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id="toc-Microcanonical_ensemble_(NVE)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Canonical_ensemble_(NVT)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Canonical_ensemble_(NVT)"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Canonical ensemble (NVT)</span> </div> </a> <ul id="toc-Canonical_ensemble_(NVT)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Isothermal–isobaric_(NPT)_ensemble" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Isothermal–isobaric_(NPT)_ensemble"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Isothermal–isobaric (NPT) ensemble</span> </div> </a> <ul id="toc-Isothermal–isobaric_(NPT)_ensemble-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Generalized_ensembles" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Generalized_ensembles"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Generalized ensembles</span> </div> </a> <ul id="toc-Generalized_ensembles-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Potentials_in_MD_simulations" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Potentials_in_MD_simulations"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Potentials in MD simulations</span> </div> </a> <button aria-controls="toc-Potentials_in_MD_simulations-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 Potentials in MD simulations subsection</span> </button> <ul id="toc-Potentials_in_MD_simulations-sublist" class="vector-toc-list"> <li id="toc-Empirical_potentials" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Empirical_potentials"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Empirical potentials</span> </div> </a> <ul id="toc-Empirical_potentials-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pair_potentials_versus_many-body_potentials" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pair_potentials_versus_many-body_potentials"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Pair potentials versus many-body potentials</span> </div> </a> <ul id="toc-Pair_potentials_versus_many-body_potentials-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Semi-empirical_potentials" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Semi-empirical_potentials"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Semi-empirical potentials</span> </div> </a> <ul id="toc-Semi-empirical_potentials-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Polarizable_potentials" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Polarizable_potentials"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Polarizable potentials</span> </div> </a> <ul id="toc-Polarizable_potentials-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Potentials_in_ab_initio_methods" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Potentials_in_ab_initio_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Potentials in <i>ab initio</i> methods</span> </div> </a> <ul id="toc-Potentials_in_ab_initio_methods-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hybrid_QM/MM" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hybrid_QM/MM"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Hybrid QM/MM</span> </div> </a> <ul id="toc-Hybrid_QM/MM-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Coarse-graining_and_reduced_representations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Coarse-graining_and_reduced_representations"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7</span> <span>Coarse-graining and reduced representations</span> </div> </a> <ul id="toc-Coarse-graining_and_reduced_representations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Machine_Learning_Force_Fields" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Machine_Learning_Force_Fields"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.8</span> <span>Machine Learning Force Fields</span> </div> </a> <ul id="toc-Machine_Learning_Force_Fields-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Incorporating_solvent_effects" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Incorporating_solvent_effects"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Incorporating solvent effects</span> </div> </a> <ul id="toc-Incorporating_solvent_effects-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Long-range_forces" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Long-range_forces"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Long-range forces</span> </div> </a> <ul id="toc-Long-range_forces-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Steered_molecular_dynamics_(SMD)" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Steered_molecular_dynamics_(SMD)"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Steered molecular dynamics (SMD)</span> </div> </a> <ul id="toc-Steered_molecular_dynamics_(SMD)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Examples_of_applications" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Examples_of_applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Examples of applications</span> </div> </a> <ul id="toc-Examples_of_applications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Molecular_dynamics_algorithms" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Molecular_dynamics_algorithms"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Molecular dynamics algorithms</span> </div> </a> <button aria-controls="toc-Molecular_dynamics_algorithms-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 Molecular dynamics algorithms subsection</span> </button> <ul id="toc-Molecular_dynamics_algorithms-sublist" class="vector-toc-list"> <li id="toc-Integrators" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Integrators"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.1</span> <span>Integrators</span> </div> </a> <ul id="toc-Integrators-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Short-range_interaction_algorithms" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Short-range_interaction_algorithms"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.2</span> <span>Short-range interaction algorithms</span> </div> </a> <ul id="toc-Short-range_interaction_algorithms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Long-range_interaction_algorithms" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Long-range_interaction_algorithms"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.3</span> <span>Long-range interaction algorithms</span> </div> </a> <ul id="toc-Long-range_interaction_algorithms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Parallelization_strategies" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Parallelization_strategies"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.4</span> <span>Parallelization strategies</span> </div> </a> <ul id="toc-Parallelization_strategies-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ab-initio_molecular_dynamics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ab-initio_molecular_dynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.5</span> <span>Ab-initio molecular dynamics</span> </div> </a> <ul id="toc-Ab-initio_molecular_dynamics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Specialized_hardware_for_MD_simulations" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Specialized_hardware_for_MD_simulations"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Specialized hardware for MD simulations</span> </div> </a> <ul id="toc-Specialized_hardware_for_MD_simulations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Graphics_card_as_a_hardware_for_MD_simulations" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Graphics_card_as_a_hardware_for_MD_simulations"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Graphics card as a hardware for MD simulations</span> </div> </a> <ul id="toc-Graphics_card_as_a_hardware_for_MD_simulations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</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"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>References</span> </div> </a> <button aria-controls="toc-References-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 References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-General_references" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#General_references"> <div class="vector-toc-text"> <span class="vector-toc-numb">13.1</span> <span>General references</span> </div> </a> <ul id="toc-General_references-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Molecular dynamics</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 29 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-29" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">29 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Molekuuldinamieksimulasie" title="Molekuuldinamieksimulasie – Afrikaans" lang="af" hreflang="af" data-title="Molekuuldinamieksimulasie" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D9%8A%D9%86%D8%A7%D9%85%D9%8A%D9%83%D8%A7_%D8%AC%D8%B2%D9%8A%D8%A6%D9%8A%D8%A9" title="ديناميكا جزيئية – Arabic" lang="ar" hreflang="ar" data-title="ديناميكا جزيئية" data-language-autonym="العربية" data-language-local-name="Arabic" 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/Din%C3%A0mica_molecular" title="Dinàmica molecular – Catalan" lang="ca" hreflang="ca" data-title="Dinàmica molecular" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Molekulardynamik-Simulation" title="Molekulardynamik-Simulation – German" lang="de" hreflang="de" data-title="Molekulardynamik-Simulation" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Molekulaard%C3%BCnaamika" title="Molekulaardünaamika – Estonian" lang="et" hreflang="et" data-title="Molekulaardünaamika" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Din%C3%A1mica_molecular" title="Dinámica molecular – Spanish" lang="es" hreflang="es" data-title="Dinámica molecular" 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/%D8%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9_%D9%85%D9%88%D9%84%DA%A9%D9%88%D9%84%DB%8C" title="دینامیک مولکولی – Persian" lang="fa" hreflang="fa" data-title="دینامیک مولکولی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Dynamique_mol%C3%A9culaire" title="Dynamique moléculaire – French" lang="fr" hreflang="fr" data-title="Dynamique moléculaire" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B6%84%EC%9E%90%EB%8F%99%EC%97%AD%ED%95%99" title="분자동역학 – Korean" lang="ko" hreflang="ko" data-title="분자동역학" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%B8%D5%AC%D5%A5%D5%AF%D5%B8%D6%82%D5%AC%D5%A1%D5%B5%D5%AB%D5%B6_%D5%A4%D5%AB%D5%B6%D5%A1%D5%B4%D5%AB%D5%AF%D5%A1" title="Մոլեկուլային դինամիկա – Armenian" lang="hy" hreflang="hy" data-title="Մոլեկուլային դինամիկա" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Dinamika_molekuler" title="Dinamika molekuler – Indonesian" lang="id" hreflang="id" data-title="Dinamika molekuler" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Dinamica_molecolare" title="Dinamica molecolare – Italian" lang="it" hreflang="it" data-title="Dinamica molecolare" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%93%D7%99%D7%A0%D7%9E%D7%99%D7%A7%D7%94_%D7%9E%D7%95%D7%9C%D7%A7%D7%95%D7%9C%D7%A8%D7%99%D7%AA" title="דינמיקה מולקולרית – Hebrew" lang="he" hreflang="he" data-title="דינמיקה מולקולרית" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D0%B0%D1%80%D0%BD%D0%B0_%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Молекуларна динамика – Macedonian" lang="mk" hreflang="mk" data-title="Молекуларна динамика" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Moleculaire_dynamica" title="Moleculaire dynamica – Dutch" lang="nl" hreflang="nl" data-title="Moleculaire dynamica" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%88%86%E5%AD%90%E5%8B%95%E5%8A%9B%E5%AD%A6%E6%B3%95" title="分子動力学法 – Japanese" lang="ja" hreflang="ja" data-title="分子動力学法" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Molekyl%C3%A6rdynamikk" title="Molekylærdynamikk – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Molekylærdynamikk" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Dynamika_molekularna" title="Dynamika molekularna – Polish" lang="pl" hreflang="pl" data-title="Dynamika molekularna" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Din%C3%A2mica_molecular" title="Dinâmica molecular – Portuguese" lang="pt" hreflang="pt" data-title="Dinâmica molecular" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Dinamic%C4%83_molecular%C4%83" title="Dinamică moleculară – Romanian" lang="ro" hreflang="ro" data-title="Dinamică moleculară" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D0%BA%D0%BB%D0%B0%D1%81%D1%81%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B9_%D0%BC%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D1%8F%D1%80%D0%BD%D0%BE%D0%B9_%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B8" title="Метод классической молекулярной динамики – Russian" lang="ru" hreflang="ru" data-title="Метод классической молекулярной динамики" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Molekulov%C3%A1_dynamika" title="Molekulová dynamika – Slovak" lang="sk" hreflang="sk" data-title="Molekulová dynamika" data-language-autonym="Slovenčina" 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free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Computer simulations to discover and understand chemical properties</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cudeposition.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Cudeposition.gif/300px-Cudeposition.gif" decoding="async" width="300" height="356" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/4/42/Cudeposition.gif 1.5x" data-file-width="320" data-file-height="380" /></a><figcaption>Example of a molecular dynamics simulation in a simple system: deposition of one <a href="/wiki/Copper" title="Copper">copper</a> (Cu) <a href="/wiki/Atom" title="Atom">atom</a> on a cold crystal of copper (<a href="/wiki/Miller_index" title="Miller index">Miller index</a> (001) <a href="/wiki/Surface_science" title="Surface science">surface</a>). Each circle represents the position of one atom. The kinetic energy of the atom approaching from the top is redistributed among the other atoms, so instead of bouncing off it remains attached due to attractive forces between the atoms.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:MD_water.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/MD_water.gif/300px-MD_water.gif" decoding="async" width="300" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/MD_water.gif/450px-MD_water.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/f/f4/MD_water.gif 2x" data-file-width="480" data-file-height="270" /></a><figcaption>Molecular dynamics simulations are often used to study biophysical systems. Depicted here is a 100 ps simulation of water.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Molecular_dynamics_algorithm.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Molecular_dynamics_algorithm.png/400px-Molecular_dynamics_algorithm.png" decoding="async" width="400" height="360" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Molecular_dynamics_algorithm.png/600px-Molecular_dynamics_algorithm.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Molecular_dynamics_algorithm.png/800px-Molecular_dynamics_algorithm.png 2x" data-file-width="1009" data-file-height="909" /></a><figcaption>A simplified description of the standard molecular dynamics simulation algorithm, when a predictor-corrector-type integrator is used. The forces may come either from classical <a href="/wiki/Interatomic_potential" title="Interatomic potential">interatomic potentials</a> (described mathematically as <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 F=-\nabla V({\vec {r}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∇</mi> <mi>V</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=-\nabla V({\vec {r}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd7059426ae61837bb659d01725a0728e9eb67c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.403ex; height:2.843ex;" alt="{\displaystyle F=-\nabla V({\vec {r}})}"></span>) or quantum mechanical (described mathematically as <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 F=F(\Psi ({\vec {r}}))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=F(\Psi ({\vec {r}}))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d303fa4bb9544781cfcbb7087feba919b5dfe30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.23ex; height:2.843ex;" alt="{\displaystyle F=F(\Psi ({\vec {r}}))}"></span>) methods. Large differences exist between different integrators; some do not have exactly the same highest-order terms as indicated in the flow chart, many also use higher-order time derivatives, and some use both the current and prior time step in variable-time step schemes.</figcaption></figure> <p><b>Molecular dynamics</b> (<b>MD</b>) is a <a href="/wiki/Computer_simulation" title="Computer simulation">computer simulation</a> method for analyzing the <a href="/wiki/Motion_(physics)" class="mw-redirect" title="Motion (physics)">physical movements</a> of <a href="/wiki/Atoms" class="mw-redirect" title="Atoms">atoms</a> and <a href="/wiki/Molecules" class="mw-redirect" title="Molecules">molecules</a>. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the <a href="/wiki/Dynamics_(mechanics)" class="mw-redirect" title="Dynamics (mechanics)">dynamic</a> "evolution" of the system. In the most common version, the <a href="/wiki/Trajectory" title="Trajectory">trajectories</a> of atoms and molecules are determined by <a href="/wiki/Numerical_integration" title="Numerical integration">numerically solving</a> <a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's equations of motion</a> for a system of interacting particles, where <a href="/wiki/Force_(physics)" class="mw-redirect" title="Force (physics)">forces</a> between the particles and their <a href="/wiki/Potential_energy" title="Potential energy">potential energies</a> are often calculated using <a href="/wiki/Interatomic_potential" title="Interatomic potential">interatomic potentials</a> or <a href="/wiki/Molecular_mechanics" title="Molecular mechanics">molecular mechanical</a> <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force fields</a>. The method is applied mostly in <a href="/wiki/Chemical_physics" title="Chemical physics">chemical physics</a>, <a href="/wiki/Materials_science" title="Materials science">materials science</a>, and <a href="/wiki/Biophysics" title="Biophysics">biophysics</a>. </p><p>Because molecular systems typically consist of a vast number of particles, it is impossible to determine the properties of such <a href="/wiki/Complex_systems" class="mw-redirect" title="Complex systems">complex systems</a> analytically; MD simulation circumvents this problem by using <a href="/wiki/Numerical_analysis" title="Numerical analysis">numerical</a> methods. However, long MD simulations are mathematically <a href="/wiki/Condition_number" title="Condition number">ill-conditioned</a>, generating cumulative errors in numerical integration that can be minimized with proper selection of algorithms and parameters, but not eliminated. </p><p>For systems that obey the <a href="/wiki/Ergodic_hypothesis" title="Ergodic hypothesis">ergodic hypothesis</a>, the evolution of one molecular dynamics simulation may be used to determine the macroscopic <a href="/wiki/Thermodynamic" class="mw-redirect" title="Thermodynamic">thermodynamic</a> properties of the system: the time averages of an ergodic system correspond to <a href="/wiki/Microcanonical_ensemble" title="Microcanonical ensemble">microcanonical ensemble</a> averages. MD has also been termed "<a href="/wiki/Statistical_mechanics" title="Statistical mechanics">statistical mechanics</a> by numbers" and "<a href="/wiki/Laplace" class="mw-redirect" title="Laplace">Laplace</a>'s vision of <a href="/wiki/Newtonian_mechanics" class="mw-redirect" title="Newtonian mechanics">Newtonian mechanics</a>" of predicting the future by animating nature's forces<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and allowing insight into molecular motion on an atomic scale. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>MD was originally developed in the early 1950s, following earlier successes with <a href="/wiki/Monte_Carlo_simulation" class="mw-redirect" title="Monte Carlo simulation">Monte Carlo simulations</a>—which themselves date back to the eighteenth century, in the <a href="/wiki/Buffon%27s_needle_problem" title="Buffon's needle problem">Buffon's needle problem</a> for example—but was popularized for <a href="/wiki/Statistical_mechanics" title="Statistical mechanics">statistical mechanics</a> at <a href="/wiki/Los_Alamos_National_Laboratory" title="Los Alamos National Laboratory">Los Alamos National Laboratory</a> by <a href="/wiki/Marshall_Rosenbluth" title="Marshall Rosenbluth">Marshall Rosenbluth</a> and <a href="/wiki/Nicholas_Metropolis" title="Nicholas Metropolis">Nicholas Metropolis</a> in what is known today as the <a href="/wiki/Metropolis%E2%80%93Hastings_algorithm" title="Metropolis–Hastings algorithm">Metropolis–Hastings algorithm</a>. Interest in the time evolution of <a href="/wiki/N-body_problem" title="N-body problem">N-body systems</a> dates much earlier to the seventeenth century, beginning with <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a>, and continued into the following century largely with a focus on <a href="/wiki/Celestial_mechanics" title="Celestial mechanics">celestial mechanics</a> and issues such as the <a href="/wiki/Stability_of_the_Solar_System" title="Stability of the Solar System">stability of the solar system</a>. Many of the numerical methods used today were developed during this time period, which predates the use of computers; for example, the most common integration algorithm used today, the <a href="/wiki/Verlet_integration" title="Verlet integration">Verlet integration</a> algorithm, was used as early as 1791 by <a href="/wiki/Jean_Baptiste_Joseph_Delambre" title="Jean Baptiste Joseph Delambre">Jean Baptiste Joseph Delambre</a>. Numerical calculations with these algorithms can be considered to be MD done "by hand". </p><p> As early as 1941, integration of the many-body equations of motion was carried out with <a href="/wiki/Analog_computer" title="Analog computer">analog computers</a>. Some undertook the labor-intensive work of modeling atomic motion by constructing physical models, e.g., using macroscopic spheres. The aim was to arrange them in such a way as to replicate the structure of a liquid and use this to examine its behavior. <a href="/wiki/J.D._Bernal" class="mw-redirect" title="J.D. Bernal">J.D. Bernal</a> describes this process in 1962, writing:<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><blockquote><p>... I took a number of rubber balls and stuck them together with rods of a selection of different lengths ranging from 2.75 to 4 inches. I tried to do this in the first place as casually as possible, working in my own office, being interrupted every five minutes or so and not remembering what I had done before the interruption.</p></blockquote><p>Following the discovery of microscopic particles and the development of computers, interest expanded beyond the proving ground of gravitational systems to the statistical properties of matter. In an attempt to understand the origin of <a href="/wiki/Irreversibility" class="mw-redirect" title="Irreversibility">irreversibility</a>, <a href="/wiki/Enrico_Fermi" title="Enrico Fermi">Enrico Fermi</a> proposed in 1953, and published in 1955,<sup id="cite_ref-fput_3-0" class="reference"><a href="#cite_note-fput-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> the use of the early computer <a href="/wiki/MANIAC_I" title="MANIAC I">MANIAC I</a>, also at <a href="/wiki/Los_Alamos_National_Laboratory" title="Los Alamos National Laboratory">Los Alamos National Laboratory</a>, to solve the time evolution of the equations of motion for a many-body system subject to several choices of force laws. Today, this seminal work is known as the <a href="/wiki/Fermi%E2%80%93Pasta%E2%80%93Ulam%E2%80%93Tsingou_problem" title="Fermi–Pasta–Ulam–Tsingou problem">Fermi–Pasta–Ulam–Tsingou problem</a>. The time evolution of the energy from the original work is shown in the figure to the right. </p><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Time_evolution_of_energy_for_FPUT_N-body_dynamics.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Time_evolution_of_energy_for_FPUT_N-body_dynamics.jpg/300px-Time_evolution_of_energy_for_FPUT_N-body_dynamics.jpg" decoding="async" width="300" height="333" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Time_evolution_of_energy_for_FPUT_N-body_dynamics.jpg/450px-Time_evolution_of_energy_for_FPUT_N-body_dynamics.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/9/9d/Time_evolution_of_energy_for_FPUT_N-body_dynamics.jpg 2x" data-file-width="461" data-file-height="512" /></a><figcaption>One of the earliest simulations of an N-body system was carried out on the MANIAC-I by Fermi and coworkers to understand the origins of irreversibility in nature. Shown here is the energy versus time for a 64-particle system.</figcaption></figure> <p>In 1957, <a href="/wiki/Berni_Alder" title="Berni Alder">Berni Alder</a> and Thomas Wainwright used an <a href="/wiki/IBM_704" title="IBM 704">IBM 704</a> computer to simulate perfectly <a href="/wiki/Elastic_collision" title="Elastic collision">elastic collisions</a> between <a href="/wiki/Hard_spheres" title="Hard spheres">hard spheres</a>.<sup id="cite_ref-a&w_4-0" class="reference"><a href="#cite_note-a&w-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> In 1960, in perhaps the first realistic simulation of matter, J.B. Gibson <i>et al</i>. simulated radiation damage of <a href="/wiki/Native_copper" title="Native copper">solid copper</a> by using a <a href="/wiki/Born%E2%80%93Mayer_equation" title="Born–Mayer equation">Born–Mayer</a> type of repulsive interaction along with a <a href="/wiki/Cohesion_(chemistry)" title="Cohesion (chemistry)">cohesive</a> surface force.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> In 1964, <a href="/wiki/Aneesur_Rahman" title="Aneesur Rahman">Aneesur Rahman</a> published simulations of liquid <a href="/wiki/Argon" title="Argon">argon</a> that used a <a href="/wiki/Lennard-Jones_potential" title="Lennard-Jones potential">Lennard-Jones potential</a>; calculations of system properties, such as the coefficient of <a href="/wiki/Self-diffusion" title="Self-diffusion">self-diffusion</a>, compared well with experimental data.<sup id="cite_ref-a.rahman_6-0" class="reference"><a href="#cite_note-a.rahman-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Today, the Lennard-Jones potential is still one of the most frequently used <a href="/wiki/Interatomic_potential" title="Interatomic potential">intermolecular potentials</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> It is used for describing simple substances (a.k.a. <a href="/wiki/Lennard-Jones_potential" title="Lennard-Jones potential">Lennard-Jonesium</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><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>) for conceptual and model studies and as a building block in many <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force fields</a> of real substances.<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><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> </p> <div class="mw-heading mw-heading2"><h2 id="Areas_of_application_and_limits">Areas of application and limits</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=2" title="Edit section: Areas of application and limits"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>First used in <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a>, the molecular dynamics method gained popularity in <a href="/wiki/Materials_science" title="Materials science">materials science</a> soon afterward, and since the 1970s it has also been commonly used in <a href="/wiki/Biochemistry" title="Biochemistry">biochemistry</a> and <a href="/wiki/Biophysics" title="Biophysics">biophysics</a>. MD is frequently used to refine 3-dimensional structures of <a href="/wiki/Protein" title="Protein">proteins</a> and other <a href="/wiki/Macromolecule" title="Macromolecule">macromolecules</a> based on experimental constraints from <a href="/wiki/X-ray_crystallography" title="X-ray crystallography">X-ray crystallography</a> or <a href="/wiki/Nuclear_magnetic_resonance_spectroscopy" title="Nuclear magnetic resonance spectroscopy">NMR spectroscopy</a>. In physics, MD is used to examine the dynamics of atomic-level phenomena that cannot be observed directly, such as <a href="/wiki/Thin_film" title="Thin film">thin film</a> growth and ion subplantation, and to examine the physical properties of <a href="/wiki/Nanotechnology" title="Nanotechnology">nanotechnological</a> devices that have not or cannot yet be created. In biophysics and <a href="/wiki/Structural_biology" title="Structural biology">structural biology</a>, the method is frequently applied to study the motions of macromolecules such as proteins and <a href="/wiki/Nucleic_acid" title="Nucleic acid">nucleic acids</a>, which can be useful for interpreting the results of certain biophysical experiments and for modeling interactions with other molecules, as in <a href="/wiki/Ligand_docking" class="mw-redirect" title="Ligand docking">ligand docking</a>. In principle, MD can be used for <a href="/wiki/De_novo_protein_structure_prediction" title="De novo protein structure prediction"><i>ab initio</i> prediction</a> of <a href="/wiki/Protein_structure" title="Protein structure">protein structure</a> by simulating <a href="/wiki/Protein_folding" title="Protein folding">folding</a> of the <a href="/wiki/Polypeptide_chain" class="mw-redirect" title="Polypeptide chain">polypeptide chain</a> from a <a href="/wiki/Random_coil" title="Random coil">random coil</a>. </p><p>The results of MD simulations can be tested through comparison to experiments that measure molecular dynamics, of which a popular method is NMR spectroscopy. MD-derived structure predictions can be tested through community-wide experiments in Critical Assessment of Protein Structure Prediction (<a href="/wiki/CASP" title="CASP">CASP</a>), although the method has historically had limited success in this area. <a href="/wiki/Michael_Levitt_(biophysicist)" title="Michael Levitt (biophysicist)">Michael Levitt</a>, who shared the <a href="/wiki/Nobel_Prize" title="Nobel Prize">Nobel Prize</a> partly for the application of MD to proteins, wrote in 1999 that CASP participants usually did not use the method due to "... a central embarrassment of <a href="/wiki/Molecular_mechanics" title="Molecular mechanics">molecular mechanics</a>, namely that <a href="/wiki/Energy_minimization" title="Energy minimization">energy minimization</a> or molecular dynamics generally leads to a model that is less like the experimental structure".<sup id="cite_ref-Koehl_14-0" class="reference"><a href="#cite_note-Koehl-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Improvements in computational resources permitting more and longer MD trajectories, combined with modern improvements in the quality of <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force field</a> parameters, have yielded some improvements in both structure prediction and <a href="/wiki/Homology_model" class="mw-redirect" title="Homology model">homology model</a> refinement, without reaching the point of practical utility in these areas; many identify force field parameters as a key area for further development.<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><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><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> </p><p>MD simulation has been reported for <a href="/wiki/Pharmacophore" title="Pharmacophore">pharmacophore</a> development and <a href="/wiki/Drug_design" title="Drug design">drug design</a>.<sup id="cite_ref-pmid25751016_18-0" class="reference"><a href="#cite_note-pmid25751016-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> For example, Pinto <i>et al</i>. implemented MD simulations of <a href="/wiki/Bcl-xL" title="Bcl-xL">Bcl-xL complexes</a> to calculate average positions of critical <a href="/wiki/Amino_acid" title="Amino acid">amino acids</a> involved in ligand binding.<sup id="cite_ref-pmid15143800_19-0" class="reference"><a href="#cite_note-pmid15143800-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Carlson <i>et al</i>. implemented molecular dynamics simulations to identify compounds that complement a <a href="/wiki/Receptor_(biochemistry)" title="Receptor (biochemistry)">receptor</a> while causing minimal disruption to the conformation and flexibility of the active site. Snapshots of the protein at constant time intervals during the simulation were overlaid to identify conserved binding regions (conserved in at least three out of eleven frames) for pharmacophore development. Spyrakis <i>et al</i>. relied on a workflow of MD simulations, fingerprints for ligands and proteins (FLAP) and <a href="/wiki/Linear_discriminant_analysis" title="Linear discriminant analysis">linear discriminant analysis</a> (LDA) to identify the best ligand-protein conformations to act as pharmacophore templates based on retrospective <a href="/wiki/Receiver_operating_characteristic" title="Receiver operating characteristic">ROC</a> analysis of the resulting pharmacophores. In an attempt to ameliorate structure-based drug discovery modeling, <i>vis-à-vis</i> the need for many modeled compounds, Hatmal <i>et al</i>. proposed a combination of MD simulation and ligand-receptor intermolecular contacts analysis to discern critical intermolecular contacts (binding interactions) from redundant ones in a single ligand–protein complex. Critical contacts can then be converted into pharmacophore models that can be used for virtual screening.<sup id="cite_ref-pmid27722817_20-0" class="reference"><a href="#cite_note-pmid27722817-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>An important factor is intramolecular <a href="/wiki/Hydrogen_bond" title="Hydrogen bond">hydrogen bonds</a>,<sup id="cite_ref-Myers_21-0" class="reference"><a href="#cite_note-Myers-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> which are not explicitly included in modern force fields, but described as <a href="/wiki/Coulomb_interaction" class="mw-redirect" title="Coulomb interaction">Coulomb interactions</a> of atomic <a href="/wiki/Point_charge" class="mw-redirect" title="Point charge">point charges</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="Needs a citation to show this is a general issue and not an issue with specific forcefields (February 2024)">citation needed</span></a></i>]</sup> This is a crude approximation because hydrogen bonds have a partially <a href="/wiki/Quantum_mechanical" class="mw-redirect" title="Quantum mechanical">quantum mechanical</a> and <a href="/wiki/Quantum_chemistry" title="Quantum chemistry">chemical</a> nature. Furthermore, electrostatic interactions are usually calculated using the <a href="/wiki/Vacuum_permittivity" title="Vacuum permittivity">dielectric constant of a vacuum</a>, even though the surrounding <a href="/wiki/Aqueous_solution" title="Aqueous solution">aqueous solution</a> has a much higher dielectric constant. Thus, using the <a href="/wiki/Macroscopic" class="mw-redirect" title="Macroscopic">macroscopic</a> dielectric constant at short interatomic distances is questionable. Finally, <a href="/wiki/Van_der_Waals_force" title="Van der Waals force">van der Waals interactions</a> in MD are usually described by <a href="/wiki/Lennard-Jones_potential" title="Lennard-Jones potential">Lennard-Jones potentials</a><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><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> based on the <a href="/wiki/Fritz_London" title="Fritz London">Fritz London</a> theory that is only applicable in a vacuum.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="needs a citation to show this true in the general case and not just specific forcefields. (February 2024)">citation needed</span></a></i>]</sup> However, all types of van der Waals forces are ultimately of electrostatic origin and therefore depend on <a href="/wiki/Permittivity" title="Permittivity">dielectric properties of the environment</a>.<sup id="cite_ref-Israelachvili_24-0" class="reference"><a href="#cite_note-Israelachvili-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> The direct measurement of attraction forces between different materials (as <a href="/wiki/Hamaker_constant" title="Hamaker constant">Hamaker constant</a>) shows that "the interaction between <a href="/wiki/Hydrocarbon" title="Hydrocarbon">hydrocarbons</a> across water is about 10% of that across vacuum".<sup id="cite_ref-Israelachvili_24-1" class="reference"><a href="#cite_note-Israelachvili-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> The environment-dependence of van der Waals forces is neglected in standard simulations, but can be included by developing polarizable force fields. </p> <div class="mw-heading mw-heading2"><h2 id="Design_constraints">Design constraints</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=3" title="Edit section: Design constraints"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The design of a molecular dynamics simulation should account for the available computational power. Simulation size (<i>n</i> = number of particles), timestep, and total time duration must be selected so that the calculation can finish within a reasonable time period. However, the simulations should be long enough to be relevant to the time scales of the natural processes being studied. To make statistically valid conclusions from the simulations, the time span simulated should match the <a href="/wiki/Kinetics_(physics)" title="Kinetics (physics)">kinetics</a> of the natural process. Otherwise, it is analogous to making conclusions about how a human walks when only looking at less than one footstep. Most scientific publications about the dynamics of proteins and DNA<sup id="cite_ref-ReferenceB_25-0" class="reference"><a href="#cite_note-ReferenceB-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ReferenceC_26-0" class="reference"><a href="#cite_note-ReferenceC-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> use data from simulations spanning nanoseconds (10<sup>−9</sup> s) to microseconds (10<sup>−6</sup> s). To obtain these simulations, several <a href="/wiki/CPU_time" title="CPU time">CPU-days</a> to CPU-years are needed. <a href="/wiki/Parallel_algorithm" title="Parallel algorithm">Parallel algorithms</a> allow the load to be distributed among <a href="/wiki/Central_processing_unit" title="Central processing unit">CPUs</a>; an example is the spatial or force decomposition algorithm.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p><p>During a classical MD simulation, the most CPU intensive task is the evaluation of the potential as a function of the particles' internal coordinates. Within that energy evaluation, the most expensive one is the non-bonded or non-covalent part. In <a href="/wiki/Big_O_notation" title="Big O notation">big O notation</a>, common molecular dynamics simulations <a href="/wiki/Analysis_of_algorithms" title="Analysis of algorithms">scale</a> by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(n^{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(n^{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cd9594a16cb898b8f2a2dff9227a385ec183392" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.032ex; height:3.176ex;" alt="{\displaystyle O(n^{2})}"></span> if all pair-wise <a href="/wiki/Electrostatic" class="mw-redirect" title="Electrostatic">electrostatic</a> and <a href="/wiki/Van_der_Waals_forces" class="mw-redirect" title="Van der Waals forces">van der Waals interactions</a> must be accounted for explicitly. This computational cost can be reduced by employing <a href="/wiki/Electrostatics" title="Electrostatics">electrostatics</a> methods such as particle mesh <a href="/wiki/Ewald_summation" title="Ewald summation">Ewald summation</a> ( <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(n\log(n))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mi>log</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(n\log(n))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85994022c28e938772bd858cd8281328643e8b3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.54ex; height:2.843ex;" alt="{\displaystyle O(n\log(n))}"></span> ), particle-particle-particle mesh (<a href="/wiki/P3M" title="P3M">P<sup>3</sup>M</a>), or good spherical cutoff methods ( <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 O(n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34109fe397fdcff370079185bfdb65826cb5565a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.977ex; height:2.843ex;" alt="{\displaystyle O(n)}"></span> ). <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. (December 2017)">citation needed</span></a></i>]</sup> </p><p>Another factor that impacts total CPU time needed by a simulation is the size of the integration timestep. This is the time length between evaluations of the potential. The timestep must be chosen small enough to avoid <a href="/wiki/Discretization_error" title="Discretization error">discretization errors</a> (i.e., smaller than the period related to fastest vibrational frequency in the system). Typical timesteps for classical MD are on the order of 1 femtosecond (10<sup>−15</sup> s). This value may be extended by using algorithms such as the SHAKE <a href="/wiki/Constraint_algorithm" class="mw-redirect" title="Constraint algorithm">constraint algorithm</a>, which fix the vibrations of the fastest atoms (e.g., hydrogens) into place. Multiple time scale methods have also been developed, which allow extended times between updates of slower long-range forces.<sup id="cite_ref-Streett_28-0" class="reference"><a href="#cite_note-Streett-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Tuckerman1991_29-0" class="reference"><a href="#cite_note-Tuckerman1991-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Tuckerman1992_30-0" class="reference"><a href="#cite_note-Tuckerman1992-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p><p>For simulating molecules in a <a href="/wiki/Solvent" title="Solvent">solvent</a>, a choice should be made between an <a href="/wiki/Water_model" title="Water model">explicit</a> and <a href="/wiki/Implicit_solvent" class="mw-redirect" title="Implicit solvent">implicit solvent</a>. Explicit solvent particles (such as the <a href="/wiki/TIP3P" class="mw-redirect" title="TIP3P">TIP3P</a>, SPC/E and <a href="/wiki/Flexible_SPC_water_model" class="mw-redirect" title="Flexible SPC water model">SPC-f</a> water models) must be calculated expensively by the force field, while implicit solvents use a <a href="/wiki/Mean-field_particle_methods" title="Mean-field particle methods">mean-field</a> approach. Using an explicit solvent is computationally expensive, requiring inclusion of roughly ten times more particles in the simulation. But the granularity and viscosity of explicit solvent is essential to reproduce certain properties of the solute molecules. This is especially important to reproduce <a href="/wiki/Chemical_kinetics" title="Chemical kinetics">chemical kinetics</a>. </p><p>In all kinds of molecular dynamics simulations, the simulation box size must be large enough to avoid <a href="/wiki/Boundary_condition" class="mw-redirect" title="Boundary condition">boundary condition</a> artifacts. Boundary conditions are often treated by choosing fixed values at the edges (which may cause artifacts), or by employing <a href="/wiki/Periodic_boundary_conditions" title="Periodic boundary conditions">periodic boundary conditions</a> in which one side of the simulation loops back to the opposite side, mimicking a bulk phase (which may cause artifacts too). </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Sampling_in_Monte_Carlo_and_molecular_dynamics.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Sampling_in_Monte_Carlo_and_molecular_dynamics.png/330px-Sampling_in_Monte_Carlo_and_molecular_dynamics.png" decoding="async" width="330" height="252" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Sampling_in_Monte_Carlo_and_molecular_dynamics.png/495px-Sampling_in_Monte_Carlo_and_molecular_dynamics.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Sampling_in_Monte_Carlo_and_molecular_dynamics.png/660px-Sampling_in_Monte_Carlo_and_molecular_dynamics.png 2x" data-file-width="1484" data-file-height="1131" /></a><figcaption>Schematic representation of the sampling of the system's potential energy surface with molecular dynamics (in red) compared to Monte Carlo methods (in blue)</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Microcanonical_ensemble_(NVE)"><span id="Microcanonical_ensemble_.28NVE.29"></span>Microcanonical ensemble (NVE)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=4" title="Edit section: Microcanonical ensemble (NVE)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the <a href="/wiki/Microcanonical_ensemble" title="Microcanonical ensemble">microcanonical ensemble</a>, the system is isolated from changes in <a href="/wiki/Mole_(unit)" title="Mole (unit)">moles</a> (N), volume (V), and energy (E). It corresponds to an <a href="/wiki/Adiabatic_process" title="Adiabatic process">adiabatic process</a> with no heat exchange. A microcanonical molecular dynamics trajectory may be seen as an exchange of potential and kinetic energy, with total energy being conserved. For a system of <i>N</i> particles with coordinates <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 X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> and velocities <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span>, the following pair of first order differential equations may be written in <a href="/wiki/Newton%27s_notation_for_differentiation" class="mw-redirect" title="Newton's notation for differentiation">Newton's notation</a> 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 F(X)=-\nabla U(X)=M{\dot {V}}(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∇</mi> <mi>U</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>V</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(X)=-\nabla U(X)=M{\dot {V}}(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f7560efa135d8a5473945a4377527c4925cad9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.921ex; height:3.176ex;" alt="{\displaystyle F(X)=-\nabla U(X)=M{\dot {V}}(t)}"></span></dd> <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(t)={\dot {X}}(t).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V(t)={\dot {X}}(t).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/606da6e62c5039e523b71f8d58c05a064e9813b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.81ex; height:3.176ex;" alt="{\displaystyle V(t)={\dot {X}}(t).}"></span></dd></dl> <p>The <a href="/wiki/Potential_energy" title="Potential energy">potential energy function</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53cec1a859eb7949bada671f6c1566e0d9cfe4b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.572ex; height:2.843ex;" alt="{\displaystyle U(X)}"></span> of the system is a function of the particle coordinates <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 X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span>. It is referred to simply as the <i>potential</i> in physics, or the <i><a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force field</a></i> in chemistry. The first equation comes from <a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's laws of motion</a>; the force <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 F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span> acting on each particle in the system can be calculated as the negative gradient of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53cec1a859eb7949bada671f6c1566e0d9cfe4b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.572ex; height:2.843ex;" alt="{\displaystyle U(X)}"></span>. </p><p>For every time step, each particle's position <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 X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> and velocity <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> may be integrated with a <a href="/wiki/Symplectic_integrator" title="Symplectic integrator">symplectic integrator</a> method such as <a href="/wiki/Verlet_integration" title="Verlet integration">Verlet integration</a>. The time evolution of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> is called a trajectory. Given the initial positions (e.g., from theoretical knowledge) and velocities (e.g., randomized <a href="/wiki/Gaussian" class="mw-redirect" title="Gaussian">Gaussian</a>), we can calculate all future (or past) positions and velocities. </p><p>One frequent source of confusion is the meaning of <a href="/wiki/Temperature" title="Temperature">temperature</a> in MD. Commonly we have experience with macroscopic temperatures, which involve a huge number of particles, but temperature is a statistical quantity. If there is a large enough number of atoms, statistical temperature can be estimated from the <i>instantaneous temperature</i>, which is found by equating the kinetic energy of the system to <i>nk<sub>B</sub>T</i>/2, where <i>n</i> is the number of degrees of freedom of the system. </p><p>A temperature-related phenomenon arises due to the small number of atoms that are used in MD simulations. For example, consider simulating the growth of a copper film starting with a substrate containing 500 atoms and a deposition energy of 100 <a href="/wiki/Electronvolt" title="Electronvolt">eV</a>. In the real world, the 100 eV from the deposited atom would rapidly be transported through and shared among a large number of atoms (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 10^{10}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10^{10}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b086010e3cc3b0a4e22c858243d32ec1cc648e6a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.201ex; height:2.676ex;" alt="{\displaystyle 10^{10}}"></span> or more) with no big change in temperature. When there are only 500 atoms, however, the substrate is almost immediately vaporized by the deposition. Something similar happens in biophysical simulations. The temperature of the system in NVE is naturally raised when macromolecules such as proteins undergo exothermic conformational changes and binding. </p> <div class="mw-heading mw-heading3"><h3 id="Canonical_ensemble_(NVT)"><span id="Canonical_ensemble_.28NVT.29"></span>Canonical ensemble (NVT)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=5" title="Edit section: Canonical ensemble (NVT)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the <a href="/wiki/Canonical_ensemble" title="Canonical ensemble">canonical ensemble</a>, amount of substance (N), volume (V) and temperature (T) are conserved. It is also sometimes called constant temperature molecular dynamics (CTMD). In NVT, the energy of endothermic and exothermic processes is exchanged with a <a href="/wiki/Thermostat" title="Thermostat">thermostat</a>. </p><p>A variety of thermostat algorithms are available to add and remove energy from the boundaries of an MD simulation in a more or less realistic way, approximating the <a href="/wiki/Canonical_ensemble" title="Canonical ensemble">canonical ensemble</a>. Popular methods to control temperature include velocity rescaling, the <a href="/wiki/Nos%C3%A9%E2%80%93Hoover_thermostat" title="Nosé–Hoover thermostat">Nosé–Hoover thermostat</a>, Nosé–Hoover chains, the <a href="/wiki/Berendsen_thermostat" title="Berendsen thermostat">Berendsen thermostat</a>, the <a href="/wiki/Andersen_thermostat" title="Andersen thermostat">Andersen thermostat</a> and <a href="/wiki/Langevin_dynamics" title="Langevin dynamics">Langevin dynamics</a>. The Berendsen thermostat might introduce the <a href="/wiki/Flying_ice_cube" title="Flying ice cube">flying ice cube</a> effect, which leads to unphysical translations and rotations of the simulated system. </p><p>It is not trivial to obtain a canonical ensemble distribution of conformations and velocities using these algorithms. How this depends on system size, thermostat choice, thermostat parameters, time step and integrator is the subject of many articles in the field. </p> <div class="mw-heading mw-heading3"><h3 id="Isothermal–isobaric_(NPT)_ensemble"><span id="Isothermal.E2.80.93isobaric_.28NPT.29_ensemble"></span>Isothermal–isobaric (NPT) ensemble</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=6" title="Edit section: Isothermal–isobaric (NPT) ensemble"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the <a href="/wiki/Isothermal%E2%80%93isobaric_ensemble" title="Isothermal–isobaric ensemble">isothermal–isobaric ensemble</a>, amount of substance (N), pressure (P) and temperature (T) are conserved. In addition to a thermostat, a <a href="/wiki/Barostat" title="Barostat">barostat</a> is needed. It corresponds most closely to laboratory conditions with a flask open to ambient temperature and pressure. </p><p>In the simulation of <a href="/wiki/Biological_membrane" title="Biological membrane">biological membranes</a>, <a href="/wiki/Isotropic" class="mw-redirect" title="Isotropic">isotropic</a> pressure control is not appropriate. For <a href="/wiki/Lipid_bilayer" title="Lipid bilayer">lipid bilayers</a>, pressure control occurs under constant membrane area (NPAT) or constant surface tension "gamma" (NPγT). </p> <div class="mw-heading mw-heading3"><h3 id="Generalized_ensembles">Generalized ensembles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=7" title="Edit section: Generalized ensembles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Replica_exchange" class="mw-redirect" title="Replica exchange">replica exchange</a> method is a generalized ensemble. It was originally created to deal with the slow dynamics of disordered spin systems. It is also called parallel tempering. The replica exchange MD (REMD) formulation<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> tries to overcome the multiple-minima problem by exchanging the temperature of non-interacting replicas of the system running at several temperatures. </p> <div class="mw-heading mw-heading2"><h2 id="Potentials_in_MD_simulations">Potentials in MD simulations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=8" title="Edit section: Potentials in MD simulations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Interatomic_potential" title="Interatomic potential">Interatomic potential</a>, <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">Force field</a>, and <a href="/wiki/Comparison_of_force_field_implementations" class="mw-redirect" title="Comparison of force field implementations">Comparison of force field implementations</a></div> <p>A molecular dynamics simulation requires the definition of a <a href="/wiki/Function_(mathematics)" title="Function (mathematics)">potential function</a>, or a description of the terms by which the particles in the simulation will interact. In chemistry and biology this is usually referred to as a <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force field</a> and in materials physics as an <a href="/wiki/Interatomic_potential" title="Interatomic potential">interatomic potential</a>. Potentials may be defined at many levels of physical accuracy; those most commonly used in chemistry are based on <a href="/wiki/Molecular_mechanics" title="Molecular mechanics">molecular mechanics</a> and embody a <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical mechanics</a> treatment of particle-particle interactions that can reproduce structural and <a href="/wiki/Conformational_change" title="Conformational change">conformational changes</a> but usually cannot reproduce <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reactions</a>. </p><p>The reduction from a fully quantum description to a classical potential entails two main approximations. The first one is the <a href="/wiki/Born%E2%80%93Oppenheimer_approximation" title="Born–Oppenheimer approximation">Born–Oppenheimer approximation</a>, which states that the dynamics of electrons are so fast that they can be considered to react instantaneously to the motion of their nuclei. As a consequence, they may be treated separately. The second one treats the nuclei, which are much heavier than electrons, as point particles that follow classical Newtonian dynamics. In classical molecular dynamics, the effect of the electrons is approximated as one potential energy surface, usually representing the ground state. </p><p>When finer levels of detail are needed, potentials based on <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> are used; some methods attempt to create hybrid <a href="/wiki/QM/MM" title="QM/MM">classical/quantum</a> potentials where the bulk of the system is treated classically but a small region is treated as a quantum system, usually undergoing a chemical transformation. </p> <div class="mw-heading mw-heading3"><h3 id="Empirical_potentials">Empirical potentials</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=9" title="Edit section: Empirical potentials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Empirical potentials used in chemistry are frequently called <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force fields</a>, while those used in materials physics are called <a href="/wiki/Interatomic_potential" title="Interatomic potential">interatomic potentials</a>. </p><p>Most <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force fields</a> in chemistry are empirical and consist of a summation of bonded forces associated with <a href="/wiki/Chemical_bond" title="Chemical bond">chemical bonds</a>, bond angles, and bond <a href="/wiki/Dihedral_angle" title="Dihedral angle">dihedrals</a>, and non-bonded forces associated with <a href="/wiki/Van_der_Waals_force" title="Van der Waals force">van der Waals forces</a> and <a href="/wiki/Electrostatic_charge" class="mw-redirect" title="Electrostatic charge">electrostatic charge</a>.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> Empirical potentials represent quantum-mechanical effects in a limited way through ad hoc functional approximations. These potentials contain free parameters such as <a href="/wiki/Electrostatic_charge" class="mw-redirect" title="Electrostatic charge">atomic charge</a>, van der Waals parameters reflecting estimates of <a href="/wiki/Atomic_radius" title="Atomic radius">atomic radius</a>, and equilibrium <a href="/wiki/Bond_length" title="Bond length">bond length</a>, angle, and dihedral; these are obtained by fitting against detailed electronic calculations (quantum chemical simulations) or experimental physical properties such as <a href="/wiki/Young%27s_modulus" title="Young's modulus">elastic constants</a>, lattice parameters and <a href="/wiki/Spectroscopy" title="Spectroscopy">spectroscopic</a> measurements. </p><p>Because of the non-local nature of non-bonded interactions, they involve at least weak interactions between all particles in the system. Its calculation is normally the bottleneck in the speed of MD simulations. To lower the computational cost, <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force fields</a> employ numerical approximations such as shifted cutoff radii, <a href="/wiki/Reaction_field_method" title="Reaction field method">reaction field</a> algorithms, particle mesh <a href="/wiki/Ewald_summation" title="Ewald summation">Ewald summation</a>, or the newer particle–particle-particle–mesh (<a href="/wiki/P3M" title="P3M">P3M</a>). </p><p>Chemistry force fields commonly employ preset bonding arrangements (an exception being <i><a href="/wiki/Ab_initio_quantum_chemistry_methods" title="Ab initio quantum chemistry methods">ab initio</a></i> dynamics), and thus are unable to model the process of chemical bond breaking and reactions explicitly. On the other hand, many of the potentials used in physics, such as those based on the <a href="/wiki/Bond_order_potential" title="Bond order potential">bond order formalism</a> can describe several different coordinations of a system and bond breaking.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> Examples of such potentials include the <a href="/wiki/Brenner_potential" class="mw-redirect" title="Brenner potential">Brenner potential</a><sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> for hydrocarbons and its further developments for the C-Si-H<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> and C-O-H<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> systems. The <a href="/wiki/ReaxFF" title="ReaxFF">ReaxFF</a> potential<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> can be considered a fully reactive hybrid between bond order potentials and chemistry force fields. </p> <div class="mw-heading mw-heading3"><h3 id="Pair_potentials_versus_many-body_potentials">Pair potentials versus many-body potentials</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=10" title="Edit section: Pair potentials versus many-body potentials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The potential functions representing the non-bonded energy are formulated as a sum over interactions between the particles of the system. The simplest choice, employed in many popular <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force fields</a>, is the "pair potential", in which the total potential energy can be calculated from the sum of energy contributions between pairs of atoms. Therefore, these force fields are also called "additive force fields". An example of such a pair potential is the non-bonded <a href="/wiki/Lennard-Jones_potential" title="Lennard-Jones potential">Lennard-Jones potential</a> (also termed the 6–12 potential), used for calculating van der Waals forces. </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 U(r)=4\varepsilon \left[\left({\frac {\sigma }{r}}\right)^{12}-\left({\frac {\sigma }{r}}\right)^{6}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>4</mn> <mi>ε</mi> <mrow> <mo>[</mo> <mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>σ</mi> <mi>r</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>σ</mi> <mi>r</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U(r)=4\varepsilon \left[\left({\frac {\sigma }{r}}\right)^{12}-\left({\frac {\sigma }{r}}\right)^{6}\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/374024e23ac5eb77e91b68ad9ba86ad3bbf5f113" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:28.48ex; height:6.176ex;" alt="{\displaystyle U(r)=4\varepsilon \left[\left({\frac {\sigma }{r}}\right)^{12}-\left({\frac {\sigma }{r}}\right)^{6}\right]}"></span></dd></dl> <p>Another example is the Born (ionic) model of the ionic lattice. The first term in the next equation is <a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb's law</a> for a pair of ions, the second term is the short-range repulsion explained by Pauli's exclusion principle and the final term is the dispersion interaction term. Usually, a simulation only includes the dipolar term, although sometimes the quadrupolar term is also included.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> When <i>n<sub>l</sub></i> = 6, this potential is also called the <a href="/wiki/Buckingham_potential" title="Buckingham potential">Coulomb–Buckingham potential</a>. </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 U_{ij}(r_{ij})={\frac {z_{i}z_{j}}{4\pi \epsilon _{0}}}{\frac {1}{r_{ij}}}+A_{l}\exp {\frac {-r_{ij}}{p_{l}}}+C_{l}r_{ij}^{-n_{l}}+\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> <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 class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mi>exp</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <msubsup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> </mrow> </msubsup> <mo>+</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{ij}(r_{ij})={\frac {z_{i}z_{j}}{4\pi \epsilon _{0}}}{\frac {1}{r_{ij}}}+A_{l}\exp {\frac {-r_{ij}}{p_{l}}}+C_{l}r_{ij}^{-n_{l}}+\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d02a6c2df80cbb23f264386895ab20b804c1ad2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:48.888ex; height:6.009ex;" alt="{\displaystyle U_{ij}(r_{ij})={\frac {z_{i}z_{j}}{4\pi \epsilon _{0}}}{\frac {1}{r_{ij}}}+A_{l}\exp {\frac {-r_{ij}}{p_{l}}}+C_{l}r_{ij}^{-n_{l}}+\cdots }"></span></dd></dl> <p>In <a href="/wiki/Many-body_problem" title="Many-body problem">many-body potentials</a>, the potential energy includes the effects of three or more particles interacting with each other.<sup id="cite_ref-ReferenceA_41-0" class="reference"><a href="#cite_note-ReferenceA-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> In simulations with pairwise potentials, global interactions in the system also exist, but they occur only through pairwise terms. In many-body potentials, the potential energy cannot be found by a sum over pairs of atoms, as these interactions are calculated explicitly as a combination of higher-order terms. In the statistical view, the dependency between the variables cannot in general be expressed using only pairwise products of the degrees of freedom. For example, the <a href="/wiki/Tersoff_potential" class="mw-redirect" title="Tersoff potential">Tersoff potential</a>,<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> which was originally used to simulate <a href="/wiki/Carbon" title="Carbon">carbon</a>, <a href="/wiki/Silicon" title="Silicon">silicon</a>, and <a href="/wiki/Germanium" title="Germanium">germanium</a>, and has since been used for a wide range of other materials, involves a sum over groups of three atoms, with the angles between the atoms being an important factor in the potential. Other examples are the <a href="/wiki/Embedded_atom_model" title="Embedded atom model">embedded-atom method</a> (EAM),<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> the EDIP,<sup id="cite_ref-ReferenceA_41-1" class="reference"><a href="#cite_note-ReferenceA-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> and the Tight-Binding Second Moment Approximation (TBSMA) potentials,<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> where the electron density of states in the region of an atom is calculated from a sum of contributions from surrounding atoms, and the potential energy contribution is then a function of this sum. </p> <div class="mw-heading mw-heading3"><h3 id="Semi-empirical_potentials">Semi-empirical potentials</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=11" title="Edit section: Semi-empirical potentials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Semi-empirical_quantum_chemistry_methods" class="mw-redirect" title="Semi-empirical quantum chemistry methods">Semi-empirical</a> potentials make use of the matrix representation from quantum mechanics. However, the values of the matrix elements are found through empirical formulae that estimate the degree of overlap of specific atomic orbitals. The matrix is then diagonalized to determine the occupancy of the different atomic orbitals, and empirical formulae are used once again to determine the energy contributions of the orbitals. </p><p>There are a wide variety of semi-empirical potentials, termed <a href="/wiki/Tight_binding_(physics)" class="mw-redirect" title="Tight binding (physics)">tight-binding</a> potentials, which vary according to the atoms being modeled. </p> <div class="mw-heading mw-heading3"><h3 id="Polarizable_potentials">Polarizable potentials</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=12" title="Edit section: Polarizable potentials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">Force field</a></div> <p>Most classical force fields implicitly include the effect of <a href="/wiki/Polarizability" title="Polarizability">polarizability</a>, e.g., by scaling up the partial charges obtained from quantum chemical calculations. These partial charges are stationary with respect to the mass of the atom. But molecular dynamics simulations can explicitly model polarizability with the introduction of induced dipoles through different methods, such as <a href="/wiki/Drude_particle" title="Drude particle">Drude particles</a> or fluctuating charges. This allows for a dynamic redistribution of charge between atoms which responds to the local chemical environment. </p><p>For many years, polarizable MD simulations have been touted as the next generation. For homogenous liquids such as water, increased accuracy has been achieved through the inclusion of polarizability.<sup id="cite_ref-Lamoureux3_45-0" class="reference"><a href="#cite_note-Lamoureux3-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Sokhan2015_46-0" class="reference"><a href="#cite_note-Sokhan2015-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Cipcigan_47-0" class="reference"><a href="#cite_note-Cipcigan-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> Some promising results have also been achieved for proteins.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Patel2004b_49-0" class="reference"><a href="#cite_note-Patel2004b-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> However, it is still uncertain how to best approximate polarizability in a simulation.<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. (April 2009)">citation needed</span></a></i>]</sup> The point becomes more important when a particle experiences different environments during its simulation trajectory, e.g. translocation of a drug through a cell membrane.<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Potentials_in_ab_initio_methods">Potentials in <i>ab initio</i> methods</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=13" title="Edit section: Potentials in ab initio methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Quantum_chemistry" title="Quantum chemistry">Quantum chemistry</a> and <a href="/wiki/List_of_quantum_chemistry_and_solid_state_physics_software" class="mw-redirect" title="List of quantum chemistry and solid state physics software">List of quantum chemistry and solid state physics software</a></div> <p>In classical molecular dynamics, one potential energy surface (usually the ground state) is represented in the force field. This is a consequence of the <a href="/wiki/Born%E2%80%93Oppenheimer_approximation" title="Born–Oppenheimer approximation">Born–Oppenheimer approximation</a>. In excited states, chemical reactions or when a more accurate representation is needed, electronic behavior can be obtained from first principles using a quantum mechanical method, such as <a href="/wiki/Density_functional_theory" title="Density functional theory">density functional theory</a>. This is named <i>Ab Initio Molecular Dynamics</i> (AIMD). Due to the cost of treating the electronic degrees of freedom, the computational burden of these simulations is far higher than classical molecular dynamics. For this reason, AIMD is typically limited to smaller systems and shorter times. </p><p><i><a href="/wiki/Ab_initio" title="Ab initio">Ab initio</a></i> <a href="/wiki/Quantum_mechanical" class="mw-redirect" title="Quantum mechanical">quantum mechanical</a> and <a href="/wiki/Quantum_chemistry" title="Quantum chemistry">chemical</a> methods may be used to calculate the <a href="/wiki/Potential_energy_surface" title="Potential energy surface">potential energy</a> of a system on the fly, as needed for conformations in a trajectory. This calculation is usually made in the close neighborhood of the <a href="/wiki/Reaction_coordinate" title="Reaction coordinate">reaction coordinate</a>. Although various approximations may be used, these are based on theoretical considerations, not on empirical fitting. <i>Ab initio</i> calculations produce a vast amount of information that is not available from empirical methods, such as density of electronic states or other electronic properties. A significant advantage of using <i>ab initio</i> methods is the ability to study reactions that involve breaking or formation of covalent bonds, which correspond to multiple electronic states. Moreover, <i>ab initio</i> methods also allow recovering effects beyond the Born–Oppenheimer approximation using approaches like <a href="/wiki/Mixed_quantum-classical_dynamics" title="Mixed quantum-classical dynamics">mixed quantum-classical dynamics</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Hybrid_QM/MM"><span id="Hybrid_QM.2FMM"></span>Hybrid QM/MM</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=14" title="Edit section: Hybrid QM/MM"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/QM/MM" title="QM/MM">QM/MM</a></div> <p>QM (quantum-mechanical) methods are very powerful. However, they are computationally expensive, while the MM (classical or molecular mechanics) methods are fast but suffer from several limits (require extensive parameterization; energy estimates obtained are not very accurate; cannot be used to simulate reactions where covalent bonds are broken/formed; and are limited in their abilities for providing accurate details regarding the chemical environment). A new class of method has emerged that combines the good points of QM (accuracy) and MM (speed) calculations. These methods are termed mixed or hybrid quantum-mechanical and molecular mechanics methods (hybrid QM/MM).<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> </p><p>The most important advantage of hybrid QM/MM method is the speed. The cost of doing classical molecular dynamics (MM) in the most straightforward case scales O(n<sup>2</sup>), where n is the number of atoms in the system. This is mainly due to electrostatic interactions term (every particle interacts with every other particle). However, use of cutoff radius, periodic pair-list updates and more recently the variations of the particle-mesh Ewald's (PME) method has reduced this to between O(n) to O(n<sup>2</sup>). In other words, if a system with twice as many atoms is simulated then it would take between two and four times as much computing power. On the other hand, the simplest <i>ab initio</i> calculations typically scale O(n<sup>3</sup>) or worse (restricted <a href="/wiki/Hartree%E2%80%93Fock" class="mw-redirect" title="Hartree–Fock">Hartree–Fock</a> calculations have been suggested to scale ~O(n<sup>2.7</sup>)). To overcome the limit, a small part of the system is treated quantum-mechanically (typically active-site of an enzyme) and the remaining system is treated classically. </p><p>In more sophisticated implementations, QM/MM methods exist to treat both light nuclei susceptible to quantum effects (such as hydrogens) and electronic states. This allows generating hydrogen wave-functions (similar to electronic wave-functions). This methodology has been useful in investigating phenomena such as hydrogen tunneling. One example where QM/MM methods have provided new discoveries is the calculation of hydride transfer in the enzyme liver <a href="/wiki/Alcohol_dehydrogenase" title="Alcohol dehydrogenase">alcohol dehydrogenase</a>. In this case, <a href="/wiki/Quantum_tunneling" class="mw-redirect" title="Quantum tunneling">quantum tunneling</a> is important for the hydrogen, as it determines the reaction rate.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Coarse-graining_and_reduced_representations">Coarse-graining and reduced representations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=15" title="Edit section: Coarse-graining and reduced representations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>At the other end of the detail scale are <a href="/wiki/Coarse-grained_modeling" title="Coarse-grained modeling">coarse-grained</a> and lattice models. Instead of explicitly representing every atom of the system, one uses "pseudo-atoms" to represent groups of atoms. MD simulations on very large systems may require such large computer resources that they cannot easily be studied by traditional all-atom methods. Similarly, simulations of processes on long timescales (beyond about 1 microsecond) are prohibitively expensive, because they require so many time steps. In these cases, one can sometimes tackle the problem by using reduced representations, which are also called <a href="/wiki/Coarse-grained_modeling" title="Coarse-grained modeling">coarse-grained models</a>.<sup id="cite_ref-:0_53-0" class="reference"><a href="#cite_note-:0-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> </p><p>Examples for coarse graining (CG) methods are discontinuous molecular dynamics (CG-DMD)<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> and Go-models.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> Coarse-graining is done sometimes taking larger pseudo-atoms. Such united atom approximations have been used in MD simulations of biological membranes. Implementation of such approach on systems where electrical properties are of interest can be challenging owing to the difficulty of using a proper charge distribution on the pseudo-atoms.<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> The aliphatic tails of lipids are represented by a few pseudo-atoms by gathering 2 to 4 methylene groups into each pseudo-atom. </p><p>The parameterization of these very coarse-grained models must be done empirically, by matching the behavior of the model to appropriate experimental data or all-atom simulations. Ideally, these parameters should account for both <a href="/wiki/Enthalpy" title="Enthalpy">enthalpic</a> and <a href="/wiki/Entropy" title="Entropy">entropic</a> contributions to free energy in an implicit way.<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> When coarse-graining is done at higher levels, the accuracy of the dynamic description may be less reliable. But very coarse-grained models have been used successfully to examine a wide range of questions in structural biology, liquid crystal organization, and polymer glasses. </p><p>Examples of applications of coarse-graining: </p> <ul><li><a href="/wiki/Protein_folding" title="Protein folding">protein folding</a> and <a href="/wiki/Protein_structure_prediction" title="Protein structure prediction">protein structure prediction</a> studies are often carried out using one, or a few, pseudo-atoms per amino acid;<sup id="cite_ref-:0_53-1" class="reference"><a href="#cite_note-:0-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Liquid_crystal" title="Liquid crystal">liquid crystal</a> phase transitions have been examined in confined geometries and/or during flow using the <a href="/w/index.php?title=Gay-Berne_potential&action=edit&redlink=1" class="new" title="Gay-Berne potential (page does not exist)">Gay-Berne potential</a>, which describes anisotropic species;</li> <li><a href="/wiki/Polymer" title="Polymer">Polymer</a> glasses during deformation have been studied using simple harmonic or <a href="/wiki/FENE" class="mw-redirect" title="FENE">FENE</a> springs to connect spheres described by the <a href="/wiki/Lennard-Jones_potential" title="Lennard-Jones potential">Lennard-Jones potential</a>;</li> <li><a href="/wiki/Supercoiling" class="mw-redirect" title="Supercoiling">DNA supercoiling</a> has been investigated using 1–3 pseudo-atoms per basepair, and at even lower resolution;</li> <li>Packaging of <a href="/wiki/DNA" title="DNA">double-helical DNA</a> into <a href="/wiki/Bacteriophage" title="Bacteriophage">bacteriophage</a> has been investigated with models where one pseudo-atom represents one turn (about 10 basepairs) of the double helix;</li> <li>RNA structure in the <a href="/wiki/Ribosome" title="Ribosome">ribosome</a> and other large systems has been modeled with one pseudo-atom per nucleotide.</li></ul> <p>The simplest form of coarse-graining is the <i>united atom</i> (sometimes called <i>extended atom</i>) and was used in most early MD simulations of proteins, lipids, and nucleic acids. For example, instead of treating all four atoms of a CH<sub>3</sub> methyl group explicitly (or all three atoms of CH<sub>2</sub> methylene group), one represents the whole group with one pseudo-atom. It must, of course, be properly parameterized so that its van der Waals interactions with other groups have the proper distance-dependence. Similar considerations apply to the bonds, angles, and torsions in which the pseudo-atom participates. In this kind of united atom representation, one typically eliminates all explicit hydrogen atoms except those that have the capability to participate in hydrogen bonds (<i>polar hydrogens</i>). An example of this is the <a href="/wiki/CHARMM" title="CHARMM">CHARMM</a> 19 force-field. </p><p>The polar hydrogens are usually retained in the model, because proper treatment of hydrogen bonds requires a reasonably accurate description of the directionality and the electrostatic interactions between the donor and acceptor groups. A hydroxyl group, for example, can be both a hydrogen bond donor, and a hydrogen bond acceptor, and it would be impossible to treat this with one OH pseudo-atom. About half the atoms in a protein or nucleic acid are non-polar hydrogens, so the use of united atoms can provide a substantial savings in computer time. </p> <div class="mw-heading mw-heading3"><h3 id="Machine_Learning_Force_Fields">Machine Learning Force Fields</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=16" title="Edit section: Machine Learning Force Fields"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Machine Learning Force Fields] (MLFFs) represent one approach to modeling interatomic interactions in molecular dynamics simulations.<sup id="cite_ref-Unke_2021_59-0" class="reference"><a href="#cite_note-Unke_2021-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> MLFFs can achieve accuracy close to that of <a href="/wiki/Ab_initio_quantum_chemistry_methods" title="Ab initio quantum chemistry methods">ab initio methods</a>. Once trained, MLFFs are much faster than direct quantum mechanical calculations. MLFFs address the limitations of traditional force fields by learning complex potential energy surfaces directly from high-level quantum mechanical data. Several software packages now support MLFFs, including <a href="/wiki/Vienna_Ab_initio_Simulation_Package" title="Vienna Ab initio Simulation Package">VASP</a><sup id="cite_ref-Hafner_2008_60-0" class="reference"><a href="#cite_note-Hafner_2008-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> and open-source libraries like DeePMD-kit<sup id="cite_ref-Wang_2018_61-0" class="reference"><a href="#cite_note-Wang_2018-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Zeng_2023_62-0" class="reference"><a href="#cite_note-Zeng_2023-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> and <a rel="nofollow" class="external text" href="https://schnetpack.readthedocs.io/en/latest/">SchNetPack</a>.<sup id="cite_ref-Schütt_2019_63-0" class="reference"><a href="#cite_note-Schütt_2019-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Schütt_2023_64-0" class="reference"><a href="#cite_note-Schütt_2023-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Incorporating_solvent_effects">Incorporating solvent effects</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=17" title="Edit section: Incorporating solvent effects"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In many simulations of a solute-solvent system the main focus is on the behavior of the solute with little interest of the solvent behavior particularly in those solvent molecules residing in regions far from the solute molecule.<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> Solvents may influence the dynamic behavior of solutes via random collisions and by imposing a frictional drag on the motion of the solute through the solvent. The use of non-rectangular periodic boundary conditions, stochastic boundaries and solvent shells can all help reduce the number of solvent molecules required and enable a larger proportion of the computing time to be spent instead on simulating the solute. It is also possible to incorporate the effects of a solvent without needing any explicit solvent molecules present. One example of this approach is to use a <a href="/wiki/Potential_of_mean_force" title="Potential of mean force">potential mean force</a> (PMF) which describes how the free energy changes as a particular coordinate is varied. The free energy change described by PMF contains the averaged effects of the solvent. </p><p>Without incorporating the effects of solvent simulations of macromolecules (such as proteins) may yield unrealistic behavior and even small molecules may adopt more compact conformations due to favourable van der Waals forces and electrostatic interactions which would be dampened in the presence of a solvent.<sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Long-range_forces">Long-range forces</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=18" title="Edit section: Long-range forces"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A long range interaction is an interaction in which the spatial interaction falls off no faster than <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r^{-d}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>d</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r^{-d}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3be14f13e14a864328609401819c38c57e0060a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.419ex; height:2.676ex;" alt="{\displaystyle r^{-d}}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></span> is the dimensionality of the system. Examples include charge-charge interactions between ions and dipole-dipole interactions between molecules. Modelling these forces presents quite a challenge as they are significant over a distance which may be larger than half the box length with simulations of many thousands of particles. Though one solution would be to significantly increase the size of the box length, this brute force approach is less than ideal as the simulation would become computationally very expensive. Spherically truncating the potential is also out of the question as unrealistic behaviour may be observed when the distance is close to the cut off distance.<sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Steered_molecular_dynamics_(SMD)"><span id="Steered_molecular_dynamics_.28SMD.29"></span>Steered molecular dynamics (SMD)</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=19" title="Edit section: Steered molecular dynamics (SMD)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Steered molecular dynamics (SMD) simulations, or force probe simulations, apply forces to a protein in order to manipulate its structure by pulling it along desired degrees of freedom. These experiments can be used to reveal structural changes in a protein at the atomic level. SMD is often used to simulate events such as mechanical unfolding or stretching.<sup id="cite_ref-Nienhaus_68-0" class="reference"><a href="#cite_note-Nienhaus-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> </p><p>There are two typical protocols of SMD: one in which pulling velocity is held constant, and one in which applied force is constant. Typically, part of the studied system (e.g., an atom in a protein) is restrained by a harmonic potential. Forces are then applied to specific atoms at either a constant velocity or a constant force. <a href="/wiki/Umbrella_sampling" title="Umbrella sampling">Umbrella sampling</a> is used to move the system along the desired reaction coordinate by varying, for example, the forces, distances, and angles manipulated in the simulation. Through umbrella sampling, all of the system's configurations—both high-energy and low-energy—are adequately sampled. Then, each configuration's change in free energy can be calculated as the <a href="/wiki/Potential_of_mean_force" title="Potential of mean force">potential of mean force</a>.<sup id="cite_ref-Leszczyński_69-0" class="reference"><a href="#cite_note-Leszczyński-69"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> A popular method of computing PMF is through the weighted histogram analysis method (WHAM), which analyzes a series of umbrella sampling simulations.<sup id="cite_ref-70" class="reference"><a href="#cite_note-70"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-71" class="reference"><a href="#cite_note-71"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> </p><p>A lot of important applications of SMD are in the field of drug discovery and biomolecular sciences. For e.g. SMD was used to investigate the stability of Alzheimer's protofibrils,<sup id="cite_ref-72" class="reference"><a href="#cite_note-72"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup> to study the protein ligand interaction in cyclin-dependent kinase 5<sup id="cite_ref-73" class="reference"><a href="#cite_note-73"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup> and even to show the effect of electric field on thrombin (protein) and aptamer (nucleotide) complex<sup id="cite_ref-74" class="reference"><a href="#cite_note-74"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup> among many other interesting studies. </p> <div class="mw-heading mw-heading2"><h2 id="Examples_of_applications">Examples of applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=20" title="Edit section: Examples of applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:MD_rotor_250K_1ns.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/MD_rotor_250K_1ns.gif/250px-MD_rotor_250K_1ns.gif" decoding="async" width="250" height="262" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/b/b6/MD_rotor_250K_1ns.gif 1.5x" data-file-width="300" data-file-height="314" /></a><figcaption>Molecular dynamics simulation of a <a href="/wiki/Synthetic_molecular_motor" title="Synthetic molecular motor">synthetic molecular motor</a> composed of three molecules in a nanopore (outer diameter 6.7 nm) at 250 K<sup id="cite_ref-75" class="reference"><a href="#cite_note-75"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup></figcaption></figure><style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Primary_sources plainlinks metadata ambox ambox-content ambox-Primary_sources" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>relies excessively on <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">references</a> to <a href="/wiki/Wikipedia:No_original_research#Primary,_secondary_and_tertiary_sources" title="Wikipedia:No original research">primary sources</a></b>.<span class="hide-when-compact"> Please improve this section by adding <a href="/wiki/Wikipedia:No_original_research#Primary,_secondary_and_tertiary_sources" title="Wikipedia:No original research">secondary or tertiary sources</a>. <br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Molecular+dynamics%22">"Molecular dynamics"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Molecular+dynamics%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Molecular+dynamics%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Molecular+dynamics%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Molecular+dynamics%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Molecular+dynamics%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">January 2024</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>Molecular dynamics is used in many fields of science. </p> <ul><li>First MD simulation of a simplified biological folding process was published in 1975. Its simulation published in Nature paved the way for the vast area of modern computational protein-folding.<sup id="cite_ref-76" class="reference"><a href="#cite_note-76"><span class="cite-bracket">[</span>76<span class="cite-bracket">]</span></a></sup></li> <li>First MD simulation of a biological process was published in 1976. Its simulation published in Nature paved the way for understanding protein motion as essential in function and not just accessory.<sup id="cite_ref-77" class="reference"><a href="#cite_note-77"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup></li> <li>MD is the standard method to treat <a href="/wiki/Collision_cascade" title="Collision cascade">collision cascades</a> in the heat spike regime, i.e., the effects that energetic <a href="/wiki/Neutron" title="Neutron">neutron</a> and <a href="/wiki/Ion_irradiation" class="mw-redirect" title="Ion irradiation">ion irradiation</a> have on solids and solid surfaces.<sup id="cite_ref-Smith_78-0" class="reference"><a href="#cite_note-Smith-78"><span class="cite-bracket">[</span>78<span class="cite-bracket">]</span></a></sup></li></ul> <p>The following biophysical examples illustrate notable efforts to produce simulations of a systems of very large size (a complete virus) or very long simulation times (up to 1.112 milliseconds): </p> <ul><li>MD simulation of the full <i><a href="/wiki/Satellite_tobacco_mosaic_virus" class="mw-redirect" title="Satellite tobacco mosaic virus">satellite tobacco mosaic virus</a></i> (STMV) (2006, Size: 1 million atoms, Simulation time: 50 ns, program: <a href="/wiki/NAMD" title="NAMD">NAMD</a>) This virus is a small, icosahedral plant virus that worsens the symptoms of infection by Tobacco Mosaic Virus (TMV). Molecular dynamics simulations were used to probe the mechanisms of <a href="/wiki/Virus#Structure" title="Virus">viral assembly</a>. The entire STMV particle consists of 60 identical copies of one protein that make up the viral <a href="/wiki/Capsid" title="Capsid">capsid</a> (coating), and a 1063 nucleotide single stranded RNA <a href="/wiki/Genome" title="Genome">genome</a>. One key finding is that the capsid is very unstable when there is no RNA inside. The simulation would take one 2006 desktop computer around 35 years to complete. It was thus done in many processors in parallel with continuous communication between them.<sup id="cite_ref-79" class="reference"><a href="#cite_note-79"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup></li> <li>Folding simulations of the <a href="/wiki/Villin" class="mw-redirect" title="Villin">Villin</a> Headpiece in all-atom detail (2006, Size: 20,000 atoms; Simulation time: 500 μs= 500,000 ns, Program: <a href="/wiki/Folding@home" title="Folding@home">Folding@home</a>) This simulation was run in 200,000 CPU's of participating personal computers around the world. These computers had the Folding@home program installed, a large-scale distributed computing effort coordinated by <a href="/wiki/Vijay_Pande" class="mw-redirect" title="Vijay Pande">Vijay Pande</a> at Stanford University. The kinetic properties of the Villin Headpiece protein were probed by using many independent, short trajectories run by CPU's without continuous real-time communication. One method employed was the Pfold value analysis, which measures the probability of folding before unfolding of a specific starting conformation. Pfold gives information about <a href="/wiki/Phi_value_analysis" title="Phi value analysis">transition state</a> structures and an ordering of conformations along the <a href="/wiki/Protein_folding" title="Protein folding">folding pathway</a>. Each trajectory in a Pfold calculation can be relatively short, but many independent trajectories are needed.<sup id="cite_ref-80" class="reference"><a href="#cite_note-80"><span class="cite-bracket">[</span>80<span class="cite-bracket">]</span></a></sup></li> <li>Long continuous-trajectory simulations have been performed on <a href="/wiki/Anton_(computer)" title="Anton (computer)">Anton</a>, a massively parallel supercomputer designed and built around custom <a href="/wiki/Application-specific_integrated_circuit" title="Application-specific integrated circuit">application-specific integrated circuits</a> (ASICs) and interconnects by <a href="/wiki/D._E._Shaw_Research" title="D. E. Shaw Research">D. E. Shaw Research</a>. The longest published result of a simulation performed using Anton is a 1.112-millisecond simulation of NTL9 at 355 K; a second, independent 1.073-millisecond simulation of this configuration was also performed (and many other simulations of over 250 μs continuous chemical time).<sup id="cite_ref-DESRES-Science2011_81-0" class="reference"><a href="#cite_note-DESRES-Science2011-81"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup> In <i>How Fast-Folding Proteins Fold</i>, researchers Kresten Lindorff-Larsen, Stefano Piana, Ron O. Dror, and <a href="/wiki/David_E._Shaw" title="David E. Shaw">David E. Shaw</a> discuss "the results of atomic-level molecular dynamics simulations, over periods ranging between 100 μs and 1 ms, that reveal a set of common principles underlying the folding of 12 structurally diverse proteins." Examination of these diverse long trajectories, enabled by specialized, custom hardware, allow them to conclude that "In most cases, folding follows a single dominant route in which elements of the native structure appear in an order highly correlated with their propensity to form in the unfolded state."<sup id="cite_ref-DESRES-Science2011_81-1" class="reference"><a href="#cite_note-DESRES-Science2011-81"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup> In a separate study, Anton was used to conduct a 1.013-millisecond simulation of the native-state dynamics of bovine pancreatic trypsin inhibitor (BPTI) at 300 K.<sup id="cite_ref-82" class="reference"><a href="#cite_note-82"><span class="cite-bracket">[</span>82<span class="cite-bracket">]</span></a></sup></li></ul> <p>Another important application of MD method benefits from its ability of 3-dimensional characterization and analysis of microstructural evolution at atomic scale. </p> <ul><li>MD simulations are used in characterization of grain size evolution, for example, when describing wear and friction of nanocrystalline Al and Al(Zr) materials.<sup id="cite_ref-83" class="reference"><a href="#cite_note-83"><span class="cite-bracket">[</span>83<span class="cite-bracket">]</span></a></sup> Dislocations evolution and grain size evolution are analyzed during the friction process in this simulation. Since MD method provided the full information of the microstructure, the grain size evolution was calculated in 3D using the Polyhedral Template Matching,<sup id="cite_ref-84" class="reference"><a href="#cite_note-84"><span class="cite-bracket">[</span>84<span class="cite-bracket">]</span></a></sup> Grain Segmentation,<sup id="cite_ref-85" class="reference"><a href="#cite_note-85"><span class="cite-bracket">[</span>85<span class="cite-bracket">]</span></a></sup> and Graph clustering<sup id="cite_ref-86" class="reference"><a href="#cite_note-86"><span class="cite-bracket">[</span>86<span class="cite-bracket">]</span></a></sup> methods. In such simulation, MD method provided an accurate measurement of grain size. Making use of these information, the actual grain structures were extracted, measured, and presented. Compared to the traditional method of using SEM with a single 2-dimensional slice of the material, MD provides a 3-dimensional and accurate way to characterize the microstructural evolution at atomic scale.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Molecular_dynamics_algorithms">Molecular dynamics algorithms</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=21" title="Edit section: Molecular dynamics algorithms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Screened_Coulomb_potentials_implicit_solvent_model" title="Screened Coulomb potentials implicit solvent model">Screened Coulomb potentials implicit solvent model</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Integrators">Integrators</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=22" title="Edit section: Integrators"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Symplectic_integrator" title="Symplectic integrator">Symplectic integrator</a></li> <li><a href="/wiki/Verlet_integration" title="Verlet integration">Verlet–Stoermer integration</a></li> <li><a href="/wiki/Runge%E2%80%93Kutta_integration" class="mw-redirect" title="Runge–Kutta integration">Runge–Kutta integration</a></li> <li><a href="/wiki/Beeman%27s_algorithm" title="Beeman's algorithm">Beeman's algorithm</a></li> <li><a href="/wiki/Constraint_algorithm" class="mw-redirect" title="Constraint algorithm">Constraint algorithms</a> (for constrained systems)</li></ul> <div class="mw-heading mw-heading3"><h3 id="Short-range_interaction_algorithms">Short-range interaction algorithms</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=23" title="Edit section: Short-range interaction algorithms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Cell_lists" title="Cell lists">Cell lists</a></li> <li><a href="/wiki/Verlet_list" title="Verlet list">Verlet list</a></li> <li>Bonded interactions</li></ul> <div class="mw-heading mw-heading3"><h3 id="Long-range_interaction_algorithms">Long-range interaction algorithms</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=24" title="Edit section: Long-range interaction algorithms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Ewald_summation" title="Ewald summation">Ewald summation</a></li> <li>Particle mesh <a href="/wiki/Ewald_summation" title="Ewald summation">Ewald summation</a> (PME)</li> <li>Particle–particle-particle–mesh (<a href="/wiki/P3M" title="P3M">P3M</a>)</li> <li><a href="/wiki/Shifted_force_method" title="Shifted force method">Shifted force method</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Parallelization_strategies">Parallelization strategies</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=25" title="Edit section: Parallelization strategies"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Domain_decomposition_method" class="mw-redirect" title="Domain decomposition method">Domain decomposition method</a> (Distribution of system data for <a href="/wiki/Parallel_computing" title="Parallel computing">parallel computing</a>)</li></ul> <div class="mw-heading mw-heading3"><h3 id="Ab-initio_molecular_dynamics">Ab-initio molecular dynamics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=26" title="Edit section: Ab-initio molecular dynamics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Car%E2%80%93Parrinello_molecular_dynamics" title="Car–Parrinello molecular dynamics">Car–Parrinello molecular dynamics</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Specialized_hardware_for_MD_simulations">Specialized hardware for MD simulations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=27" title="Edit section: Specialized hardware for MD simulations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Anton_(computer)" title="Anton (computer)">Anton</a> – A specialized, massively parallel supercomputer designed to execute MD simulations</li> <li><a href="/wiki/MDGRAPE" class="mw-redirect" title="MDGRAPE">MDGRAPE</a> – A special purpose system built for molecular dynamics simulations, especially protein structure prediction</li></ul> <div class="mw-heading mw-heading2"><h2 id="Graphics_card_as_a_hardware_for_MD_simulations">Graphics card as a hardware for MD simulations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=28" title="Edit section: Graphics card as a hardware for MD simulations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="excerpt-block"><style data-mw-deduplicate="TemplateStyles:r1066933788">.mw-parser-output .excerpt-hat .mw-editsection-like{font-style:normal}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable dablink excerpt-hat selfref">This section is an excerpt from <a href="/wiki/Molecular_modeling_on_GPUs" title="Molecular modeling on GPUs">Molecular modeling on GPUs</a>.<span class="mw-editsection-like plainlinks"><span class="mw-editsection-bracket">[</span><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Molecular_modeling_on_GPUs&action=edit">edit</a><span class="mw-editsection-bracket">]</span></span></div><div class="excerpt"> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hardware-accelerated-molecular-modeling.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Hardware-accelerated-molecular-modeling.png" decoding="async" width="180" height="154" class="mw-file-element" data-file-width="180" data-file-height="154" /></a><figcaption>Ionic liquid simulation on GPU (<a href="/wiki/Abalone_(molecular_mechanics)" title="Abalone (molecular mechanics)">Abalone</a>)</figcaption></figure> <p><a href="/wiki/Molecular_modeling_on_GPUs" title="Molecular modeling on GPUs">Molecular modeling on GPU</a> is the technique of using a <a href="/wiki/Graphics_processing_unit" title="Graphics processing unit">graphics processing unit</a> (GPU) for molecular simulations.<sup id="cite_ref-87" class="reference"><a href="#cite_note-87"><span class="cite-bracket">[</span>87<span class="cite-bracket">]</span></a></sup> </p> In 2007, <a href="/wiki/Nvidia" title="Nvidia">Nvidia</a> introduced video cards that could be used not only to show graphics but also for scientific calculations. These cards include many arithmetic units (as of 2016<sup class="plainlinks noexcerpt noprint asof-tag update" style="display:none;"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Molecular_dynamics&action=edit">[update]</a></sup>, up to 3,584 in Tesla P100) working in parallel. Long before this event, the computational power of video cards was purely used to accelerate graphics calculations. What was new is that Nvidia made it possible to develop parallel programs in a high-level <a href="/wiki/Application_programming_interface" class="mw-redirect" title="Application programming interface">application programming interface</a> (API) named <a href="/wiki/CUDA" title="CUDA">CUDA</a>. This technology substantially simplified programming by enabling programs to be written in <a href="/wiki/C_(programming_language)" title="C (programming language)">C</a>/<a href="/wiki/C%2B%2B" title="C++">C++</a>. More recently, <a href="/wiki/OpenCL" title="OpenCL">OpenCL</a> allows <a href="/wiki/Cross-platform" class="mw-redirect" title="Cross-platform">cross-platform</a> GPU acceleration.</div></div> <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=Molecular_dynamics&action=edit&section=29" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 27em;"> <ul><li><a href="/wiki/Molecular_modeling" class="mw-redirect" title="Molecular modeling">Molecular modeling</a></li> <li><a href="/wiki/Computational_chemistry" title="Computational chemistry">Computational chemistry</a></li> <li><a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">Force field (chemistry)</a></li> <li><a href="/wiki/Comparison_of_force_field_implementations" class="mw-redirect" title="Comparison of force field implementations">Comparison of force field implementations</a></li> <li><a href="/wiki/Monte_Carlo_method" title="Monte Carlo method">Monte Carlo method</a></li> <li><a href="/wiki/Molecular_design_software" title="Molecular design software">Molecular design software</a></li> <li><a href="/wiki/Molecular_mechanics" title="Molecular mechanics">Molecular mechanics</a></li> <li><a href="/wiki/Multiscale_Green%27s_function" title="Multiscale Green's function">Multiscale Green's function</a></li> <li><a href="/wiki/Car%E2%80%93Parrinello_method" class="mw-redirect" title="Car–Parrinello method">Car–Parrinello method</a></li> <li><a href="/wiki/Comparison_of_software_for_molecular_mechanics_modeling" title="Comparison of software for molecular mechanics modeling">Comparison of software for molecular mechanics modeling</a></li> <li><a href="/wiki/Quantum_chemistry" title="Quantum chemistry">Quantum chemistry</a></li> <li><a href="/wiki/Discrete_element_method" title="Discrete element method">Discrete element method</a></li> <li><a href="/wiki/Comparison_of_nucleic_acid_simulation_software" title="Comparison of nucleic acid simulation software">Comparison of nucleic acid simulation software</a></li> <li><a href="/wiki/Molecule_editor" title="Molecule editor">Molecule editor</a></li> <li><a href="/wiki/Mixed_quantum-classical_dynamics" title="Mixed quantum-classical dynamics">Mixed quantum-classical dynamics</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=30" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFSchlick1996" class="citation book cs1">Schlick T (1996). 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Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-855645-4" title="Special:BookSources/0-19-855645-4"><bdi>0-19-855645-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computer+simulation+of+liquids&rft.pub=Oxford+University+Press&rft.date=1989&rft.isbn=0-19-855645-4&rft.aulast=Allen&rft.aufirst=MP&rft.au=Tildesley%2C+DJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+dynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcCammonHarvey1987" class="citation book cs1">McCammon JA, Harvey SC (1987). <i>Dynamics of Proteins and Nucleic Acids</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-30750-3" title="Special:BookSources/0-521-30750-3"><bdi>0-521-30750-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dynamics+of+Proteins+and+Nucleic+Acids&rft.pub=Cambridge+University+Press&rft.date=1987&rft.isbn=0-521-30750-3&rft.aulast=McCammon&rft.aufirst=JA&rft.au=Harvey%2C+SC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+dynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRapaport1996" class="citation book cs1">Rapaport DC (1996). <i>The Art of Molecular Dynamics Simulation</i>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-44561-2" title="Special:BookSources/0-521-44561-2"><bdi>0-521-44561-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Art+of+Molecular+Dynamics+Simulation&rft.date=1996&rft.isbn=0-521-44561-2&rft.aulast=Rapaport&rft.aufirst=DC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+dynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGriebelKnapekZumbusch2007" class="citation book cs1"><a href="/wiki/Michael_Griebel" title="Michael Griebel">Griebel M</a>, Knapek S, Zumbusch G (2007). <i>Numerical Simulation in Molecular Dynamics</i>. Berlin, Heidelberg: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-68094-9" title="Special:BookSources/978-3-540-68094-9"><bdi>978-3-540-68094-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Numerical+Simulation+in+Molecular+Dynamics&rft.place=Berlin%2C+Heidelberg&rft.pub=Springer&rft.date=2007&rft.isbn=978-3-540-68094-9&rft.aulast=Griebel&rft.aufirst=M&rft.au=Knapek%2C+S&rft.au=Zumbusch%2C+G&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+dynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFrenkelSmit2002" class="citation book cs1"><a href="/wiki/Daan_Frenkel" title="Daan Frenkel">Frenkel D</a>, Smit B (2002) [2001]. <i>Understanding Molecular Simulation : from algorithms to applications</i>. San Diego: Academic Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-267351-1" title="Special:BookSources/978-0-12-267351-1"><bdi>978-0-12-267351-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Understanding+Molecular+Simulation+%3A+from+algorithms+to+applications&rft.place=San+Diego&rft.pub=Academic+Press&rft.date=2002&rft.isbn=978-0-12-267351-1&rft.aulast=Frenkel&rft.aufirst=D&rft.au=Smit%2C+B&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+dynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHaile2001" class="citation book cs1">Haile JM (2001). <i>Molecular Dynamics Simulation: Elementary Methods</i>. Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-18439-X" title="Special:BookSources/0-471-18439-X"><bdi>0-471-18439-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Molecular+Dynamics+Simulation%3A+Elementary+Methods&rft.pub=Wiley&rft.date=2001&rft.isbn=0-471-18439-X&rft.aulast=Haile&rft.aufirst=JM&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+dynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSadus2002" class="citation book cs1">Sadus RJ (2002). <i>Molecular Simulation of Fluids: Theory, Algorithms and Object-Orientation</i>. Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-444-51082-6" title="Special:BookSources/0-444-51082-6"><bdi>0-444-51082-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Molecular+Simulation+of+Fluids%3A+Theory%2C+Algorithms+and+Object-Orientation&rft.pub=Elsevier&rft.date=2002&rft.isbn=0-444-51082-6&rft.aulast=Sadus&rft.aufirst=RJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+dynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBeckerMackerell_JrRouxWatanabe2001" class="citation book cs1">Becker OM, Mackerell Jr AD, Roux B, Watanabe M (2001). <i>Computational Biochemistry and Biophysics</i>. Marcel Dekker. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8247-0455-X" title="Special:BookSources/0-8247-0455-X"><bdi>0-8247-0455-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computational+Biochemistry+and+Biophysics&rft.pub=Marcel+Dekker&rft.date=2001&rft.isbn=0-8247-0455-X&rft.aulast=Becker&rft.aufirst=OM&rft.au=Mackerell+Jr%2C+AD&rft.au=Roux%2C+B&rft.au=Watanabe%2C+M&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+dynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLeach2001" class="citation book cs1">Leach A (2001). <i>Molecular Modelling: Principles and Applications</i> (2nd ed.). Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-582-38210-7" title="Special:BookSources/978-0-582-38210-7"><bdi>978-0-582-38210-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Molecular+Modelling%3A+Principles+and+Applications&rft.edition=2nd&rft.pub=Prentice+Hall&rft.date=2001&rft.isbn=978-0-582-38210-7&rft.aulast=Leach&rft.aufirst=A&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+dynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchlick2002" class="citation book cs1"><a href="/wiki/Tamar_Schlick" title="Tamar Schlick">Schlick T</a> (2002). <i>Molecular Modeling and Simulation</i>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-387-95404-X" title="Special:BookSources/0-387-95404-X"><bdi>0-387-95404-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Molecular+Modeling+and+Simulation&rft.pub=Springer&rft.date=2002&rft.isbn=0-387-95404-X&rft.aulast=Schlick&rft.aufirst=T&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+dynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHoover1991" class="citation book cs1"><a href="/wiki/William_G_Hoover" class="mw-redirect" title="William G Hoover">Hoover WB</a> (1991). <i>Computational Statistical Mechanics</i>. Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-444-88192-1" title="Special:BookSources/0-444-88192-1"><bdi>0-444-88192-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computational+Statistical+Mechanics&rft.pub=Elsevier&rft.date=1991&rft.isbn=0-444-88192-1&rft.aulast=Hoover&rft.aufirst=WB&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+dynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEvansMorriss2008" class="citation book cs1">Evans DJ, Morriss G (2008). <i>Statistical Mechanics of Nonequilibrium Liquids</i> (Second ed.). Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-85791-8" title="Special:BookSources/978-0-521-85791-8"><bdi>978-0-521-85791-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Statistical+Mechanics+of+Nonequilibrium+Liquids&rft.edition=Second&rft.pub=Cambridge+University+Press&rft.date=2008&rft.isbn=978-0-521-85791-8&rft.aulast=Evans&rft.aufirst=DJ&rft.au=Morriss%2C+G&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+dynamics" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_dynamics&action=edit&section=32" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> 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style="width:1%"><a href="/wiki/Analytical_chemistry" title="Analytical chemistry">Analytical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Instrumental_chemistry" title="Instrumental chemistry">Instrumental chemistry</a></li> <li><a href="/wiki/Electroanalytical_methods" title="Electroanalytical methods">Electroanalytical methods</a></li> <li><a href="/wiki/Spectroscopy" title="Spectroscopy">Spectroscopy</a> <ul><li><a href="/wiki/Infrared_spectroscopy" title="Infrared spectroscopy">IR</a></li> <li><a href="/wiki/Raman_spectroscopy" title="Raman spectroscopy">Raman</a></li> <li><a href="/wiki/Ultraviolet%E2%80%93visible_spectroscopy" title="Ultraviolet–visible spectroscopy">UV-Vis</a></li> <li><a href="/wiki/Nuclear_magnetic_resonance_spectroscopy" title="Nuclear magnetic resonance spectroscopy">NMR</a></li></ul></li> <li><a href="/wiki/Mass_spectrometry" title="Mass spectrometry">Mass spectrometry</a> <ul><li><a href="/wiki/Electron_ionization" title="Electron ionization">EI</a></li> <li><a href="/wiki/Inductively_coupled_plasma_mass_spectrometry" title="Inductively coupled plasma mass spectrometry">ICP</a></li> <li><a href="/wiki/Matrix-assisted_laser_desorption/ionization" title="Matrix-assisted laser desorption/ionization">MALDI</a></li></ul></li> <li><a href="/wiki/Separation_process" title="Separation process">Separation process</a></li> <li><a href="/wiki/Chromatography" title="Chromatography">Chromatography</a> <ul><li><a href="/wiki/Gas_chromatography" title="Gas chromatography">GC</a></li> <li><a href="/wiki/High-performance_liquid_chromatography" title="High-performance liquid chromatography">HPLC</a></li></ul></li> <li><a href="/wiki/Crystallography" title="Crystallography">Crystallography</a></li> <li><a href="/wiki/Characterization_(materials_science)" title="Characterization (materials science)">Characterization</a></li> <li><a href="/wiki/Titration" title="Titration">Titration</a></li> <li><a href="/wiki/Wet_chemistry" title="Wet chemistry">Wet chemistry</a></li> <li><a href="/wiki/Calorimetry" title="Calorimetry">Calorimetry</a></li> <li><a href="/wiki/Elemental_analysis" title="Elemental analysis">Elemental analysis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Theoretical_chemistry" title="Theoretical chemistry">Theoretical</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_chemistry" title="Quantum chemistry">Quantum chemistry</a></li> <li><a href="/wiki/Computational_chemistry" title="Computational chemistry">Computational chemistry</a> <ul><li><a href="/wiki/Mathematical_chemistry" title="Mathematical chemistry">Mathematical chemistry</a></li></ul></li> <li><a href="/wiki/Molecular_modelling" title="Molecular modelling">Molecular modelling</a></li> <li><a href="/wiki/Molecular_mechanics" title="Molecular mechanics">Molecular mechanics</a></li> <li><a class="mw-selflink selflink">Molecular dynamics</a></li> <li><a href="/wiki/Molecular_geometry" title="Molecular geometry">Molecular geometry</a> <ul><li><a href="/wiki/VSEPR_theory" title="VSEPR theory">VSEPR theory</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Physical_chemistry" title="Physical chemistry">Physical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Electrochemistry" title="Electrochemistry">Electrochemistry</a> <ul><li><a href="/wiki/Spectroelectrochemistry" title="Spectroelectrochemistry">Spectroelectrochemistry</a></li> <li><a href="/wiki/Photoelectrochemistry" title="Photoelectrochemistry">Photoelectrochemistry</a></li></ul></li> <li><a href="/wiki/Thermochemistry" title="Thermochemistry">Thermochemistry</a></li> <li><a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">Chemical thermodynamics</a></li> <li><a href="/wiki/Surface_science" title="Surface science">Surface science</a></li> <li><a href="/wiki/Interface_and_colloid_science" title="Interface and colloid science">Interface and colloid science</a> <ul><li><a href="/wiki/Micromeritics" title="Micromeritics">Micromeritics</a></li></ul></li> <li><a href="/wiki/Cryochemistry" title="Cryochemistry">Cryochemistry</a></li> <li><a href="/wiki/Sonochemistry" title="Sonochemistry">Sonochemistry</a></li> <li><a href="/wiki/Structural_chemistry" title="Structural chemistry">Structural chemistry</a></li> <li><a href="/wiki/Chemical_physics" title="Chemical physics">Chemical physics</a> <ul><li><a href="/wiki/Molecular_physics" title="Molecular physics">Molecular physics</a></li></ul></li> <li><a href="/wiki/Femtochemistry" title="Femtochemistry">Femtochemistry</a></li> <li><a href="/wiki/Chemical_kinetics" title="Chemical kinetics">Chemical kinetics</a></li> <li><a href="/wiki/Spectroscopy" title="Spectroscopy">Spectroscopy</a></li> <li><a href="/wiki/Photochemistry" title="Photochemistry">Photochemistry</a></li> <li><a href="/wiki/Spin_chemistry" title="Spin chemistry">Spin chemistry</a></li> <li><a href="/wiki/Microwave_chemistry" title="Microwave chemistry">Microwave chemistry</a></li> <li><a href="/wiki/Equilibrium_chemistry" title="Equilibrium chemistry">Equilibrium chemistry</a></li> <li><a href="/wiki/Mechanochemistry" title="Mechanochemistry">Mechanochemistry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Inorganic_chemistry" title="Inorganic chemistry">Inorganic</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Coordination_complex" title="Coordination complex">Coordination chemistry</a></li> <li><a href="/wiki/Magnetochemistry" title="Magnetochemistry">Magnetochemistry</a></li> <li><a href="/wiki/Organometallic_chemistry" title="Organometallic chemistry">Organometallic chemistry</a> <ul><li><a href="/wiki/Organolanthanide_chemistry" title="Organolanthanide chemistry">Organolanthanide chemistry</a></li></ul></li> <li><a href="/wiki/Atom_cluster" class="mw-redirect" title="Atom cluster">Cluster chemistry</a></li> <li><a href="/wiki/Solid-state_chemistry" title="Solid-state chemistry">Solid-state chemistry</a></li> <li><a href="/wiki/Ceramic_chemistry" class="mw-redirect" title="Ceramic chemistry">Ceramic chemistry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Organic_chemistry" title="Organic chemistry">Organic</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Stereochemistry" title="Stereochemistry">Stereochemistry</a> <ul><li><a href="/wiki/Alkane_stereochemistry" class="mw-redirect" title="Alkane stereochemistry">Alkane stereochemistry</a></li></ul></li> <li><a href="/wiki/Physical_organic_chemistry" title="Physical organic chemistry">Physical organic chemistry</a></li> <li><a href="/wiki/Organic_reactions" class="mw-redirect" title="Organic reactions">Organic reactions</a></li> <li><a href="/wiki/Organic_synthesis" title="Organic synthesis">Organic synthesis</a></li> <li><a href="/wiki/Retrosynthetic_analysis" title="Retrosynthetic analysis">Retrosynthetic analysis</a></li> <li><a href="/wiki/Enantioselective_synthesis" title="Enantioselective synthesis">Enantioselective synthesis</a></li> <li><a href="/wiki/Total_synthesis" title="Total synthesis">Total synthesis</a> / <a href="/wiki/Semisynthesis" title="Semisynthesis">Semisynthesis</a></li> <li><a href="/wiki/Fullerene_chemistry" title="Fullerene chemistry">Fullerene chemistry</a></li> <li><a href="/wiki/Polymer_chemistry" title="Polymer chemistry">Polymer chemistry</a></li> <li><a href="/wiki/Petrochemistry" class="mw-redirect" title="Petrochemistry">Petrochemistry</a></li> <li><a href="/wiki/Dynamic_covalent_chemistry" title="Dynamic covalent chemistry">Dynamic covalent chemistry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Biochemistry" title="Biochemistry">Biological</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biochemistry" title="Biochemistry">Biochemistry</a> <ul><li><a href="/wiki/Molecular_biology" title="Molecular biology">Molecular biology</a></li> <li><a href="/wiki/Cell_biology" title="Cell biology">Cell biology</a></li></ul></li> <li><a href="/wiki/Chemical_biology" title="Chemical biology">Chemical biology</a> <ul><li><a href="/wiki/Bioorthogonal_chemistry" title="Bioorthogonal chemistry">Bioorthogonal chemistry</a></li></ul></li> <li><a href="/wiki/Medicinal_chemistry" title="Medicinal chemistry">Medicinal chemistry</a> <ul><li><a href="/wiki/Pharmacology" title="Pharmacology">Pharmacology</a></li></ul></li> <li><a href="/wiki/Clinical_chemistry" title="Clinical chemistry">Clinical chemistry</a></li> <li><a href="/wiki/Neurochemistry" title="Neurochemistry">Neurochemistry</a></li> <li><a href="/wiki/Bioorganic_chemistry" title="Bioorganic chemistry">Bioorganic chemistry</a></li> <li><a href="/wiki/Bioorganometallic_chemistry" title="Bioorganometallic chemistry">Bioorganometallic chemistry</a></li> <li><a href="/wiki/Bioinorganic_chemistry" title="Bioinorganic chemistry">Bioinorganic chemistry</a></li> <li><a href="/wiki/Biophysical_chemistry" title="Biophysical chemistry">Biophysical chemistry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Interdisciplinarity" title="Interdisciplinarity">Interdisciplinarity</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nuclear_chemistry" title="Nuclear chemistry">Nuclear chemistry</a> <ul><li><a href="/wiki/Radiochemistry" title="Radiochemistry">Radiochemistry</a></li> <li><a href="/wiki/Radiation_chemistry" title="Radiation chemistry">Radiation chemistry</a></li> <li><a href="/wiki/Actinide_chemistry" title="Actinide chemistry">Actinide chemistry</a></li></ul></li> <li><a href="/wiki/Cosmochemistry" title="Cosmochemistry">Cosmochemistry</a> / <a href="/wiki/Astrochemistry" title="Astrochemistry">Astrochemistry</a> / <a href="/wiki/Stellar_chemistry" title="Stellar chemistry">Stellar chemistry</a></li> <li><a href="/wiki/Geochemistry" title="Geochemistry">Geochemistry</a> <ul><li><a href="/wiki/Biogeochemistry" title="Biogeochemistry">Biogeochemistry</a></li> <li><a href="/wiki/Photogeochemistry" title="Photogeochemistry">Photogeochemistry</a></li></ul></li></ul> <ul><li><a href="/wiki/Environmental_chemistry" title="Environmental chemistry">Environmental chemistry</a> <ul><li><a href="/wiki/Atmospheric_chemistry" title="Atmospheric chemistry">Atmospheric chemistry</a></li> <li><a href="/wiki/Ocean_chemistry" class="mw-redirect" title="Ocean chemistry">Ocean chemistry</a></li></ul></li> <li><a href="/wiki/Clay_chemistry" title="Clay chemistry">Clay chemistry</a></li> <li><a href="/wiki/Carbochemistry" title="Carbochemistry">Carbochemistry</a></li> <li><a href="/wiki/Food_chemistry" title="Food chemistry">Food chemistry</a> <ul><li><a href="/wiki/Carbohydrate_chemistry" class="mw-redirect" title="Carbohydrate chemistry">Carbohydrate chemistry</a></li> <li><a href="/wiki/Food_physical_chemistry" title="Food physical chemistry">Food physical chemistry</a></li></ul></li> <li><a href="/wiki/Agricultural_chemistry" title="Agricultural chemistry">Agricultural chemistry</a> <ul><li><a href="/wiki/Soil_chemistry" title="Soil chemistry">Soil chemistry</a></li></ul></li></ul> <ul><li><a href="/wiki/Chemistry_education" title="Chemistry education">Chemistry education</a> <ul><li><a href="/wiki/Amateur_chemistry" title="Amateur chemistry">Amateur chemistry</a></li> <li><a href="/wiki/General_chemistry" title="General chemistry">General chemistry</a></li></ul></li> <li><a href="/wiki/Clandestine_chemistry" title="Clandestine chemistry">Clandestine chemistry</a></li> <li><a href="/wiki/Forensic_chemistry" title="Forensic chemistry">Forensic chemistry</a> <ul><li><a href="/wiki/Forensic_toxicology" title="Forensic toxicology">Forensic toxicology</a></li> <li><a href="/wiki/Post-mortem_chemistry" title="Post-mortem chemistry">Post-mortem chemistry</a></li></ul></li></ul> <ul><li><a href="/wiki/Nanochemistry" title="Nanochemistry">Nanochemistry</a> <ul><li><a href="/wiki/Supramolecular_chemistry" title="Supramolecular chemistry">Supramolecular chemistry</a></li></ul></li> <li><a href="/wiki/Chemical_synthesis" title="Chemical synthesis">Chemical synthesis</a> <ul><li><a href="/wiki/Green_chemistry" title="Green chemistry">Green chemistry</a></li> <li><a href="/wiki/Click_chemistry" title="Click chemistry">Click chemistry</a></li> <li><a href="/wiki/Combinatorial_chemistry" title="Combinatorial chemistry">Combinatorial chemistry</a></li> <li><a href="/wiki/Biosynthesis" title="Biosynthesis">Biosynthesis</a></li></ul></li> <li><a href="/wiki/Chemical_engineering" title="Chemical engineering">Chemical engineering</a> <ul><li><a href="/wiki/Stoichiometry" title="Stoichiometry">Stoichiometry</a></li></ul></li> <li><a href="/wiki/Materials_science" title="Materials science">Materials science</a> <ul><li><a href="/wiki/Metallurgy" title="Metallurgy">Metallurgy</a></li> <li><a href="/wiki/Ceramic_engineering" title="Ceramic engineering">Ceramic engineering</a></li> <li><a href="/wiki/Polymer_science" title="Polymer science">Polymer science</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">See also</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/History_of_chemistry" title="History of chemistry">History of chemistry</a></li> <li><a href="/wiki/Nobel_Prize_in_Chemistry" title="Nobel Prize in Chemistry">Nobel Prize in Chemistry</a></li> <li><a href="/wiki/Timeline_of_chemistry" title="Timeline of chemistry">Timeline of chemistry</a> <ul><li><a href="/wiki/Discovery_of_chemical_elements" title="Discovery of chemical elements">of element discoveries</a></li></ul></li> <li>"<a href="/wiki/The_central_science" title="The central science">The central science</a>"</li> <li><a href="/wiki/Chemical_reaction" title="Chemical reaction">Chemical reaction</a> <ul><li><a href="/wiki/Catalysis" title="Catalysis">Catalysis</a></li></ul></li> <li><a href="/wiki/Chemical_element" title="Chemical element">Chemical element</a></li> <li><a href="/wiki/Chemical_compound" title="Chemical compound">Chemical compound</a></li> <li><a href="/wiki/Atom" title="Atom">Atom</a></li> <li><a href="/wiki/Molecule" title="Molecule">Molecule</a></li> <li><a href="/wiki/Ion" title="Ion">Ion</a></li> <li><a href="/wiki/Chemical_substance" title="Chemical substance">Chemical substance</a></li> <li><a href="/wiki/Chemical_bond" title="Chemical bond">Chemical bond</a></li> <li><a href="/wiki/Alchemy" title="Alchemy">Alchemy</a></li> <li><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" 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