=n+1}"></span> bedraagt <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 \Delta E=(2+2n)hcB}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>E</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>+</mo> <mn>2</mn> <mi>n</mi> <mo stretchy="false">)</mo> <mi>h</mi> <mi>c</mi> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E=(2+2n)hcB}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dadc10814a62dbe1571672f9980f6f3368b57da7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.289ex; height:2.843ex;" alt="{\displaystyle \Delta E=(2+2n)hcB}"></span>. Deze afstand neemt dus toe bij groter wordend kwantumgetal. De <a href="/w/index.php?title=Selectieregel&action=edit&redlink=1" class="new" title="Selectieregel (de pagina bestaat niet)">selectieregel</a> voor overgangen met absorptie of emissie van een foton is <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 \Delta J=\pm 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>J</mi> <mo>=</mo> <mo>±</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta J=\pm 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35803d1c0393614d659718c69d6cad918591ca2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.476ex; height:2.176ex;" alt="{\displaystyle \Delta J=\pm 1}"></span>; bovendien moet het molecuul een permanent dipoolmoment hebben, hetgeen bij moleculen met twee gelijksoortige atomen niet het geval is. Daarom hebben deze moleculen geen rotatiespectrum. </p><p>De energieverschillen tussen rotatieniveaus zitten in de grootteorde van de thermische energie van deeltjes bij kamertemperatuur. In thermisch evenwicht zijn de energietoestanden bezet volgens de <a href="/wiki/Maxwell-Boltzmann-verdeling" title="Maxwell-Boltzmann-verdeling">boltzmannverdeling</a>. Daarbij dient men zich te realiseren dat het bij een toestand met kwantumgetal <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 J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/359e4f407b49910e02c27c2f52e87a36cd74c053" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.471ex; height:2.176ex;" alt="{\displaystyle J}"></span> eigenlijk om <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 2J+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>J</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2J+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af84ba0091d0322eb8e12725eda45497519095e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.637ex; height:2.343ex;" alt="{\displaystyle 2J+1}"></span> ontaarde toestanden gaat met richtingsquantumgetallen <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_{J}=-J,-J+1,\ldots ,-1,0,1,\ldots ,J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>J</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi>J</mi> <mo>,</mo> <mo>−</mo> <mi>J</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{J}=-J,-J+1,\ldots ,-1,0,1,\ldots ,J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b9077c04a6e94ed275d747c5976bbe91d8bffa2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:37.198ex; height:2.509ex;" alt="{\displaystyle m_{J}=-J,-J+1,\ldots ,-1,0,1,\ldots ,J}"></span>. De bezettingsgraad is daarom evenredig met </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 (2J+1)\cdot e^{-{\frac {hcBJ(J+1)}{kT}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>2</mn> <mi>J</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>⋅</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>h</mi> <mi>c</mi> <mi>B</mi> <mi>J</mi> <mo stretchy="false">(</mo> <mi>J</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>k</mi> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (2J+1)\cdot e^{-{\frac {hcBJ(J+1)}{kT}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70c91a88dc6315b24445c7bd14ada95b13117e6a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.348ex; height:4.509ex;" alt="{\displaystyle (2J+1)\cdot e^{-{\frac {hcBJ(J+1)}{kT}}}}"></span></dd></dl> <p>Het rotatiespectrum is bovendien nog afhankelijk van de overgangswaarschijnlijkheden tussen de toestanden. Wanneer deze ongeveer gelijk zijn, geven de intensiteiten van de spectraallijnen ongeveer de overgangswaarschijnlijkheden weer. Typisch neemt de bezettingsgraad vanaf <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 J=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/602b5a2850816186aad083feaa57acd3276e3dc9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.732ex; height:2.176ex;" alt="{\displaystyle J=0}"></span> met toenemende <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 J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/359e4f407b49910e02c27c2f52e87a36cd74c053" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.471ex; height:2.176ex;" alt="{\displaystyle J}"></span> aanvankelijk met een factor <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 2J+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>J</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2J+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af84ba0091d0322eb8e12725eda45497519095e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.637ex; height:2.343ex;" alt="{\displaystyle 2J+1}"></span> tot een maximum, om dan weer exponentieel af te nemen. De rotatiespectra zien er dan ook vaak zo uit. De afstanden tussen de spectraallijnen zijn daarbij allemaal gelijk, omdat de afstanden tussen de energieniveaus bij een toename van <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 J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/359e4f407b49910e02c27c2f52e87a36cd74c053" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.471ex; height:2.176ex;" alt="{\displaystyle J}"></span> met 1 steeds met <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 2hcB}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>h</mi> <mi>c</mi> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2hcB}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eca2a566ba36df68701a835178ecc2e4803a5559" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.272ex; height:2.176ex;" alt="{\displaystyle 2hcB}"></span> toenemen en door de selectieregel alleen overgangen naar het eerstvolgende niveau mogelijk zijn. </p> <div class="mw-heading mw-heading3"><h3 id="Trillingen_van_een_tweeatomig_molecuul">Trillingen van een tweeatomig molecuul</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecuulfysica&veaction=edit&section=3" title="Bewerk dit kopje: Trillingen van een tweeatomig molecuul" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Molecuulfysica&action=edit&section=3" title="De broncode bewerken van de sectie: Trillingen van een tweeatomig molecuul"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>De atomen van een tweeatomig, haltervormig molecuul kunnen ook ten opzichte van elkaar trillen. De eenvoudigste benadering is hierbij een harmonische trilling; de potentiële energie van een atoom moet hierbij toenemen met het kwadraat van de afstand tot de evenwichtsafstand <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb12fcfddb65e3d1e6a044215f6e833f0cd4337b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.103ex; height:2.009ex;" alt="{\displaystyle r_{0}}"></span> ten opzichte van het andere atoom. De energieniveaus van een kwantummechanische <a href="/wiki/Harmonische_oscillator" title="Harmonische oscillator">harmonische oscillator</a> (kwantumgetal <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 \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span>) zijn equidistant: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\nu }=\hbar \omega _{0}\cdot (\nu +{\tfrac {1}{2}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>ν</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\nu }=\hbar \omega _{0}\cdot (\nu +{\tfrac {1}{2}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cc30624153780b61539db2957bf9739d896eabc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:18.943ex; height:3.509ex;" alt="{\displaystyle E_{\nu }=\hbar \omega _{0}\cdot (\nu +{\tfrac {1}{2}})}"></span></dd></dl> <p>Reële moleculen wijken echter sterk af van dit gedrag. De potentiaal is niet harmonisch en neemt bij afnemende afstand tot het andere molecuul veel sterker toe dan bij het toenemende afstand – hier nadert hij asymptotisch naar de dissociatie-energie <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_{\text{dis}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>dis</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\text{dis}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4c5c75b0a069a72a090858e8adf4ba1e9084fbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.967ex; height:2.509ex;" alt="{\displaystyle E_{\text{dis}}}"></span> van het molecuul. Een betere benadering dan de harmonische potentiaal is de zogenaamde <a href="/w/index.php?title=Morsepotentiaal&action=edit&redlink=1" class="new" title="Morsepotentiaal (de pagina bestaat niet)">Morsepotentiaal</a>. Deze functie geeft de werkelijke potentiaal veel beter weer en de <a href="/wiki/Schr%C3%B6dingervergelijking" title="Schrödingervergelijking">schrödingervergelijking</a> is desondanks nog analytisch oplosbaar. Voor zeer kleine afstanden wordt hij niet oneindig groot: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\text{pot}}=E_{0}+E_{\text{dis}}\cdot \left(1-e^{-a\cdot (r-r_{0})}\right)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>pot</mtext> </mrow> </msub> <mo>=</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"> <mtext>dis</mtext> </mrow> </msub> <mo>⋅</mo> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>a</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>r</mi> <mo>−</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\text{pot}}=E_{0}+E_{\text{dis}}\cdot \left(1-e^{-a\cdot (r-r_{0})}\right)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af5409f0e643316be246e7d950f35f5ca5c883ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:35.304ex; height:5.176ex;" alt="{\displaystyle E_{\text{pot}}=E_{0}+E_{\text{dis}}\cdot \left(1-e^{-a\cdot (r-r_{0})}\right)^{2}}"></span></dd></dl> <p><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}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/411d268de7b1cf300d7481e3fe59f3b20887e0d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.769ex; height:2.509ex;" alt="{\displaystyle E_{0}}"></span> is de nulpuntsenergie van de potentiaal, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> is een parameter: </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 a={\sqrt {\frac {k}{2\cdot E_{\text{dis}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mi>k</mi> <mrow> <mn>2</mn> <mo>⋅</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>dis</mtext> </mrow> </msub> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a={\sqrt {\frac {k}{2\cdot E_{\text{dis}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/234cbf8ef308f5a52447849f903badd3eb9e251a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:14.296ex; height:7.509ex;" alt="{\displaystyle a={\sqrt {\frac {k}{2\cdot E_{\text{dis}}}}}}"></span></dd></dl> <p>Hierin is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> de veerconstante van de best-passende harmonische potentiaal. </p><p>De energieniveaus kunnen nu met de schrödingervergelijking worden berekend: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\nu }=\hbar \omega _{0}\cdot (\nu +{\tfrac {1}{2}})-{\frac {\hbar ^{2}\omega _{0}^{2}}{4E_{\text{dis}}}}\cdot (\nu +{\tfrac {1}{2}})^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>ν</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo stretchy="false">)</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mrow> <mn>4</mn> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>dis</mtext> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>ν</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\nu }=\hbar \omega _{0}\cdot (\nu +{\tfrac {1}{2}})-{\frac {\hbar ^{2}\omega _{0}^{2}}{4E_{\text{dis}}}}\cdot (\nu +{\tfrac {1}{2}})^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a56ef8d6320297309f07c876dd41d5e5324d9eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:38.022ex; height:6.343ex;" alt="{\displaystyle E_{\nu }=\hbar \omega _{0}\cdot (\nu +{\tfrac {1}{2}})-{\frac {\hbar ^{2}\omega _{0}^{2}}{4E_{\text{dis}}}}\cdot (\nu +{\tfrac {1}{2}})^{2}}"></span></dd></dl> <p>In tegenstelling tot de harmonische oscillator zijn de toegestane trillingsniveaus nu niet meer equidistant, maar neemt hun afstand bij benadering af met <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 1/\nu ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/\nu ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9fd98d63543224031d630801550b320508f3d2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.636ex; height:3.176ex;" alt="{\displaystyle 1/\nu ^{2}}"></span>. Daarmee is voldaan aan het <a href="/wiki/Correspondentieprincipe" title="Correspondentieprincipe">correspondentieprincipe</a>: bij naderen van de dissociatie-energie liggen de toegestane niveaus praktisch oneindig dicht bij elkaar. </p><p>De selectieregels voor overgangen tussen trillingsniveaus zijn <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 \Delta \nu =\pm 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>ν</mi> <mo>=</mo> <mo>±</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \nu =\pm 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12f3baa4627d002426f277c8f0ee75e54dd8e602" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.237ex; height:2.176ex;" alt="{\displaystyle \Delta \nu =\pm 1}"></span> voor een harmonische oscillator; voor de niet-harmonische oscillator zijn ook <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 \Delta \nu =\pm 2,\pm 3,\ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>ν</mi> <mo>=</mo> <mo>±</mo> <mn>2</mn> <mo>,</mo> <mo>±</mo> <mn>3</mn> <mo>,</mo> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \nu =\pm 2,\pm 3,\ldots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d083a4f442ec406fbba2668755de8e2f7a26b1f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.999ex; height:2.509ex;" alt="{\displaystyle \Delta \nu =\pm 2,\pm 3,\ldots }"></span> met afnemende waarschijnlijkheid toegestaan. Men neemt zelden zuivere trillingsspectra waar, omdat er rotatiespectra op gesuperponeerd zitten. </p> <div class="mw-heading mw-heading3"><h3 id="Rotatie-trillingswisselwerking">Rotatie-trillingswisselwerking</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecuulfysica&veaction=edit&section=4" title="Bewerk dit kopje: Rotatie-trillingswisselwerking" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Molecuulfysica&action=edit&section=4" title="De broncode bewerken van de sectie: Rotatie-trillingswisselwerking"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Bestand:Carbon_monoxide_rotational-vibrational_spectrum.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carbon_monoxide_rotational-vibrational_spectrum.svg/260px-Carbon_monoxide_rotational-vibrational_spectrum.svg.png" decoding="async" width="260" height="191" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carbon_monoxide_rotational-vibrational_spectrum.svg/390px-Carbon_monoxide_rotational-vibrational_spectrum.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carbon_monoxide_rotational-vibrational_spectrum.svg/520px-Carbon_monoxide_rotational-vibrational_spectrum.svg.png 2x" data-file-width="367" data-file-height="269" /></a><figcaption>Rotatie-trillings spectrum van <a href="/wiki/Koolstofmonoxide" title="Koolstofmonoxide">koolstofmonoxide</a>.</figcaption></figure> <p>Doordat het traagheidsmoment van een molecuul ten gevolge van de trillingen schommelt, moet men voor nauwkeurigere berekeningen bij de energie van het molecuul de energie van de trillings-rotatiewisselwerking optellen. Als men voor de totale energie uitgaat van de volgende benadering: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\nu J}=\sum _{j=0}^{\infty }\sum _{k=0}^{\infty }Y_{jk}(\nu +{\tfrac {1}{2}})^{j}J^{k}(J+1)^{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> <mi>J</mi> </mrow> </msub> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>ν</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msup> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mi>J</mi> <mo>+</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\nu J}=\sum _{j=0}^{\infty }\sum _{k=0}^{\infty }Y_{jk}(\nu +{\tfrac {1}{2}})^{j}J^{k}(J+1)^{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cbcab676bd1ff44008dab20496c552a6d45cbe3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:36.995ex; height:7.176ex;" alt="{\displaystyle E_{\nu J}=\sum _{j=0}^{\infty }\sum _{k=0}^{\infty }Y_{jk}(\nu +{\tfrac {1}{2}})^{j}J^{k}(J+1)^{k}}"></span></dd></dl> <p>dan kan men de zogenaamde Dunhamcoëfficiënten <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 Y_{jk}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{jk}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91d4c31e0a5b0008e57a1dce06449a4cb63f20fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.117ex; height:2.843ex;" alt="{\displaystyle Y_{jk}}"></span> aan de experimentele resultaten aanpassen. </p><p>De effectieve potentiaal voor de molecuultrilling van een tweeatomig molecuul wordt door de rotatie verhoogd: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\text{pot}}=E_{\text{pot,0}}+{\frac {J(J+1)\hbar ^{2}}{2Mr^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>pot</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>pot,0</mtext> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>J</mi> <mo stretchy="false">(</mo> <mi>J</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <mi>M</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\text{pot}}=E_{\text{pot,0}}+{\frac {J(J+1)\hbar ^{2}}{2Mr^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87d17fde2cb021564c73dbfa5ef6557c4e4ee616" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:27.832ex; height:6.176ex;" alt="{\displaystyle E_{\text{pot}}=E_{\text{pot,0}}+{\frac {J(J+1)\hbar ^{2}}{2Mr^{2}}}}"></span></dd></dl> <p>waarin <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_{\text{pot}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>pot</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\text{pot}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0b009b781f13e91a3cd74b47f2f0b8fe3a12269" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.323ex; height:2.843ex;" alt="{\displaystyle E_{\text{pot}}}"></span> de potentiaal zonder trilling is. </p><p>Daardoor ontstaat bij hogere rotatiekwantumgetallen een zogenaamde rotatiebarrière: bij toenemende afstand tot de atoomkernen neemt de effectieve potentiaal toe van een minimum (evenwichtstoestand) tot een maximum (de rotatiebarrière), dat reeds boven de dissociatie-energie ligt, om daarna weer af te nemen tot de dissociatie-energie. Daardoor kan het molecuul zich in een trillingstoestand „achter” de rotatiebarrière bevinden waarvan de energie hoger is dan de dissociatie-energie. Er kan dan door het <a href="/wiki/Tunneleffect" title="Tunneleffect">tunneleffect</a> dissociatie optreden. Bij zeer hoge rotatiekwantumgetallen komt ook het potentiaalminimum boven de dissociatie-energie te liggen; bij nog hogere rotatiekwantumgetallen is er ten slotte geen minimum meer en zijn er daardoor ook geen stabiele toestanden meer. </p> <div class="mw-heading mw-heading3"><h3 id="Elektronentoestanden_van_tweeatomige_moleculen">Elektronentoestanden van tweeatomige moleculen</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecuulfysica&veaction=edit&section=5" title="Bewerk dit kopje: Elektronentoestanden van tweeatomige moleculen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Molecuulfysica&action=edit&section=5" title="De broncode bewerken van de sectie: Elektronentoestanden van tweeatomige moleculen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Net als bij atomen wordt ook hier de toestand van en elektron beschreven door een hoofdkwantumgetal <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> en een baanimpulsmoment-kwantumgetal <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span>, waaraan, net als bij atomen, bij verschillende waarden de letters (s, p, d, f, ...) worden toegekend. Het elektrische veld is echter niet meer bolsymmetrisch, waardoor het baanimpulsmoment zich moet instellen ten opzichte van de verbindingslijn tussen de kernen. De projectie van het baanimpulsmoment <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 {\vec {L}}_{l}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {L}}_{l}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c156e841962575ed8a97ab54dfc5fab97c596c18" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.305ex; height:3.176ex;" alt="{\displaystyle {\vec {L}}_{l}}"></span> op deze verbindingslijn noemt men <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 {\vec {L}}_{\lambda }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {L}}_{\lambda }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66f55406a45b5c0482c600ebcef74399d7b60b67" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.773ex; height:3.176ex;" alt="{\displaystyle {\vec {L}}_{\lambda }}"></span>, met het bijbehorende kwantumgetal <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 \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span>. Voor de verschillende waarden van <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 \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span> gebruikt men Griekse letters die overeenkomen met de Latijnse letters voor de waarden van <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> (<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 \sigma ,\pi ,\delta ,\phi ,\ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mo>,</mo> <mi>π</mi> <mo>,</mo> <mi>δ</mi> <mo>,</mo> <mi>ϕ</mi> <mo>,</mo> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma ,\pi ,\delta ,\phi ,\ldots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16661a68dc3a897b97561b6a641b49cf2077f550" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.955ex; height:2.676ex;" alt="{\displaystyle \sigma ,\pi ,\delta ,\phi ,\ldots }"></span>). Men schrijft dan bijvoorbeeld de grondtoestand van het waterstofmolecuul als <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 (1s\sigma ^{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mi>s</mi> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1s\sigma ^{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9790704a40fe1496520d4640401a99abe2bdc062" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.447ex; height:3.176ex;" alt="{\displaystyle (1s\sigma ^{2})}"></span>: 2 elektronen bevinden zich in de grondtoestand <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=1,l=0,\lambda =0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>l</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>λ</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=1,l=0,\lambda =0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd0295caced3e47bd30c8be79a01d569e8509ee7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.294ex; height:2.509ex;" alt="{\displaystyle n=1,l=0,\lambda =0}"></span>. </p><p>De koppeling van de afzonderlijke impulsmomenten tot een molecuulimpulsmoment geschiedt in de praktijk in verschillende volgordes, afhankelijk van de sterkte van de wisselwerkingen; men spreekt dan van de <a href="/wiki/Regel_van_Hund" title="Regel van Hund">regels van Hund</a> (a) - (e) (genoemd naar <a href="/wiki/Friedrich_Hund" title="Friedrich Hund">Friedrich Hund</a>). </p><p>De som van de op de verbindingslijn door de kernen geprojecteerde banimpulsmomenten noemt men <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 {\vec {L}}_{\Lambda }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Λ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {L}}_{\Lambda }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04795324fca172d34e496a8ca39edc439561b25a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.956ex; height:3.176ex;" alt="{\displaystyle {\vec {L}}_{\Lambda }}"></span>, met het kwantumgetal <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 \Lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ac0a4a98a414e3480335f9ba652d12571ec6733" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.613ex; height:2.176ex;" alt="{\displaystyle \Lambda }"></span>. De som van de eigen impulsmomenten van de elektronen (spins) noemt men, net als bij een atoom, <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 {\vec {L}}_{S}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {L}}_{S}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4292c68490981d640007b3ac18ef1be9cea52769" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.875ex; height:3.176ex;" alt="{\displaystyle {\vec {L}}_{S}}"></span>, met het kwantumgetal <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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>. De projectie van deze totale spin op de verbindingslijn door de kernen wordt <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 {\vec {L}}_{\Sigma }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Σ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {L}}_{\Sigma }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f1c63a7352e3a7c79fef1fee2e0c048f4dd9eeb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.002ex; height:3.176ex;" alt="{\displaystyle {\vec {L}}_{\Sigma }}"></span> genoemd, met het kwantumgetal <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 \Sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e1f558f53cda207614abdf90162266c70bc5c1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Sigma }"></span>. De som van <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 {\vec {L}}_{\Lambda }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Λ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {L}}_{\Lambda }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04795324fca172d34e496a8ca39edc439561b25a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.956ex; height:3.176ex;" alt="{\displaystyle {\vec {L}}_{\Lambda }}"></span> en <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 {\vec {L}}_{\Sigma }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Σ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {L}}_{\Sigma }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f1c63a7352e3a7c79fef1fee2e0c048f4dd9eeb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.002ex; height:3.176ex;" alt="{\displaystyle {\vec {L}}_{\Sigma }}"></span> heet <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 {\vec {L}}_{\Omega }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Ω</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {L}}_{\Omega }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83fd090e9fd62ec0a89914c8d767230bc396dcdf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.002ex; height:3.176ex;" alt="{\displaystyle {\vec {L}}_{\Omega }}"></span>, met het kwantumgetal <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 \Omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24b0d5ca6f381068d756f6337c08e0af9d1eeb6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Omega }"></span>. Het mechanische impulsmoment van het molecuul heeft ook nog een wisselwerking met de impulsmomenten van de elektronen. </p><p>Voor de elektronentoestanden worden vaak ook andere notaties gebruikt: X is dan de grondtoestand; A, B, C, ... staan voor de aangeslagen toestanden (kleine letters a, b, c, ... worden meestal gebruikt voor triplettoestanden). </p> <div class="mw-heading mw-heading2"><h2 id="De_totale_energie_van_een_molecuul">De totale energie van een molecuul</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecuulfysica&veaction=edit&section=6" title="Bewerk dit kopje: De totale energie van een molecuul" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Molecuulfysica&action=edit&section=6" title="De broncode bewerken van de sectie: De totale energie van een molecuul"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>De totale energie van een molecuul in formule-vorm: </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 T_{\text{totaal}}=T_{\text{e}}+T_{\text{k}}+V_{\text{ee}}+V_{\text{kk}}+V_{\text{ek}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>totaal</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>k</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ee</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>kk</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ek</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\text{totaal}}=T_{\text{e}}+T_{\text{k}}+V_{\text{ee}}+V_{\text{kk}}+V_{\text{ek}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac9e75adf329075255eb6c3827a16e4c42a7edda" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:34.587ex; height:2.509ex;" alt="{\displaystyle T_{\text{totaal}}=T_{\text{e}}+T_{\text{k}}+V_{\text{ee}}+V_{\text{kk}}+V_{\text{ek}}}"></span></dd></dl> <p>waarin </p> <table> <tbody><tr> <td style="padding: 0.75em 0 0.75em 2em;"><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 T_{\text{e}}=-{\tfrac {1}{2}}\sum _{i=1}^{N}\Delta _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\text{e}}=-{\tfrac {1}{2}}\sum _{i=1}^{N}\Delta _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19a44b31c38b2908db7cbd37c1bf78bdfd98cc5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:15.749ex; height:7.343ex;" alt="{\displaystyle T_{\text{e}}=-{\tfrac {1}{2}}\sum _{i=1}^{N}\Delta _{i}}"></span> </td> <td style="padding-left: 1.5em;">de kinetische energie van de elektronen </td></tr> <tr> <td style="padding: 0.75em 0 0.75em 2em;"><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 T_{\text{k}}=-{\tfrac {1}{2}}\sum _{\mu =1}^{N}{\frac {1}{m_{\mu }}}\Delta _{\mu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>k</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> </mfrac> </mrow> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\text{k}}=-{\tfrac {1}{2}}\sum _{\mu =1}^{N}{\frac {1}{m_{\mu }}}\Delta _{\mu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f58b0c4328511b543603f1e62f75b36ac74d4ed9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:20.411ex; height:7.676ex;" alt="{\displaystyle T_{\text{k}}=-{\tfrac {1}{2}}\sum _{\mu =1}^{N}{\frac {1}{m_{\mu }}}\Delta _{\mu }}"></span> </td> <td style="padding-left: 1.5em;">de kinetische energie van de atoomkernen </td></tr> <tr> <td style="padding: 0.75em 0 0.75em 2em;"><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 V_{\text{ee}}=\sum _{i=1}^{N-1}\sum _{j>i}^{N}{\frac {1}{r_{ij}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ee</mtext> </mrow> </msub> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> <mo>−</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>></mo> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\text{ee}}=\sum _{i=1}^{N-1}\sum _{j>i}^{N}{\frac {1}{r_{ij}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c2914527f07033858c1721d4e860e8ae333f912" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:17.197ex; height:7.676ex;" alt="{\displaystyle V_{\text{ee}}=\sum _{i=1}^{N-1}\sum _{j>i}^{N}{\frac {1}{r_{ij}}}}"></span> </td> <td style="padding-left: 1.5em;">de potentiële energie van de wisselwerking tussen de elektronen </td></tr> <tr> <td style="padding: 0.75em 0 0.75em 2em;"><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 V_{\text{kk}}=\sum _{\mu =1}^{M-1}\sum _{\nu >\mu }^{M}{\frac {Z_{\mu }Z_{\nu }}{R_{\mu \nu }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>kk</mtext> </mrow> </msub> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> <mo>−</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> <mo>></mo> <mi>μ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> </mrow> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\text{kk}}=\sum _{\mu =1}^{M-1}\sum _{\nu >\mu }^{M}{\frac {Z_{\mu }Z_{\nu }}{R_{\mu \nu }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca2a6598a4afb4d31780a3e175bef5016a0bc0d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:20.717ex; height:7.676ex;" alt="{\displaystyle V_{\text{kk}}=\sum _{\mu =1}^{M-1}\sum _{\nu >\mu }^{M}{\frac {Z_{\mu }Z_{\nu }}{R_{\mu \nu }}}}"></span> </td> <td style="padding-left: 1.5em;">de potentiële energie van de wisselwerking tussen de kernen </td></tr> <tr> <td style="padding: 0.75em 0 0.75em 2em;"><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 V_{\text{ek}}=-\sum _{i=1}^{N}\sum _{\mu =1}^{M}{\frac {Z_{\mu }}{R_{i\mu }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ek</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>μ</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\text{ek}}=-\sum _{i=1}^{N}\sum _{\mu =1}^{M}{\frac {Z_{\mu }}{R_{i\mu }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a05f9e67a3e0b52439ac8d142971b2d9a6ad04f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:20.354ex; height:7.676ex;" alt="{\displaystyle V_{\text{ek}}=-\sum _{i=1}^{N}\sum _{\mu =1}^{M}{\frac {Z_{\mu }}{R_{i\mu }}}}"></span> </td> <td style="padding-left: 1.5em;">de potentiële energie van de wisselwerking tussen de elektronen en de atoomkernen. </td></tr></tbody></table> <p>Hierbij zijn <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> en <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 j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span> de indices voor de elektronen, <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 \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span> en <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 \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span> respectievelijk de indices voor de atoomkernen, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{ij}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/857845aef8b93395ad10279211c6c49180bb8791" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.526ex; height:2.343ex;" alt="{\displaystyle r_{ij}}"></span> de afstand tussen de elektronen <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> en <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 j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\mu \nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\mu \nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5ee22d1a052bee0115efb8b5ffdaf10b04e42aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.859ex; height:2.843ex;" alt="{\displaystyle R_{\mu \nu }}"></span> de afstand tussen de kernen <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 \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span> en <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 \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{i\mu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>μ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{i\mu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1906fdd54e0defaaa8d7299199ccc7828f36d71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.555ex; height:2.843ex;" alt="{\displaystyle R_{i\mu }}"></span> de afstand tussen elektron <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> en kern <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 \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span>, en <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 Z_{\mu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{\mu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d767f086f2662e890e203c2bc7f0b621e3eefdf7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.811ex; height:2.843ex;" alt="{\displaystyle Z_{\mu }}"></span> het atoomnummer (kernladingsgetal) van atoomkern <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 \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span>. </p><p>In de praktijk wordt de volledige schrödingervegrelijking met behulp van de <a href="/wiki/Born-Oppenheimerbenadering" title="Born-Oppenheimerbenadering">Born-Oppenheimerbenaderingen</a> in een schrödingervergelijking voor elektronen (met vaste kerncoördinaten) en een schrödingervergelijking voor de kernen opgesplitst. De oplossing van de schrödingervergelijking voor de kernen vereist dan dat de oplossing van de schrödingervergelijking voor de elektronen voor alle relevante kerngeometrieën bekend is, omdat hij de energie als functie van de kerngeometrie nodig heeft. De schrödingervergelijking voor de elektronen verkrijgt men formeel door <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 T_{\text{k}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>k</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\text{k}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f6e456514fdf4356a8217a5b6c63a4c24452451" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.458ex; height:2.509ex;" alt="{\displaystyle T_{\text{k}}}"></span> te stellen. </p> <div class="mw-heading mw-heading2"><h2 id="Zie_ook">Zie ook</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecuulfysica&veaction=edit&section=7" title="Bewerk dit kopje: Zie ook" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Molecuulfysica&action=edit&section=7" title="De broncode bewerken van de sectie: Zie ook"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Atoomfysica" title="Atoomfysica">Atoomfysica</a></li> <li><a href="/wiki/Fysische_chemie" title="Fysische chemie">Fysische chemie</a></li> <li><a href="/wiki/Spectroscopie" title="Spectroscopie">Spectroscopie</a></li> <li><a href="/wiki/Franck-Condon-principe" title="Franck-Condon-principe">Franck-Condon-principe</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Literatuur">Literatuur</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecuulfysica&veaction=edit&section=8" title="Bewerk dit kopje: Literatuur" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Molecuulfysica&action=edit&section=8" title="De broncode bewerken van de sectie: Literatuur"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Hermann Haken, Hans-Christoph Wolf: <i>Molekülphysik und Quantenchemie: Einführung in die experimentellen und theoretischen Grundlagen.</i> Springer 2006, <span class="ISBN"><a href="/wiki/Speciaal:Boekbronnen/978-3-540-30315-2" title="Speciaal:Boekbronnen/978-3-540-30315-2">ISBN 978-3-540-30315-2</a></span>.</li></ul> <div class="interProject commons mw-list-item" style="display:none;"><a href="https://commons.wikimedia.org/wiki/Category:Molecular_physics#mw-subcategories" class="extiw" title="commons:Category:Molecular physics">Mediabestanden</a></div> <div class="interProjectTemplate interProject-groot toccolours" style="display:flex; gap:1em; align-items:center; clear:both; margin:1em 0 -0.5em 0;"> <div style="min-width:max-content;"><span class="noviewer noresize" typeof="mw:File"><a href="/wiki/Bestand:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/25px-Commons-logo.svg.png" decoding="async" width="25" height="34" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/38px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/50px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div>Zie de categorie <i><b><a href="https://commons.wikimedia.org/wiki/Category:Molecular_physics#mw-subcategories" class="extiw" title="commons:Category:Molecular physics">Molecuulfysica</a></b></i> van <a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons">Wikimedia Commons</a> voor mediabestanden over dit onderwerp.</div> </div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Overgenomen van "<a dir="ltr" href="https://nl.wikipedia.org/w/index.php?title=Molecuulfysica&oldid=59749132">https://nl.wikipedia.org/w/index.php?title=Molecuulfysica&oldid=59749132</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Categorie:Alles" title="Categorie:Alles">Categorieën</a>: <ul><li><a href="/wiki/Categorie:Molecuulfysica" title="Categorie:Molecuulfysica">Molecuulfysica</a></li><li><a href="/wiki/Categorie:Fysische_chemie" title="Categorie:Fysische chemie">Fysische chemie</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Deze pagina is voor het laatst bewerkt op 20 aug 2021 om 10:33.</li> <li id="footer-info-copyright">De tekst is beschikbaar onder de licentie <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.nl">Creative Commons Naamsvermelding/Gelijk delen</a>, er kunnen aanvullende voorwaarden van toepassing zijn. 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