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class="vector-toc-numb">2.1.2</span> <span>The solutions of the clamped-nuclei Schrödinger equation</span> </div> </a> <ul id="toc-The_solutions_of_the_clamped-nuclei_Schrödinger_equation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Born-Oppenheimer_approximation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Born-Oppenheimer_approximation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Born-Oppenheimer approximation</span> </div> </a> <ul id="toc-Born-Oppenheimer_approximation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-High-accuracy_ab_initio_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#High-accuracy_ab_initio_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>High-accuracy ab initio theory</span> </div> </a> <ul id="toc-High-accuracy_ab_initio_theory-sublist" class="vector-toc-list"> </ul> </li> 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id="toc-Occurrence_in_space" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Occurrence_in_space"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Occurrence in space</span> </div> </a> <button aria-controls="toc-Occurrence_in_space-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Occurrence in space subsection</span> </button> <ul id="toc-Occurrence_in_space-sublist" class="vector-toc-list"> <li id="toc-Formation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Formation"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Formation</span> </div> </a> <ul id="toc-Formation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Destruction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Destruction"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Destruction</span> </div> </a> <ul id="toc-Destruction-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Production_in_the_laboratory" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Production_in_the_laboratory"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Production in the laboratory</span> </div> </a> <ul id="toc-Production_in_the_laboratory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled 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class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Cati%C3%B3_dihidrogen" title="Catió dihidrogen – Catalan" lang="ca" hreflang="ca" data-title="Catió dihidrogen" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Dihydrogen-kation" title="Dihydrogen-kation – Danish" lang="da" hreflang="da" data-title="Dihydrogen-kation" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Diwasserstoff-Kation" title="Diwasserstoff-Kation – German" lang="de" hreflang="de" data-title="Diwasserstoff-Kation" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Cati%C3%B3n_dihidr%C3%B3geno" title="Catión dihidrógeno – Spanish" lang="es" hreflang="es" data-title="Catión dihidrógeno" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%A9%D8%A7%D8%AA%DB%8C%D9%88%D9%86_%D8%AF%DB%8C%E2%80%8C%D9%87%DB%8C%D8%AF%D8%B1%D9%88%DA%98%D9%86" title="کاتیون دی‌هیدروژن – Persian" lang="fa" hreflang="fa" data-title="کاتیون دی‌هیدروژن" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Dihydrog%C3%A8ne_(cation)" 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href="https://ja.wikipedia.org/wiki/%E6%B0%B4%E7%B4%A0%E5%88%86%E5%AD%90%E3%82%A4%E3%82%AA%E3%83%B3" title="水素分子イオン – Japanese" lang="ja" hreflang="ja" data-title="水素分子イオン" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%8Don_molecular_de_hidrog%C3%AAnio" title="Íon molecular de hidrogênio – Portuguese" lang="pt" hreflang="pt" data-title="Íon molecular de hidrogênio" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</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%D1%8B%D0%B9_%D0%B8%D0%BE%D0%BD_%D0%B2%D0%BE%D0%B4%D0%BE%D1%80%D0%BE%D0%B4%D0%B0" title="Молекулярный ион водорода – Russian" lang="ru" hreflang="ru" 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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Molecular ion</div> <style data-mw-deduplicate="TemplateStyles:r1084375498">.mw-parser-output .ib-chembox{border-collapse:collapse;text-align:left}.mw-parser-output .ib-chembox td,.mw-parser-output .ib-chembox th{border:1px solid #a2a9b1;width:40%}.mw-parser-output .ib-chembox td+td{width:60%}</style> <table class="infobox ib-chembox"> <caption>Dihydrogen cation </caption> <tbody><tr> <td colspan="2" style="text-align:center; padding:2px;"><span typeof="mw:File"><a href="/wiki/File:H2%2B_structure.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/H2%2B_structure.png/150px-H2%2B_structure.png" decoding="async" width="150" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/H2%2B_structure.png/225px-H2%2B_structure.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d0/H2%2B_structure.png/300px-H2%2B_structure.png 2x" data-file-width="366" data-file-height="208" /></a></span> </td></tr> <tr> <th colspan="2" style="background: #f8eaba; text-align: center;">Identifiers </th></tr> <tr> <td><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/CAS_Registry_Number" title="CAS Registry Number">CAS Number</a></div> </td> <td><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"><ul><li><span title="commonchemistry.cas.org"><a rel="nofollow" class="external text" href="https://commonchemistry.cas.org/detail?cas_rn=12184-90-6">12184-90-6</a></span></li><li>D<sub>2</sub><sup>+</sup>: <span title="commonchemistry.cas.org"><a rel="nofollow" class="external text" href="https://commonchemistry.cas.org/detail?cas_rn=12184-84-8">12184-84-8</a></span></li></ul></div> </td></tr> <tr> <td><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">3D model (<a href="/wiki/JSmol" class="mw-redirect" title="JSmol">JSmol</a>)</div> </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><span title="chemapps.stolaf.edu (3D interactive model)"><a rel="nofollow" class="external text" href="https://chemapps.stolaf.edu/jmol/jmol.php?model=%5BHH%2B%5D">Interactive image</a></span></li><li><sup>1</sup>H<sub>2</sub><sup>+</sup>: <span title="chemapps.stolaf.edu (3D interactive model)"><a rel="nofollow" class="external text" href="https://chemapps.stolaf.edu/jmol/jmol.php?model=%5B1H%5D%5B1H%2B%5D">Interactive image</a></span></li><li>D<sub>2</sub><sup>+</sup>: <span title="chemapps.stolaf.edu (3D interactive model)"><a rel="nofollow" class="external text" href="https://chemapps.stolaf.edu/jmol/jmol.php?model=%5B2H%5D%5B2H%2B%5D">Interactive image</a></span></li><li>T<sub>2</sub><sup>+</sup>: <span title="chemapps.stolaf.edu (3D interactive model)"><a rel="nofollow" class="external text" href="https://chemapps.stolaf.edu/jmol/jmol.php?model=%5B3H%5D%5B3H%2B%5D">Interactive image</a></span></li></ul></div> </td></tr> <tr> <td><a href="/wiki/ChEBI" title="ChEBI">ChEBI</a> </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><span title="www.ebi.ac.uk"><a rel="nofollow" class="external text" href="https://www.ebi.ac.uk/chebi/searchId.do?chebiId=29293">CHEBI:29293</a></span></li><li><sup>1</sup>H<sub>2</sub><sup>+</sup>: <span title="www.ebi.ac.uk"><a rel="nofollow" class="external text" href="https://www.ebi.ac.uk/chebi/searchId.do?chebiId=29297">CHEBI:29297</a></span></li><li>D<sub>2</sub><sup>+</sup>: <span title="www.ebi.ac.uk"><a rel="nofollow" class="external text" href="https://www.ebi.ac.uk/chebi/searchId.do?chebiId=29295">CHEBI:29295</a></span></li><li>T<sub>2</sub><sup>+</sup>: <span title="www.ebi.ac.uk"><a rel="nofollow" class="external text" href="https://www.ebi.ac.uk/chebi/searchId.do?chebiId=29296">CHEBI:29296</a></span></li></ul></div> </td></tr> <tr> <td><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/CompTox_Chemicals_Dashboard" title="CompTox Chemicals Dashboard">CompTox Dashboard</a> <span style="font-weight:normal">(<abbr title="U.S. Environmental Protection Agency">EPA</abbr>)</span></div> </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><span title="comptox.epa.gov"><a rel="nofollow" class="external text" href="https://comptox.epa.gov/dashboard/chemical/details/DTXSID9029643">DTXSID9029643</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q902508#P3117" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></span></li></ul></div> </td></tr> <tr> <td colspan="2"><div class="collapsible-list mw-collapsible mw-collapsed" style="text-align: left;"> <div style="line-height: 1.6em; font-weight: bold; text-align:left; font-weight:normal; background:transparent;"><div><a href="/wiki/International_Chemical_Identifier" title="International Chemical Identifier">InChI</a></div></div> <ul class="mw-collapsible-content" style="margin-top: 0; margin-bottom: 0; line-height: inherit; list-style: none; margin-left: 0; word-break:break-all;"><li style="line-height: inherit; margin: 0"><div style="border-top:1px solid #ccc; padding:0.2em 0 0.2em 1.5em; text-align:left;"><div style="word-wrap:break-word; text-indent:-1.5em; font-size:97%; line-height:120%;">InChI=1S/H2/h1H/q+1</div><div style="word-wrap:break-word; text-indent:-1.5em; font-size:97%; line-height:120%;">Key: ZZIJOQHRUPVPQC-UHFFFAOYSA-N</div></div></li><li style="line-height: inherit; margin: 0"><div style="border-top:1px solid #ccc; padding:0.2em 0 0.2em 1.5em; text-align:left;"><div style="word-wrap:break-word; text-indent:-1.5em; font-size:97%; line-height:120%;"><sup>1</sup>H<sub>2</sub><sup>+</sup>: InChI=1S/H2/h1H/q+1/i1+0H</div><div style="word-wrap:break-word; text-indent:-1.5em; font-size:97%; line-height:120%;">Key: ZZIJOQHRUPVPQC-HXFQMGJMSA-N</div></div></li><li style="line-height: inherit; margin: 0"><div style="border-top:1px solid #ccc; padding:0.2em 0 0.2em 1.5em; text-align:left;"><div style="word-wrap:break-word; text-indent:-1.5em; font-size:97%; line-height:120%;">D<sub>2</sub><sup>+</sup>: InChI=1S/H2/h1H/q+1/i1+1D</div><div style="word-wrap:break-word; text-indent:-1.5em; font-size:97%; line-height:120%;">Key: ZZIJOQHRUPVPQC-VVKOMZTBSA-N</div></div></li><li style="line-height: inherit; margin: 0"><div style="border-top:1px solid #ccc; padding:0.2em 0 0.2em 1.5em; text-align:left;"><div style="word-wrap:break-word; text-indent:-1.5em; font-size:97%; line-height:120%;">T<sub>2</sub><sup>+</sup>: InChI=1S/H2/h1H/q+1/i1+2T</div><div style="word-wrap:break-word; text-indent:-1.5em; font-size:97%; line-height:120%;">Key: ZZIJOQHRUPVPQC-JMRXTUGHSA-N</div></div></li></ul> </div> </td></tr> <tr> <td colspan="2"><div class="collapsible-list mw-collapsible mw-collapsed" style="text-align: left;"> <div style="line-height: 1.6em; font-weight: bold; text-align:left; font-weight:normal; background:transparent;"><div><a href="/wiki/Simplified_molecular-input_line-entry_system" class="mw-redirect" title="Simplified molecular-input line-entry system">SMILES</a></div></div> <ul class="mw-collapsible-content" style="margin-top: 0; margin-bottom: 0; line-height: inherit; list-style: none; margin-left: 0; word-break:break-all;"><li style="line-height: inherit; margin: 0"><div style="border-top:1px solid #ccc; padding:0.2em 0 0.2em 1.6em; word-wrap:break-word; text-indent:-1.5em; text-align:left; font-size:97%; line-height:120%;">[HH+]</div></li><li style="line-height: inherit; margin: 0"><div style="border-top:1px solid #ccc; padding:0.2em 0 0.2em 1.6em; word-wrap:break-word; text-indent:-1.5em; text-align:left; font-size:97%; line-height:120%;"><sup>1</sup>H<sub>2</sub><sup>+</sup>: [1H][1H+]</div></li><li style="line-height: inherit; margin: 0"><div style="border-top:1px solid #ccc; padding:0.2em 0 0.2em 1.6em; word-wrap:break-word; text-indent:-1.5em; text-align:left; font-size:97%; line-height:120%;">D<sub>2</sub><sup>+</sup>: [2H][2H+]</div></li><li style="line-height: inherit; margin: 0"><div style="border-top:1px solid #ccc; padding:0.2em 0 0.2em 1.6em; word-wrap:break-word; text-indent:-1.5em; text-align:left; font-size:97%; line-height:120%;">T<sub>2</sub><sup>+</sup>: [3H][3H+]</div></li></ul> </div> </td></tr> <tr> <th colspan="2" style="background: #f8eaba; text-align: center;">Properties </th></tr> <tr> <td><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Chemical_formula" title="Chemical formula">Chemical formula</a></div> </td> <td><span title="Hydrogen">H</span><sub>2</sub><sup>+</sup> </td></tr> <tr> <td><a href="/wiki/Molar_mass" title="Molar mass">Molar mass</a> </td> <td><span class="nowrap"><span data-sort-value="7000201500000000000♠"></span>2.015</span> g·mol<sup>−1</sup>   </td></tr> <tr> <td colspan="2" style="text-align:left; background:#f8eaba; border:1px solid #a2a9b1;"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Except where otherwise noted, data are given for materials in their <a href="/wiki/Standard_state" title="Standard state">standard state</a> (at 25 °C [77 °F], 100 kPa).</div> <div style="margin-top: 0.3em;"></div> <div style="margin-top: 0.3em; text-align: center;"><a href="/wiki/Wikipedia:Chemical_infobox#References" title="Wikipedia:Chemical infobox">Infobox references</a></div> </td></tr> </tbody></table><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Chemical compound</div> <p class="mw-empty-elt"> </p><p>The <b>dihydrogen cation</b> or <b>hydrogen molecular ion</b> is a <a href="/wiki/Cation" class="mw-redirect" title="Cation">cation</a> (positive <a href="/wiki/Ion" title="Ion">ion</a>) with <a href="/wiki/Chemical_formula" title="Chemical formula">formula</a> <b><span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span></b>. It consists of two <a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a> nuclei (<a href="/wiki/Proton" title="Proton">protons</a>), each sharing a single <a href="/wiki/Electron" title="Electron">electron</a>. It is the simplest <a href="/wiki/Polyatomic_ion" title="Polyatomic ion">molecular ion</a>. </p><p>The ion can be formed from the <a href="/wiki/Ionization" title="Ionization">ionization</a> of a neutral <a href="/wiki/Hydrogen_molecule" class="mw-redirect" title="Hydrogen molecule">hydrogen molecule</a> (<span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span>) by electron impact. It is commonly formed in <a href="/wiki/Molecular_cloud" title="Molecular cloud">molecular clouds</a> in space by the action of <a href="/wiki/Cosmic_ray" title="Cosmic ray">cosmic rays</a>. </p><p>The dihydrogen cation is of great historical, theoretical, and experimental interest. Historically it is of interest because, having only one electron, the equations of <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> that describe its structure can be solved approximately in a relatively straightforward way, as long as the motion of the nuclei and relativistic and quantum electrodynamic effects are neglected. The first such solution was derived by <a href="/wiki/%C3%98yvind_Burrau" title="Øyvind Burrau">Ø. Burrau</a> in 1927,<sup id="cite_ref-burr1927_1-0" class="reference"><a href="#cite_note-burr1927-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> just one year after the wave theory of quantum mechanics was published. </p><p>The theoretical interest arises because an accurate mathematical description, taking into account the quantum motion of all constituents and also the interaction of the electron with the radiation field, is feasible. The description's accuracy has steadily improved over more than half a century, eventually resulting in a theoretical framework allowing ultra-high-accuracy predictions for the energies of the rotational and vibrational levels in the electronic ground state, which are mostly metastable. </p><p>In parallel, the experimental approach to the study of the cation has undergone a fundamental evolution with respect to earlier experimental techniques used in the 1960s and 1980s. Employing advanced techniques, such as ion trapping and laser cooling, the rotational and vibrational transitions can be investigated in extremely fine detail. The corresponding transition frequencies can be precisely measured and the results can be compared with the precise theoretical predictions. Another approach for precision spectroscopy relies on cooling in a cryogenic magneto-electric trap (<a href="/wiki/Penning_trap" title="Penning trap">Penning trap</a>); here the cations' motion is cooled resistively and the internal vibration and rotation decays by spontaneous emission. Then, electron spin resonance transitions can be precisely studied. </p><p>These advances have turned the dihydrogen cations into one more family of bound systems relevant for the determination of <a href="/wiki/Fundamental_constants" class="mw-redirect" title="Fundamental constants">fundamental constants</a> of atomic and nuclear physics, after the <a href="/wiki/Hydrogen_atom" title="Hydrogen atom">hydrogen atom</a> family (including <a href="/wiki/Hydrogen-like_atom" title="Hydrogen-like atom">hydrogen-like ions</a>) and the <a href="/wiki/Helium_atom" title="Helium atom">helium atom</a> family.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Physical_properties">Physical properties</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=1" title="Edit section: Physical properties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bonding in <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> can be described as a covalent <a href="/wiki/One-electron_bond" class="mw-redirect" title="One-electron bond">one-electron bond</a>, which has a formal <a href="/wiki/Bond_order" title="Bond order">bond order</a> of one half.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>The ground state energy of the ion is -0.597 <a href="/wiki/Hartree" title="Hartree">Hartree</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>The bond length in the ground state is 2.00 <a href="/wiki/Bohr_radius" title="Bohr radius">Bohr radius</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Isotopologues">Isotopologues</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=2" title="Edit section: Isotopologues"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The dihydrogen cation has six <a href="/wiki/Isotopologues" class="mw-redirect" title="Isotopologues">isotopologues</a>. Each of the two nuclei can be one of the following: <a href="/wiki/Proton" title="Proton">proton</a> (p, the most common one), <a href="/wiki/Deuteron" class="mw-redirect" title="Deuteron">deuteron</a> (d), or <a href="/wiki/Tritium" title="Tritium">triton</a> (t).<sup id="cite_ref-fabr2009_5-0" class="reference"><a href="#cite_note-fabr2009-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-scar2017_6-0" class="reference"><a href="#cite_note-scar2017-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <ul><li><style data-mw-deduplicate="TemplateStyles:r1123817410">.mw-parser-output .template-chem2-su{display:inline-block;font-size:80%;line-height:1;vertical-align:-0.35em}.mw-parser-output .template-chem2-su>span{display:block;text-align:left}.mw-parser-output sub.template-chem2-sub{font-size:80%;vertical-align:-0.35em}.mw-parser-output sup.template-chem2-sup{font-size:80%;vertical-align:0.65em}</style><span class="chemf nowrap">H<span class="template-chem2-su"><span>+</span><span>2</span></span></span> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap"><sup class="template-chem2-sup">1</sup>H<span class="template-chem2-su"><span>+</span><span>2</span></span></span> (dihydrogen cation, the common one)<sup id="cite_ref-fabr2009_5-1" class="reference"><a href="#cite_note-fabr2009-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-scar2017_6-1" class="reference"><a href="#cite_note-scar2017-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">[HD]<sup>+</sup></span> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">[<sup class="template-chem2-sup">1</sup>H<sup class="template-chem2-sup">2</sup>H]<sup>+</sup></span> (hydrogen deuterium cation)<sup id="cite_ref-fabr2009_5-2" class="reference"><a href="#cite_note-fabr2009-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">D<span class="template-chem2-su"><span>+</span><span>2</span></span></span> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap"><sup class="template-chem2-sup">2</sup>H<span class="template-chem2-su"><span>+</span><span>2</span></span></span> (dideuterium cation)<sup id="cite_ref-fabr2009_5-3" class="reference"><a href="#cite_note-fabr2009-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-scar2017_6-2" class="reference"><a href="#cite_note-scar2017-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">[HT]<sup>+</sup></span> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">[<sup class="template-chem2-sup">1</sup>H<sup class="template-chem2-sup">3</sup>H]<sup>+</sup></span> (hydrogen tritium cation)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">[DT]<sup>+</sup></span> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">[<sup class="template-chem2-sup">2</sup>H<sup class="template-chem2-sup">3</sup>H]<sup>+</sup></span> (deuterium tritium cation)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">T<span class="template-chem2-su"><span>+</span><span>2</span></span></span> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap"><sup class="template-chem2-sup">3</sup>H<span class="template-chem2-su"><span>+</span><span>2</span></span></span> (ditritium cation)<sup id="cite_ref-scar2017_6-3" class="reference"><a href="#cite_note-scar2017-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Quantum_mechanical_analysis">Quantum mechanical analysis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=3" title="Edit section: Quantum mechanical analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Clamped-nuclei_approximation">Clamped-nuclei approximation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=4" title="Edit section: Clamped-nuclei approximation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An approximate description of the dihydrogen cation starts with the neglect of the motion of the nuclei - the so-called clamped-nuclei approximation. This is a good approximation because the nuclei (proton, deuteron or triton) are more than a factor 1000 heavier than the electron. Therefore, the motion of the electron is treated first, for a given (arbitrary) nucleus-nucleus distance <i>R</i>. The electronic energy of the molecule <i>E</i> is computed and the computation is repeated for different values of <i>R</i>. The nucleus-nucleus repulsive energy <i>e</i><sup>2</sup>/(4<span class="texhtml mvar" style="font-style:italic;">π</span><i>ε</i><sub>0</sub><i>R</i>) has to be added to the electronic energy, resulting in the total molecular energy <i>E</i><sub>tot</sub>(<i>R</i>). </p><p>The energy <i>E</i> is the eigenvalue of the <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a> for the single electron. The equation can be solved in a relatively straightforward way due to the lack of electron–electron repulsion (<a href="/wiki/Electron_correlation" class="mw-redirect" title="Electron correlation">electron correlation</a>). The wave equation (a <a href="/wiki/Partial_differential_equation" title="Partial differential equation">partial differential equation</a>) separates into two coupled <a href="/wiki/Ordinary_differential_equations" class="mw-redirect" title="Ordinary differential equations">ordinary differential equations</a> when using <a href="/wiki/Prolate_spheroidal_coordinates" title="Prolate spheroidal coordinates">prolate spheroidal coordinates</a> instead of cartesian coordinates. The analytical solution of the equation, the <a href="/wiki/Wave_function" title="Wave function">wave function</a>, is therefore proportional to a product of two infinite <a href="/wiki/Power_series" title="Power series">power series</a>.<sup id="cite_ref-Correction_for_nuclear_motion_in_H_7-0" class="reference"><a href="#cite_note-Correction_for_nuclear_motion_in_H-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The numerical evaluation of the series can be readily performed on a computer. The analytical solutions for the electronic energy eigenvalues are also a <i>generalization</i> of the <a href="/wiki/Lambert_W_function" title="Lambert W function">Lambert W function</a><sup id="cite_ref-scott2005_8-0" class="reference"><a href="#cite_note-scott2005-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> which can be obtained using a <a href="/wiki/Computer_algebra_system" title="Computer algebra system">computer algebra system</a> within an <a href="/wiki/Experimental_mathematics" title="Experimental mathematics">experimental mathematics</a> approach. </p><p><a href="/wiki/Quantum_chemistry" title="Quantum chemistry">Quantum chemistry</a> and Physics textbooks usually treat the binding of the molecule in the electronic ground state by the simplest possible <a href="/wiki/Ansatz" title="Ansatz">ansatz</a> for the wave function: the (normalized) sum of two 1s hydrogen wave functions centered on each nucleus. This ansatz correctly reproduces the binding but is numerically unsatisfactory. </p> <div class="mw-heading mw-heading4"><h4 id="Historical_notes">Historical notes</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=5" title="Edit section: Historical notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Early attempts to treat <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> using the <a href="/wiki/Old_quantum_theory" title="Old quantum theory">old quantum theory</a> were published in 1922 by <a href="/wiki/Karel_Niessen" title="Karel Niessen">Karel Niessen</a><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Wolfgang Pauli</a>,<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> and in 1925 by <a href="/wiki/Harold_Urey" title="Harold Urey">Harold Urey</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>The first successful quantum mechanical treatment of <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> was published by the Danish physicist <a href="/wiki/%C3%98yvind_Burrau" title="Øyvind Burrau">Øyvind Burrau</a> in 1927,<sup id="cite_ref-burr1927_1-1" class="reference"><a href="#cite_note-burr1927-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> just one year after the publication of wave mechanics by <a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">Erwin Schrödinger</a>. </p><p>In 1928, <a href="/wiki/Linus_Pauling" title="Linus Pauling">Linus Pauling</a> published a review putting together the work of Burrau with the work of <a href="/wiki/Walter_Heitler" title="Walter Heitler">Walter Heitler</a> and <a href="/wiki/Fritz_London" title="Fritz London">Fritz London</a> on the hydrogen molecule.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> The complete mathematical solution of the electronic energy problem for <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> in the clamped-nuclei approximation was provided by <a href="/wiki/Alan_Herries_Wilson" title="Alan Herries Wilson">Wilson</a> (1928) and <a href="/wiki/George_Cecil_Jaffe" title="George Cecil Jaffe">Jaffé</a> (1934). Johnson (1940) gives a succinct summary of their solution,.<sup id="cite_ref-Correction_for_nuclear_motion_in_H_7-1" class="reference"><a href="#cite_note-Correction_for_nuclear_motion_in_H-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="The_solutions_of_the_clamped-nuclei_Schrödinger_equation"><span id="The_solutions_of_the_clamped-nuclei_Schr.C3.B6dinger_equation"></span>The solutions of the clamped-nuclei Schrödinger equation</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=6" title="Edit section: The solutions of the clamped-nuclei Schrödinger equation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Hydrogen_molecular_ion.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Hydrogen_molecular_ion.png/300px-Hydrogen_molecular_ion.png" decoding="async" width="300" height="267" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/0/00/Hydrogen_molecular_ion.png 1.5x" data-file-width="431" data-file-height="384" /></a><figcaption> Hydrogen molecular ion <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> with clamped nuclei <i>A</i> and <i>B</i>, internuclear distance <i>R</i> and plane of symmetry <i>M</i>.</figcaption></figure><p>The electronic Schrödinger wave equation for the hydrogen molecular ion <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> with two fixed nuclear centers, labeled <i>A</i> and <i>B</i>, and one electron can be written as </p><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}+V\right)\psi =E\psi ~,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </mfrac> </mrow> <msup> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>V</mi> </mrow> <mo>)</mo> </mrow> <mi>ψ</mi> <mo>=</mo> <mi>E</mi> <mi>ψ</mi> <mtext> </mtext> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}+V\right)\psi =E\psi ~,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d1d5aa0cfd91f12936a8aa82bc224bfd2a2874b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:26.401ex; height:6.343ex;" alt="{\displaystyle \left(-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}+V\right)\psi =E\psi ~,}"></span></dd></dl> <p>where <i>V</i> is the electron-nuclear Coulomb potential energy function: </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 V=-{\frac {e^{2}}{4\pi \varepsilon _{0}}}\left({\frac {1}{r_{a}}}+{\frac {1}{r_{b}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V=-{\frac {e^{2}}{4\pi \varepsilon _{0}}}\left({\frac {1}{r_{a}}}+{\frac {1}{r_{b}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0497b71c16b8aaa1866f19ca4832d133fd680f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:24.62ex; height:6.343ex;" alt="{\displaystyle V=-{\frac {e^{2}}{4\pi \varepsilon _{0}}}\left({\frac {1}{r_{a}}}+{\frac {1}{r_{b}}}\right)}"></span></dd></dl> <p>and <i>E</i> is the (electronic) energy of a given quantum mechanical state (eigenstate), with the electronic state function <i>ψ</i> = <i>ψ</i>(<b>r</b>) depending on the spatial coordinates of the electron. An additive term <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den"><i>R</i></span></span>⁠</span>, which is constant for fixed internuclear distance <i>R</i>, has been omitted from the potential <i>V</i>, since it merely shifts the eigenvalue. The distances between the electron and the nuclei are denoted <i>r<sub>a</sub></i> and <i>r<sub>b</sub></i>. In atomic units (<i>ħ</i> = <i>m</i> = <i>e</i> = 4<span class="texhtml mvar" style="font-style:italic;">π</span><i>ε</i><sub>0</sub> = 1) the wave equation is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(-{\tfrac {1}{2}}\nabla ^{2}+V\right)\psi =E\psi \qquad {\mbox{with}}\qquad V=-{\frac {1}{r_{a}}}-{\frac {1}{r_{b}}}\;.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <msup> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>V</mi> </mrow> <mo>)</mo> </mrow> <mi>ψ</mi> <mo>=</mo> <mi>E</mi> <mi>ψ</mi> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>with</mtext> </mstyle> </mrow> <mspace width="2em" /> <mi>V</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mfrac> </mrow> <mspace width="thickmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(-{\tfrac {1}{2}}\nabla ^{2}+V\right)\psi =E\psi \qquad {\mbox{with}}\qquad V=-{\frac {1}{r_{a}}}-{\frac {1}{r_{b}}}\;.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d331b5dfb1d54bf2f2bc9429f1cdbdf95ec40de8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:51.949ex; height:5.509ex;" alt="{\displaystyle \left(-{\tfrac {1}{2}}\nabla ^{2}+V\right)\psi =E\psi \qquad {\mbox{with}}\qquad V=-{\frac {1}{r_{a}}}-{\frac {1}{r_{b}}}\;.}"></span></dd></dl> <p>We choose the midpoint between the nuclei as the origin of coordinates. It follows from general symmetry principles that the wave functions can be characterized by their symmetry behavior with respect to the point group inversion operation <i><b>i</b></i> (<b>r</b> ↦ −<b>r</b>). There are wave functions <i>ψ</i><sub>g</sub>(<b>r</b>), which are <i>symmetric</i> with respect to <i><b>i</b></i>, and there are wave functions <i>ψ</i><sub>u</sub>(<b>r</b>), which are <i>antisymmetric</i> under this symmetry operation: </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 \psi _{g/u}(-{\mathbf {r} })={}\pm \psi _{g/u}({\mathbf {r} })\;.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>u</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mo>±</mo> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>u</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> </mrow> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi _{g/u}(-{\mathbf {r} })={}\pm \psi _{g/u}({\mathbf {r} })\;.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/245fdaec0c9f4a16e1b21b160bf6a7d2b5afbbea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:23.455ex; height:3.176ex;" alt="{\displaystyle \psi _{g/u}(-{\mathbf {r} })={}\pm \psi _{g/u}({\mathbf {r} })\;.}"></span></dd></dl> <p>The suffixes <a href="/wiki/Molecular_term_symbol" title="Molecular term symbol"><i>g</i> and <i>u</i></a> are from the German <i>gerade</i> and <i>ungerade</i>) occurring here denote the <a href="/wiki/Symmetry_in_quantum_mechanics" title="Symmetry in quantum mechanics">symmetry</a> behavior under the point group inversion operation <i><b>i</b></i>. Their use is standard practice for the designation of electronic states of diatomic molecules, whereas for atomic states the terms <i>even</i> and <i>odd</i> are used. The ground state (the lowest state) of <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> is denoted X<sup>2</sup>Σ<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><i>g</i></sub></span></span><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> or 1sσ<sub>g</sub> and it is gerade. There is also the first excited state A<sup>2</sup>Σ<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">u</sub></span></span> (2pσ<sub><i>u</i></sub>), which is ungerade. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:H2plus_figure_2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/H2plus_figure_2.png/400px-H2plus_figure_2.png" decoding="async" width="400" height="280" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/H2plus_figure_2.png/600px-H2plus_figure_2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/04/H2plus_figure_2.png/800px-H2plus_figure_2.png 2x" data-file-width="3000" data-file-height="2100" /></a><figcaption> Total energies (<i>E</i><sub>tot</sub>, in units Hartree, the atomic unit of energy) of the lowest states of the hydrogen molecular ion <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> as a function of internuclear distance (<i>R</i>, in Bohr radii, the atomic unit of length). See text for details.</figcaption></figure> <p>Asymptotically, the (total) eigenenergies <i>E</i><sub><i>g</i>/<i>u</i></sub> for these two lowest lying states have the same asymptotic expansion in inverse powers of the internuclear distance <i>R</i>:<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <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_{g/u}=-{\frac {1}{2}}-{\frac {9}{4R^{4}}}+O\left(R^{-6}\right)+\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>u</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>9</mn> <mrow> <mn>4</mn> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>O</mi> <mrow> <mo>(</mo> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>6</mn> </mrow> </msup> <mo>)</mo> </mrow> <mo>+</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{g/u}=-{\frac {1}{2}}-{\frac {9}{4R^{4}}}+O\left(R^{-6}\right)+\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea2da82b7a9dfbd69c30fba8942c9e92e7e8c8ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:35.852ex; height:5.509ex;" alt="{\displaystyle E_{g/u}=-{\frac {1}{2}}-{\frac {9}{4R^{4}}}+O\left(R^{-6}\right)+\cdots }"></span></dd></dl> <p>This and the energy curves include the internuclear <i>1/R</i> term. The actual difference between these two energies is called the <a href="/wiki/Exchange_interaction" title="Exchange interaction">exchange energy</a> splitting and is given by:<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <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 \Delta E=E_{u}-E_{g}={\frac {4}{e}}\,R\,e^{-R}\left[\,1+{\frac {1}{2R}}+O\left(R^{-2}\right)\,\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>E</mi> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mi>e</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>R</mi> <mspace width="thinmathspace" /> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>R</mi> </mrow> </msup> <mrow> <mo>[</mo> <mrow> <mspace width="thinmathspace" /> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>R</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>O</mi> <mrow> <mo>(</mo> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E=E_{u}-E_{g}={\frac {4}{e}}\,R\,e^{-R}\left[\,1+{\frac {1}{2R}}+O\left(R^{-2}\right)\,\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9abc25405617f09082349bc59b37b3afde137f84" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:49.361ex; height:6.176ex;" alt="{\displaystyle \Delta E=E_{u}-E_{g}={\frac {4}{e}}\,R\,e^{-R}\left[\,1+{\frac {1}{2R}}+O\left(R^{-2}\right)\,\right]}"></span></dd></dl> <p>which exponentially vanishes as the internuclear distance <i>R</i> gets greater. The lead term <span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">4</span><span class="sr-only">/</span><span class="den"><i>e</i></span></span>⁠</span><i>Re</i><sup>−<i>R</i></sup></span> was first obtained by the <a href="/wiki/Holstein%E2%80%93Herring_method" title="Holstein–Herring method">Holstein–Herring method</a>. Similarly, asymptotic expansions in powers of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den"><i>R</i></span></span>⁠</span> have been obtained to high order by Cizek <i>et al.</i> for the lowest ten discrete states of the hydrogen molecular ion (clamped nuclei case). For general diatomic and polyatomic molecular systems, the exchange energy is thus very elusive to calculate at large internuclear distances but is nonetheless needed for long-range interactions including studies related to magnetism and charge exchange effects. These are of particular importance in stellar and atmospheric physics. </p><p>The energies for the lowest discrete states are shown in the graph above. These can be obtained to within arbitrary accuracy using <a href="/wiki/Computer_algebra" title="Computer algebra">computer algebra</a> from the generalized <a href="/wiki/Lambert_W_function" title="Lambert W function">Lambert W function</a> (see eq. (3) in that site and reference<sup id="cite_ref-scott2005_8-1" class="reference"><a href="#cite_note-scott2005-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>). They were obtained initially by numerical means to within double precision by the most precise program available, namely ODKIL.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> The red solid lines are <sup>2</sup>Σ<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><i>g</i></sub></span></span> states. The green dashed lines are <sup>2</sup>Σ<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><i>u</i></sub></span></span> states. The blue dashed line is a <sup>2</sup>Π<sub><i>u</i></sub> state and the pink dotted line is a <sup>2</sup>Π<sub><i>g</i></sub> state. Note that although the generalized <a href="/wiki/Lambert_W_function" title="Lambert W function">Lambert W function</a> eigenvalue solutions supersede these asymptotic expansions, in practice, they are most useful near the <a href="/wiki/Bond_length" title="Bond length">bond length</a>. </p><p>The complete Hamiltonian of <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> (as for all centrosymmetric molecules) does not commute with the point group inversion operation <i><b>i</b></i> because of the effect of the nuclear hyperfine Hamiltonian. The nuclear hyperfine Hamiltonian can mix the rotational levels of <i>g</i> and <i>u</i> electronic states (called <i>ortho</i>-<i>para</i> mixing) and give rise to <i>ortho</i>-<i>para</i> transitions.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Critchley2001_19-0" class="reference"><a href="#cite_note-Critchley2001-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Born-Oppenheimer_approximation">Born-Oppenheimer approximation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=7" title="Edit section: Born-Oppenheimer approximation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Once the energy function <i>E</i><sub>tot</sub>(<i>R</i>) has been obtained, one can compute the quantum states of rotational and vibrational motion of the nuclei, and thus of the molecule as a whole. The corresponding `'nuclear'´ Schrödinger equation is a one-dimensional ordinary differential equation, where the nucleus-nucleus distance <i>R</i> is the independent coordinate. The equation describes the motion of a fictitious particle of mass equal to the reduced mass of the two nuclei, in the potential <i>E</i><sub>tot</sub>(<i>R</i>)+<i>V</i><sub><i>L</i></sub>(<i>R</i>), where the second term is the centrifugal potential due to rotation with angular momentum described by the quantum number <i>L</i>. The eigenenergies of this Schrödinger equation are the total energies of the whole molecule, electronic plus nuclear. </p> <div class="mw-heading mw-heading3"><h3 id="High-accuracy_ab_initio_theory">High-accuracy ab initio theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=8" title="Edit section: High-accuracy ab initio theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Born-Oppenheimer_approximation" class="mw-redirect" title="Born-Oppenheimer approximation">Born-Oppenheimer approximation</a> is unsuited for describing the dihydrogen cation accurately enough to explain the results of precision spectroscopy. </p><p>The full Schrödinger equation for this cation, without the approximation of clamped nuclei, is much more complex, but nevertheless can be solved numerically essentially exactly using a variational approach.<sup id="cite_ref-Korobov2022_20-0" class="reference"><a href="#cite_note-Korobov2022-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> Thereby, the simultaneous motion of the electron and of the nuclei is treated exactly. When the solutions are restricted to the lowest-energy orbital, one obtains the rotational and ro-vibrational states' energies and wavefunctions. The numerical uncertainty of the energies and the wave functions found in this way is negligible compared to the systematic error stemming from using the Schrödinger equation, rather than fundamentally more accurate equations. Indeed, the Schrödinger equation does not incorporate all relevant physics, as is known from the hydrogen atom problem. More accurate treatments need to consider the physics that is described by the <a href="/wiki/Dirac_equation" title="Dirac equation">Dirac equation</a> or, even more accurately, by quantum electrodynamics. The most accurate solutions of the ro-vibrational states are found by applying non-relativistic quantum electrodynamics (<a href="/wiki/NRQED" class="mw-redirect" title="NRQED">NRQED</a>) theory.<sup id="cite_ref-Korobov2021_21-0" class="reference"><a href="#cite_note-Korobov2021-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>For comparison with experiment, one requires differences of state energies, i.e. transition frequencies. For transitions between <a href="/wiki/Rotational%E2%80%93vibrational_spectroscopy" title="Rotational–vibrational spectroscopy">ro-vibrational levels</a> having small rotational and moderate vibrational <a href="/wiki/Quantum_numbers" class="mw-redirect" title="Quantum numbers">quantum numbers</a> the frequencies have been calculated with theoretical fractional uncertainty of approximately <span class="nowrap"><span data-sort-value="6988800000000000000♠"></span>8<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−12</sup></span>.<sup id="cite_ref-Korobov2021_21-1" class="reference"><a href="#cite_note-Korobov2021-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> Additional contributions to the uncertainty of the predicted frequencies arise from the uncertainties of <a href="/wiki/Fundamental_constants" class="mw-redirect" title="Fundamental constants">fundamental constants</a>, which are input to the theoretical calculation, especially from the ratio of the proton mass and the electron mass. </p><p>Using a sophisticated ab initio formalism, also the hyperfine energies can be computed accurately, see below. </p> <div class="mw-heading mw-heading2"><h2 id="Experimental_studies">Experimental studies</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=9" title="Edit section: Experimental studies"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Precision_spectroscopy">Precision spectroscopy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=10" title="Edit section: Precision spectroscopy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Because of its relative simplicity, the dihydrogen cation is the molecule that is most precisely understood, in the sense that theoretical calculations of its energy levels match the experimental results with the highest level of agreement. </p><p>Specifically, spectroscopically determined pure rotational and ro-vibrational transition frequencies of the particular isotopologue HD<sup>+</sup> agree with theoretically computed transition frequencies. Four high-precision experiments yielded comparisons with total uncertainties between <span class="nowrap"><span data-sort-value="6989200000000000000♠"></span>2<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−11</sup></span> and <span class="nowrap"><span data-sort-value="6989500000000000000♠"></span>5<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−11</sup></span>, fractionally.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> The level of agreement is actually limited neither by theory not by experiment but rather by the uncertainty of the current values of the masses of the particles, that are used as input parameters to the calculation. </p><p>In order to measure the transition frequencies with high accuracy, the spectroscopy of the dihydrogen cation had to be performed under special conditions. Therefore, ensembles of HD<sup>+</sup> ions were trapped in a <a href="/wiki/Quadrupole_ion_trap" title="Quadrupole ion trap">quadrupole ion trap</a> under ultra-high vacuum, sympathetically cooled by <a href="/wiki/Laser-cooled" class="mw-redirect" title="Laser-cooled">laser-cooled</a> beryllium ions, and interrogated using particular spectroscopic techniques. </p><p>The hyperfine structure of the homonuclear isotopologue H<sub>2</sub><sup>+</sup> has been measured extensively and precisely by Jefferts in 1969. Finally, in 2021, ab initio theory computations were able to provide the quantitative details of the structure with uncertainty smaller than that of the experimental data, <span class="nowrap"><span data-sort-value="7003100000000000000♠"></span>1 kHz</span>. Some contributions to the measured hyperfine structure have been theoretically confirmed at the level of approximately <span class="nowrap"><span data-sort-value="7001500000000000000♠"></span>50 Hz</span>.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>The implication of these agreements is that one can deduce a spectroscopic value of the ratio of electron mass to reduced proton-deuteron mass, <span class="nowrap"><i>m</i><sub>e</sub>/<i>m</i><sub>p</sub></span>+<span class="nowrap"><i>m</i><sub>e</sub>/<i>m</i><sub>d</sub></span>, that is an input to the ab initio theory. The ratio is fitted such that theoretical prediction and experimental results agree. The uncertainty of the obtained ratio is comparable to the one obtained from direct mass measurements of proton, deuteron, electron, and HD<sup>+</sup> via <a href="/wiki/Cyclotron_resonance" title="Cyclotron resonance">cyclotron resonance</a> in <a href="/wiki/Penning_trap" title="Penning trap">Penning traps</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Occurrence_in_space">Occurrence in space</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=11" title="Edit section: Occurrence in space"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Formation">Formation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=12" title="Edit section: Formation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The dihydrogen ion is formed in nature by the interaction of <a href="/wiki/Cosmic_ray" title="Cosmic ray">cosmic rays</a> and the hydrogen molecule. An electron is knocked off leaving the cation behind.<sup id="cite_ref-eherbstastro_24-0" class="reference"><a href="#cite_note-eherbstastro-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <dl><dd>H<sub>2</sub> + cosmic ray → <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> + e<sup>−</sup> + cosmic ray.</dd></dl> <p>Cosmic ray particles have enough energy to ionize many molecules before coming to a stop. </p><p>The ionization energy of the hydrogen molecule is 15.603 eV. High speed electrons also cause ionization of hydrogen molecules with a peak cross section around 50 eV. The peak cross section for ionization for high speed protons is <span class="nowrap"><span data-sort-value="6986112152354090000♠"></span>70<span style="margin-left:.25em;">000</span> eV</span> with a cross section of <span class="nowrap"><span data-sort-value="6984250000000000000♠"></span>2.5<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−16</sup> cm<sup>2</sup></span>. A cosmic ray proton at lower energy can also strip an electron off a neutral hydrogen molecule to form a neutral hydrogen atom and the dihydrogen cation, (<span class="nowrap">p<sup>+</sup> + H<sub>2</sub> → H + <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span></span>) with a peak cross section at around <span class="nowrap"><span data-sort-value="6985128174118959999♠"></span>8000 eV</span> of <span class="nowrap"><span data-sort-value="6984800000000000000♠"></span>8<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−16</sup> cm<sup>2</sup></span>.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Destruction">Destruction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=13" title="Edit section: Destruction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In nature the ion is destroyed by reacting with other hydrogen molecules: </p> <dl><dd><span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> + H<sub>2</sub> → <a href="/wiki/Trihydrogen_cation" title="Trihydrogen cation"><span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sub></span></span></span></a> + H.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Production_in_the_laboratory">Production in the laboratory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=14" title="Edit section: Production in the laboratory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the laboratory, the ion is easily produced by electron bombardment from an electron gun. </p><p>An artificial <a href="/w/index.php?title=Plasma_discharge&action=edit&redlink=1" class="new" title="Plasma discharge (page does not exist)">plasma discharge</a> cell can also produce the ion.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2013)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=15" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Symmetry_of_diatomic_molecules" title="Symmetry of diatomic molecules">Symmetry of diatomic molecules</a></li> <li><a href="/wiki/Delta_potential#Double-well_Dirac_delta_function_model" title="Delta potential">Dirac Delta function model</a> (one-dimensional version of <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span>)</li> <li><a href="/wiki/Di-positronium" title="Di-positronium">Di-positronium</a></li> <li><a href="/wiki/Euler%27s_three-body_problem" title="Euler's three-body problem">Euler's three-body problem</a> (classical counterpart)</li> <li><a href="/wiki/Few-body_systems" title="Few-body systems">Few-body systems</a></li> <li><a href="/wiki/Helium_atom" title="Helium atom">Helium atom</a></li> <li><a href="/wiki/Helium_hydride_ion" title="Helium hydride ion">Helium hydride ion</a></li> <li><a href="/wiki/Trihydrogen_cation" title="Trihydrogen cation">Trihydrogen cation</a></li> <li><a href="/wiki/Triatomic_hydrogen" title="Triatomic hydrogen">Triatomic hydrogen</a></li> <li><a href="/wiki/Lambert_W_function" title="Lambert W function">Lambert W function</a></li> <li><a href="/wiki/Atomic_and_molecular_astrophysics" title="Atomic and molecular astrophysics">Molecular astrophysics</a></li> <li><a href="/wiki/Holstein%E2%80%93Herring_method" title="Holstein–Herring method">Holstein–Herring method</a></li> <li><a href="/wiki/Three-body_problem" title="Three-body problem">Three-body problem</a></li> <li><a href="/wiki/List_of_quantum-mechanical_systems_with_analytical_solutions" title="List of quantum-mechanical systems with analytical solutions">List of quantum-mechanical systems with analytical solutions</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dihydrogen_cation&action=edit&section=16" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-burr1927-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-burr1927_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-burr1927_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBurrau1927" class="citation journal cs1 cs1-prop-long-vol cs1-prop-foreign-lang-source">Burrau, Ø. (1927). <a rel="nofollow" class="external text" href="http://gymarkiv.sdu.dk/MFM/kdvs/mfm%201-9/mfm-7-14.pdf">"Berechnung des Energiewertes des Wasserstoffmolekel-Ions (<span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span>) im Normalzustand"</a> <span class="cs1-format">(PDF)</span>. <i>Danske Vidensk. Selskab. Math.-fys. Meddel.</i> (in German). M 7:14: 1–18.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Danske+Vidensk.+Selskab.+Math.-fys.+Meddel.&rft.atitle=Berechnung+des+Energiewertes+des+Wasserstoffmolekel-Ions+%28%3Cspan+class%3D%22chemf+nowrap%22%3EH%3Cspan+class%3D%22nowrap%22%3E%3Cspan+style%3D%22display%3Ainline-block%3Bmargin-bottom%3A-0.3em%3Bvertical-align%3A-0.4em%3Bline-height%3A1em%3Bfont-size%3A80%25%3Btext-align%3Aleft%22%3E%3Csup+style%3D%22font-size%3Ainherit%3Bline-height%3Ainherit%3Bvertical-align%3Abaseline%22%3E%2B%3C%2Fsup%3E%3Cbr+%2F%3E%3Csub+style%3D%22font-size%3Ainherit%3Bline-height%3Ainherit%3Bvertical-align%3Abaseline%22%3E2%3C%2Fsub%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%29+im+Normalzustand.&rft.volume=M+7%3A14&rft.pages=1-18&rft.date=1927&rft.aulast=Burrau&rft.aufirst=%C3%98.&rft_id=http%3A%2F%2Fgymarkiv.sdu.dk%2FMFM%2Fkdvs%2Fmfm%25201-9%2Fmfm-7-14.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span><br /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBurrau1927" class="citation journal cs1 cs1-prop-foreign-lang-source">Burrau, Ø. (1927). "The calculation of the Energy value of Hydrogen molecule ions (<span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span>) in their normal position". <i>Naturwissenschaften</i> (in German). <b>15</b> (1): 16–7. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1927NW.....15...16B">1927NW.....15...16B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01504875">10.1007/BF01504875</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:19368939">19368939</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Naturwissenschaften&rft.atitle=The+calculation+of+the+Energy+value+of+Hydrogen+molecule+ions+%28%3Cspan+class%3D%22chemf+nowrap%22%3EH%3Cspan+class%3D%22nowrap%22%3E%3Cspan+style%3D%22display%3Ainline-block%3Bmargin-bottom%3A-0.3em%3Bvertical-align%3A-0.4em%3Bline-height%3A1em%3Bfont-size%3A80%25%3Btext-align%3Aleft%22%3E%3Csup+style%3D%22font-size%3Ainherit%3Bline-height%3Ainherit%3Bvertical-align%3Abaseline%22%3E%2B%3C%2Fsup%3E%3Cbr+%2F%3E%3Csub+style%3D%22font-size%3Ainherit%3Bline-height%3Ainherit%3Bvertical-align%3Abaseline%22%3E2%3C%2Fsub%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%29+in+their+normal+position&rft.volume=15&rft.issue=1&rft.pages=16-7&rft.date=1927&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A19368939%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF01504875&rft_id=info%3Abibcode%2F1927NW.....15...16B&rft.aulast=Burrau&rft.aufirst=%C3%98.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged February 2020">permanent dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchiller2022" class="citation journal cs1">Schiller, S. (2022). <a rel="nofollow" class="external text" href="https://www.tandfonline.com/doi/full/10.1080/00107514.2023.2180180?src=">"Precision spectroscopy of the molecular hydrogen ions: an introduction"</a>. <i>Contemporary Physics</i>. <b>63</b> (4): 247–279. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F00107514.2023.2180180">10.1080/00107514.2023.2180180</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Contemporary+Physics&rft.atitle=Precision+spectroscopy+of+the+molecular+hydrogen+ions%3A+an+introduction.&rft.volume=63&rft.issue=4&rft.pages=247-279&rft.date=2022&rft_id=info%3Adoi%2F10.1080%2F00107514.2023.2180180&rft.aulast=Schiller&rft.aufirst=S.&rft_id=https%3A%2F%2Fwww.tandfonline.com%2Fdoi%2Ffull%2F10.1080%2F00107514.2023.2180180%3Fsrc%3D&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClark_R._LandisFrank_Weinhold2005" class="citation book cs1">Clark R. Landis; Frank Weinhold (2005). <i>Valency and bonding: a natural bond orbital donor-acceptor perspective</i>. Cambridge, UK: Cambridge University Press. pp. 91–92. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-83128-4" title="Special:BookSources/978-0-521-83128-4"><bdi>978-0-521-83128-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Valency+and+bonding%3A+a+natural+bond+orbital+donor-acceptor+perspective&rft.place=Cambridge%2C+UK&rft.pages=91-92&rft.pub=Cambridge+University+Press&rft.date=2005&rft.isbn=978-0-521-83128-4&rft.au=Clark+R.+Landis&rft.au=Frank+Weinhold&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBressaniniMellaMorosi1997" class="citation journal cs1">Bressanini, Dario; Mella, Massimo; Morosi, Gabriele (1997). "Nonadiabatic wavefunctions as linear expansions of correlated exponentials. A quantum Monte Carlo application to H2+ and Ps2". <i>Chemical Physics Letters</i>. <b>272</b> (5–6): 370–375. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1997CPL...272..370B">1997CPL...272..370B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0009-2614%2897%2900571-X">10.1016/S0009-2614(97)00571-X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Chemical+Physics+Letters&rft.atitle=Nonadiabatic+wavefunctions+as+linear+expansions+of+correlated+exponentials.+A+quantum+Monte+Carlo+application+to+H2%2B+and+Ps2&rft.volume=272&rft.issue=5%E2%80%936&rft.pages=370-375&rft.date=1997&rft_id=info%3Adoi%2F10.1016%2FS0009-2614%2897%2900571-X&rft_id=info%3Abibcode%2F1997CPL...272..370B&rft.aulast=Bressanini&rft.aufirst=Dario&rft.au=Mella%2C+Massimo&rft.au=Morosi%2C+Gabriele&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-fabr2009-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-fabr2009_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-fabr2009_5-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-fabr2009_5-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-fabr2009_5-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFábriCzakóTasiCsászár2009" class="citation journal cs1">Fábri, Csaba; Czakó, Gábor; Tasi, Gyula; Császár, Attila G. (2009). "Adiabatic Jacobi corrections on the vibrational energy levels of H<sub>2</sub>(<sup>+</sup>) isotopologues". <i>Journal of Chemical Physics</i>. <b>130</b> (13): 134314. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009JChPh.130m4314F">2009JChPh.130m4314F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.3097327">10.1063/1.3097327</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/19355739">19355739</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Chemical+Physics&rft.atitle=Adiabatic+Jacobi+corrections+on+the+vibrational+energy+levels+of+H%3Csub%3E2%3C%2Fsub%3E%28%3Csup%3E%2B%3C%2Fsup%3E%29+isotopologues&rft.volume=130&rft.issue=13&rft.pages=134314&rft.date=2009&rft_id=info%3Apmid%2F19355739&rft_id=info%3Adoi%2F10.1063%2F1.3097327&rft_id=info%3Abibcode%2F2009JChPh.130m4314F&rft.aulast=F%C3%A1bri&rft.aufirst=Csaba&rft.au=Czak%C3%B3%2C+G%C3%A1bor&rft.au=Tasi%2C+Gyula&rft.au=Cs%C3%A1sz%C3%A1r%2C+Attila+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-scar2017-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-scar2017_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-scar2017_6-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-scar2017_6-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-scar2017_6-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFScarlettZammitFursaBray2017" class="citation journal cs1">Scarlett, Liam H.; Zammit, Mark C.; Fursa, Dmitry V.; Bray, Igor (2017). <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevA.96.022706">"Kinetic-energy release of fragments from electron-impact dissociation of the molecular hydrogen ion and its isotopologues"</a>. <i>Physical Review A</i>. <b>96</b> (2): 022706. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2017PhRvA..96b2706S">2017PhRvA..96b2706S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevA.96.022706">10.1103/PhysRevA.96.022706</a></span>. <a href="/wiki/OSTI_(identifier)" class="mw-redirect" title="OSTI (identifier)">OSTI</a> <a rel="nofollow" class="external text" href="https://www.osti.gov/biblio/1514929">1514929</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+A&rft.atitle=Kinetic-energy+release+of+fragments+from+electron-impact+dissociation+of+the+molecular+hydrogen+ion+and+its+isotopologues&rft.volume=96&rft.issue=2&rft.pages=022706&rft.date=2017&rft_id=info%3Adoi%2F10.1103%2FPhysRevA.96.022706&rft_id=https%3A%2F%2Fwww.osti.gov%2Fbiblio%2F1514929%23id-name%3DOSTI&rft_id=info%3Abibcode%2F2017PhRvA..96b2706S&rft.aulast=Scarlett&rft.aufirst=Liam+H.&rft.au=Zammit%2C+Mark+C.&rft.au=Fursa%2C+Dmitry+V.&rft.au=Bray%2C+Igor&rft_id=https%3A%2F%2Fdoi.org%2F10.1103%252FPhysRevA.96.022706&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-Correction_for_nuclear_motion_in_H-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-Correction_for_nuclear_motion_in_H_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Correction_for_nuclear_motion_in_H_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJohnson1941" class="citation journal cs1">Johnson, V.A. (1941). "Correction for nuclear motion in H<sub>2</sub><sup>+</sup>". <i>Phys. Rev</i>. <b>60</b> (5): 373–77. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.60.373">10.1103/PhysRev.60.373</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Rev.&rft.atitle=Correction+for+nuclear+motion+in+H%3Csub%3E2%3C%2Fsub%3E%3Csup%3E%2B%3C%2Fsup%3E&rft.volume=60&rft.issue=5&rft.pages=373-77&rft.date=1941&rft_id=info%3Adoi%2F10.1103%2FPhysRev.60.373&rft.aulast=Johnson&rft.aufirst=V.A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-scott2005-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-scott2005_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-scott2005_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFScottAubert-FréconGrotendorst2006" class="citation journal cs1">Scott, T. C.; Aubert-Frécon, M.; Grotendorst, J. (2006). "New Approach for the Electronic Energies of the Hydrogen Molecular Ion". <i>Chem. Phys</i>. <b>324</b> (2–3): 323–338. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/physics/0607081">physics/0607081</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006CP....324..323S">2006CP....324..323S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.chemphys.2005.10.031">10.1016/j.chemphys.2005.10.031</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:623114">623114</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Chem.+Phys.&rft.atitle=New+Approach+for+the+Electronic+Energies+of+the+Hydrogen+Molecular+Ion&rft.volume=324&rft.issue=2%E2%80%933&rft.pages=323-338&rft.date=2006&rft_id=info%3Aarxiv%2Fphysics%2F0607081&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A623114%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.chemphys.2005.10.031&rft_id=info%3Abibcode%2F2006CP....324..323S&rft.aulast=Scott&rft.aufirst=T.+C.&rft.au=Aubert-Fr%C3%A9con%2C+M.&rft.au=Grotendorst%2C+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">Karel F. Niessen <i>Zur Quantentheorie des Wasserstoffmolekülions</i>, doctoral dissertation, University of Utrecht, Utrecht: I. Van Druten (1922) as cited in Mehra, Volume 5, Part 2, 2001, p. 932.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPauli_W1922" class="citation journal cs1">Pauli W (1922). "Über das Modell des Wasserstoffmolekülions". <i>Annalen der Physik</i>. <b>373</b> (11): 177–240. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19223731101">10.1002/andp.19223731101</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=%C3%9Cber+das+Modell+des+Wasserstoffmolek%C3%BClions&rft.volume=373&rft.issue=11&rft.pages=177-240&rft.date=1922&rft_id=info%3Adoi%2F10.1002%2Fandp.19223731101&rft.au=Pauli+W&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span> Extended doctoral dissertation; received 4 March 1922, published in issue No. 11 of 3 August 1922.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFUrey_HC1925" class="citation journal cs1">Urey HC (October 1925). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1086173">"The Structure of the Hydrogen Molecule Ion"</a>. <i>Proc. Natl. Acad. Sci. U.S.A</i>. <b>11</b> (10): 618–21. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1925PNAS...11..618U">1925PNAS...11..618U</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.11.10.618">10.1073/pnas.11.10.618</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1086173">1086173</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16587051">16587051</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proc.+Natl.+Acad.+Sci.+U.S.A.&rft.atitle=The+Structure+of+the+Hydrogen+Molecule+Ion&rft.volume=11&rft.issue=10&rft.pages=618-21&rft.date=1925-10&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1086173%23id-name%3DPMC&rft_id=info%3Apmid%2F16587051&rft_id=info%3Adoi%2F10.1073%2Fpnas.11.10.618&rft_id=info%3Abibcode%2F1925PNAS...11..618U&rft.au=Urey+HC&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1086173&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPauling,_L.1928" class="citation journal cs1">Pauling, L. (1928). "The Application of the Quantum Mechanics to the Structure of the Hydrogen Molecule and Hydrogen Molecule-Ion and to Related Problems". <i>Chemical Reviews</i>. <b>5</b> (2): 173–213. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fcr60018a003">10.1021/cr60018a003</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Chemical+Reviews&rft.atitle=The+Application+of+the+Quantum+Mechanics+to+the+Structure+of+the+Hydrogen+Molecule+and+Hydrogen+Molecule-Ion+and+to+Related+Problems&rft.volume=5&rft.issue=2&rft.pages=173-213&rft.date=1928&rft_id=info%3Adoi%2F10.1021%2Fcr60018a003&rft.au=Pauling%2C+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHuberHerzberg1979" class="citation book cs1">Huber, K.-P.; <a href="/wiki/Gerhard_Herzberg" title="Gerhard Herzberg">Herzberg, G.</a> (1979). <i><a href="/wiki/Molecular_Spectra_and_Molecular_Structure_IV._Constants_of_Diatomic_Molecules" class="mw-redirect" title="Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules">Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules</a></i>. New York: Van Nostrand Reinhold.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Molecular+Spectra+and+Molecular+Structure+IV.+Constants+of+Diatomic+Molecules&rft.place=New+York&rft.pub=Van+Nostrand+Reinhold&rft.date=1979&rft.aulast=Huber&rft.aufirst=K.-P.&rft.au=Herzberg%2C+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFČížekDamburgGraffiGrecchi1986" class="citation journal cs1">Čížek, J.; Damburg, R. J.; Graffi, S.; Grecchi, V.; Harrel II, E. M.; Harris, J. G.; Nakai, S.; <a href="/wiki/Josef_Paldus" title="Josef Paldus">Paldus, J.</a>; Propin, R. Kh.; Silverstone, H. J. (1986). "1/<i>R</i> expansion for <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span>: Calculation of exponentially small terms and asymptotics". <i><a href="/wiki/Physical_Review" title="Physical Review">Phys. Rev. A</a></i>. <b>33</b> (1): 12–54. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1986PhRvA..33...12C">1986PhRvA..33...12C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevA.33.12">10.1103/PhysRevA.33.12</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/9896581">9896581</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Rev.+A&rft.atitle=1%2FR+expansion+for+%3Cspan+class%3D%22chemf+nowrap%22%3EH%3Cspan+class%3D%22nowrap%22%3E%3Cspan+style%3D%22display%3Ainline-block%3Bmargin-bottom%3A-0.3em%3Bvertical-align%3A-0.4em%3Bline-height%3A1em%3Bfont-size%3A80%25%3Btext-align%3Aleft%22%3E%3Csup+style%3D%22font-size%3Ainherit%3Bline-height%3Ainherit%3Bvertical-align%3Abaseline%22%3E%2B%3C%2Fsup%3E%3Cbr+%2F%3E%3Csub+style%3D%22font-size%3Ainherit%3Bline-height%3Ainherit%3Bvertical-align%3Abaseline%22%3E2%3C%2Fsub%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3A+Calculation+of+exponentially+small+terms+and+asymptotics&rft.volume=33&rft.issue=1&rft.pages=12-54&rft.date=1986&rft_id=info%3Apmid%2F9896581&rft_id=info%3Adoi%2F10.1103%2FPhysRevA.33.12&rft_id=info%3Abibcode%2F1986PhRvA..33...12C&rft.aulast=%C4%8C%C3%AD%C5%BEek&rft.aufirst=J.&rft.au=Damburg%2C+R.+J.&rft.au=Graffi%2C+S.&rft.au=Grecchi%2C+V.&rft.au=Harrel+II%2C+E.+M.&rft.au=Harris%2C+J.+G.&rft.au=Nakai%2C+S.&rft.au=Paldus%2C+J.&rft.au=Propin%2C+R.+Kh.&rft.au=Silverstone%2C+H.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMorgan_IIISimon1980" class="citation journal cs1">Morgan III, John D.; <a href="/wiki/Barry_Simon" title="Barry Simon">Simon, Barry</a> (1980). <a rel="nofollow" class="external text" href="https://doi.org/10.1002/qua.560170609">"Behavior of molecular potential energy curves for large nuclear separations"</a>. <i>Int. J. Quantum Chem</i>. <b>17</b> (6): 1143–1166. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fqua.560170609">10.1002/qua.560170609</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Int.+J.+Quantum+Chem.&rft.atitle=Behavior+of+molecular+potential+energy+curves+for+large+nuclear+separations&rft.volume=17&rft.issue=6&rft.pages=1143-1166&rft.date=1980&rft_id=info%3Adoi%2F10.1002%2Fqua.560170609&rft.aulast=Morgan+III&rft.aufirst=John+D.&rft.au=Simon%2C+Barry&rft_id=https%3A%2F%2Fdoi.org%2F10.1002%2Fqua.560170609&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFScottDalgarnoMorgan1991" class="citation journal cs1">Scott, T. C.; <a href="/wiki/Alexander_Dalgarno" title="Alexander Dalgarno">Dalgarno, A.</a>; Morgan, J. D. III (1991). "Exchange Energy of <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> Calculated from Polarization Perturbation Theory and the Holstein-Herring Method". <i><a href="/wiki/Physical_Review_Letters" title="Physical Review Letters">Phys. Rev. Lett.</a></i> <b>67</b> (11): 1419–1422. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1991PhRvL..67.1419S">1991PhRvL..67.1419S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.67.1419">10.1103/PhysRevLett.67.1419</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10044142">10044142</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Rev.+Lett.&rft.atitle=Exchange+Energy+of+%3Cspan+class%3D%22chemf+nowrap%22%3EH%3Cspan+class%3D%22nowrap%22%3E%3Cspan+style%3D%22display%3Ainline-block%3Bmargin-bottom%3A-0.3em%3Bvertical-align%3A-0.4em%3Bline-height%3A1em%3Bfont-size%3A80%25%3Btext-align%3Aleft%22%3E%3Csup+style%3D%22font-size%3Ainherit%3Bline-height%3Ainherit%3Bvertical-align%3Abaseline%22%3E%2B%3C%2Fsup%3E%3Cbr+%2F%3E%3Csub+style%3D%22font-size%3Ainherit%3Bline-height%3Ainherit%3Bvertical-align%3Abaseline%22%3E2%3C%2Fsub%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E+Calculated+from+Polarization+Perturbation+Theory+and+the+Holstein-Herring+Method&rft.volume=67&rft.issue=11&rft.pages=1419-1422&rft.date=1991&rft_id=info%3Apmid%2F10044142&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.67.1419&rft_id=info%3Abibcode%2F1991PhRvL..67.1419S&rft.aulast=Scott&rft.aufirst=T.+C.&rft.au=Dalgarno%2C+A.&rft.au=Morgan%2C+J.+D.+III&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHadingerAubert-FréconHadinger1989" class="citation journal cs1">Hadinger, G.; Aubert-Frécon, M.; Hadinger, G. (1989). "The Killingbeck method for the one-electron two-centre problem". <i><a href="/wiki/Journal_of_Physics_B" title="Journal of Physics B">J. Phys. B</a></i>. <b>22</b> (5): 697–712. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1989JPhB...22..697H">1989JPhB...22..697H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0953-4075%2F22%2F5%2F003">10.1088/0953-4075/22/5/003</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:250741775">250741775</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Phys.+B&rft.atitle=The+Killingbeck+method+for+the+one-electron+two-centre+problem&rft.volume=22&rft.issue=5&rft.pages=697-712&rft.date=1989&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A250741775%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F0953-4075%2F22%2F5%2F003&rft_id=info%3Abibcode%2F1989JPhB...22..697H&rft.aulast=Hadinger&rft.aufirst=G.&rft.au=Aubert-Fr%C3%A9con%2C+M.&rft.au=Hadinger%2C+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPique1984" class="citation journal cs1">Pique, J. P.; et al. (1984). "Hyperfine-Induced Ungerade-Gerade Symmetry Breaking in a Homonuclear Diatomic Molecule near a Dissociation Limit: <sup>127</sup>I<sub>2</sub> at the <sup>2</sup>P<sub>3/2</sub> − <sup>2</sup>P<sub>1/2</sub> Limit". <i>Phys. Rev. Lett</i>. <b>52</b> (4): 267–269. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1984PhRvL..52..267P">1984PhRvL..52..267P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.52.267">10.1103/PhysRevLett.52.267</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Rev.+Lett.&rft.atitle=Hyperfine-Induced+Ungerade-Gerade+Symmetry+Breaking+in+a+Homonuclear+Diatomic+Molecule+near+a+Dissociation+Limit%3A+%3Csup%3E127%3C%2Fsup%3EI%3Csub%3E2%3C%2Fsub%3E+at+the+%3Csup%3E2%3C%2Fsup%3EP%3Csub%3E3%2F2%3C%2Fsub%3E+%E2%88%92+%3Csup%3E2%3C%2Fsup%3EP%3Csub%3E1%2F2%3C%2Fsub%3E+Limit&rft.volume=52&rft.issue=4&rft.pages=267-269&rft.date=1984&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.52.267&rft_id=info%3Abibcode%2F1984PhRvL..52..267P&rft.aulast=Pique&rft.aufirst=J.+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-Critchley2001-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-Critchley2001_19-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCritchley2001" class="citation journal cs1">Critchley, A. D. J.; et al. (2001). "Direct Measurement of a Pure Rotation Transition in <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span>". <i>Phys. Rev. Lett</i>. <b>86</b> (9): 1725–1728. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001PhRvL..86.1725C">2001PhRvL..86.1725C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.86.1725">10.1103/PhysRevLett.86.1725</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/11290233">11290233</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Rev.+Lett.&rft.atitle=Direct+Measurement+of+a+Pure+Rotation+Transition+in+%3Cspan+class%3D%22chemf+nowrap%22%3EH%3Cspan+class%3D%22nowrap%22%3E%3Cspan+style%3D%22display%3Ainline-block%3Bmargin-bottom%3A-0.3em%3Bvertical-align%3A-0.4em%3Bline-height%3A1em%3Bfont-size%3A80%25%3Btext-align%3Aleft%22%3E%3Csup+style%3D%22font-size%3Ainherit%3Bline-height%3Ainherit%3Bvertical-align%3Abaseline%22%3E%2B%3C%2Fsup%3E%3Cbr+%2F%3E%3Csub+style%3D%22font-size%3Ainherit%3Bline-height%3Ainherit%3Bvertical-align%3Abaseline%22%3E2%3C%2Fsub%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E&rft.volume=86&rft.issue=9&rft.pages=1725-1728&rft.date=2001&rft_id=info%3Apmid%2F11290233&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.86.1725&rft_id=info%3Abibcode%2F2001PhRvL..86.1725C&rft.aulast=Critchley&rft.aufirst=A.+D.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-Korobov2022-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-Korobov2022_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKorobov2022" class="citation journal cs1">Korobov, V.I. (2022). "Variational Methods in the Quantum Mechanical Three-Body Problem with a Coulomb Interaction". <i><a href="/w/index.php?title=Physics_of_Particles_and_Nuclei&action=edit&redlink=1" class="new" title="Physics of Particles and Nuclei (page does not exist)">Physics of Particles and Nuclei</a></i>. <b>53</b> (1): 1–20. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2022PPN....53....1K">2022PPN....53....1K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1134%2FS1063779622010038">10.1134/S1063779622010038</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:258696598">258696598</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+of+Particles+and+Nuclei&rft.atitle=Variational+Methods+in+the+Quantum+Mechanical+Three-Body+Problem+with+a+Coulomb+Interaction&rft.volume=53&rft.issue=1&rft.pages=1-20&rft.date=2022&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A258696598%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1134%2FS1063779622010038&rft_id=info%3Abibcode%2F2022PPN....53....1K&rft.aulast=Korobov&rft.aufirst=V.I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-Korobov2021-21"><span class="mw-cite-backlink">^ <a href="#cite_ref-Korobov2021_21-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Korobov2021_21-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKorobovKarr2021" class="citation journal cs1">Korobov, Vladimir I.; Karr, Jean-Philippe (2021). "Rovibrational spin-averaged transitions in the hydrogen molecular ions". <i>Physical Review A</i>. <b>104</b> (3): 032806. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2107.14497">2107.14497</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2021PhRvA.104c2806K">2021PhRvA.104c2806K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevA.104.032806">10.1103/PhysRevA.104.032806</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:236635049">236635049</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+A&rft.atitle=Rovibrational+spin-averaged+transitions+in+the+hydrogen+molecular+ions&rft.volume=104&rft.issue=3&rft.pages=032806&rft.date=2021&rft_id=info%3Aarxiv%2F2107.14497&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A236635049%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevA.104.032806&rft_id=info%3Abibcode%2F2021PhRvA.104c2806K&rft.aulast=Korobov&rft.aufirst=Vladimir+I.&rft.au=Karr%2C+Jean-Philippe&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlighanbariKortunovGiriSchiller2023" class="citation journal cs1">Alighanbari, S.; Kortunov, I.V.; Giri, G.G.; Schiller, S. (2023). "Test of charged baryon interaction with high-resolution vibrational spectroscopy of molecular hydrogen ions". <i>Nature Physics</i>. <b>19</b> (9): 1263–1269. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41567-023-02088-2">10.1038/s41567-023-02088-2</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:259567529">259567529</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Physics&rft.atitle=Test+of+charged+baryon+interaction+with+high-resolution+vibrational+spectroscopy+of+molecular+hydrogen+ions&rft.volume=19&rft.issue=9&rft.pages=1263-1269&rft.date=2023&rft_id=info%3Adoi%2F10.1038%2Fs41567-023-02088-2&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A259567529%23id-name%3DS2CID&rft.aulast=Alighanbari&rft.aufirst=S.&rft.au=Kortunov%2C+I.V.&rft.au=Giri%2C+G.G.&rft.au=Schiller%2C+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHaidarKorobovHilicoKarr2022" class="citation journal cs1">Haidar, M.; Korobov, V.I.; Hilico, L.; Karr, J.Ph. (2022). "Higher-order corrections to spin–orbit and spin–spin tensor interactions in hydrogen molecular ions: theory and application to H<sub>2</sub><sup>+</sup>". <i>Physical Review A</i>. <b>106</b> (2): 022816. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2207.01535">2207.01535</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2022PhRvA.106b2816H">2022PhRvA.106b2816H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevA.106.022816">10.1103/PhysRevA.106.022816</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:251946960">251946960</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+A&rft.atitle=Higher-order+corrections+to+spin%E2%80%93orbit+and+spin%E2%80%93spin+tensor+interactions+in+hydrogen+molecular+ions%3A+theory+and+application+to+H%3Csub%3E2%3C%2Fsub%3E%3Csup%3E%2B%3C%2Fsup%3E&rft.volume=106&rft.issue=2&rft.pages=022816&rft.date=2022&rft_id=info%3Aarxiv%2F2207.01535&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A251946960%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevA.106.022816&rft_id=info%3Abibcode%2F2022PhRvA.106b2816H&rft.aulast=Haidar&rft.aufirst=M.&rft.au=Korobov%2C+V.I.&rft.au=Hilico%2C+L.&rft.au=Karr%2C+J.Ph.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-eherbstastro-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-eherbstastro_24-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHerbst2000" class="citation journal cs1">Herbst, E. (2000). "The Astrochemistry of <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sub></span></span></span>". <i><a href="/wiki/Philosophical_Transactions_of_the_Royal_Society_A" title="Philosophical Transactions of the Royal Society A">Philosophical Transactions of the Royal Society A</a></i>. <b>358</b> (1774): 2523–2534. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000RSPTA.358.2523H">2000RSPTA.358.2523H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsta.2000.0665">10.1098/rsta.2000.0665</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:97131120">97131120</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions+of+the+Royal+Society+A&rft.atitle=The+Astrochemistry+of+%3Cspan+class%3D%22chemf+nowrap%22%3EH%3Cspan+class%3D%22nowrap%22%3E%3Cspan+style%3D%22display%3Ainline-block%3Bmargin-bottom%3A-0.3em%3Bvertical-align%3A-0.4em%3Bline-height%3A1em%3Bfont-size%3A80%25%3Btext-align%3Aleft%22%3E%3Csup+style%3D%22font-size%3Ainherit%3Bline-height%3Ainherit%3Bvertical-align%3Abaseline%22%3E%2B%3C%2Fsup%3E%3Cbr+%2F%3E%3Csub+style%3D%22font-size%3Ainherit%3Bline-height%3Ainherit%3Bvertical-align%3Abaseline%22%3E3%3C%2Fsub%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E&rft.volume=358&rft.issue=1774&rft.pages=2523-2534&rft.date=2000&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A97131120%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1098%2Frsta.2000.0665&rft_id=info%3Abibcode%2F2000RSPTA.358.2523H&rft.aulast=Herbst&rft.aufirst=E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADihydrogen+cation" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPadovaniGalliGlassgold2009" class="citation journal cs1">Padovani, Marco; Galli, Daniele; Glassgold, Alfred E. (2009). "Cosmic-ray ionization of molecular clouds". <i>Astronomy & Astrophysics</i>. <b>501</b> (2): 619–631. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0904.4149">0904.4149</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009A&A...501..619P">2009A&A...501..619P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1051%2F0004-6361%2F200911794">10.1051/0004-6361/200911794</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:7897739">7897739</a>.</cite><span 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