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<div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Drug development</span> </div> </a> <ul id="toc-Drug_development-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Computational_chemistry_databases" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Computational_chemistry_databases"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Computational chemistry databases</span> </div> </a> <ul id="toc-Computational_chemistry_databases-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Methods" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Methods</span> </div> </a> <button aria-controls="toc-Methods-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 Methods subsection</span> </button> <ul id="toc-Methods-sublist" class="vector-toc-list"> <li id="toc-Ab_initio_method" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ab_initio_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span><i>Ab initio</i> method</span> </div> </a> <ul id="toc-Ab_initio_method-sublist" class="vector-toc-list"> <li id="toc-Computational_thermochemistry" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Computational_thermochemistry"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.1</span> <span>Computational thermochemistry</span> </div> </a> <ul id="toc-Computational_thermochemistry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Chemical_dynamics" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Chemical_dynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.2</span> <span>Chemical dynamics</span> </div> </a> <ul id="toc-Chemical_dynamics-sublist" class="vector-toc-list"> <li id="toc-Split_operator_technique" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Split_operator_technique"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.2.1</span> <span>Split operator technique</span> </div> </a> <ul id="toc-Split_operator_technique-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Density_functional_methods" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Density_functional_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Density functional methods</span> </div> </a> <ul id="toc-Density_functional_methods-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Semi-empirical_methods" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Semi-empirical_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Semi-empirical methods</span> </div> </a> <ul id="toc-Semi-empirical_methods-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Molecular_mechanics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Molecular_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Molecular mechanics</span> </div> </a> <ul id="toc-Molecular_mechanics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Molecular_dynamics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Molecular_dynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Molecular dynamics</span> </div> </a> <ul id="toc-Molecular_dynamics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Monte_Carlo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Monte_Carlo"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Monte Carlo</span> </div> </a> <ul id="toc-Monte_Carlo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantum_mechanics/molecular_mechanics_(QM/MM)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quantum_mechanics/molecular_mechanics_(QM/MM)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7</span> <span>Quantum mechanics/molecular mechanics (QM/MM)</span> </div> </a> <ul id="toc-Quantum_mechanics/molecular_mechanics_(QM/MM)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantum_Computational_Chemistry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quantum_Computational_Chemistry"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.8</span> <span>Quantum Computational Chemistry</span> </div> </a> <ul id="toc-Quantum_Computational_Chemistry-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Computational_costs_in_chemistry_algorithms" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Computational_costs_in_chemistry_algorithms"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Computational costs in chemistry algorithms</span> </div> </a> <button aria-controls="toc-Computational_costs_in_chemistry_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 Computational costs in chemistry algorithms subsection</span> </button> <ul id="toc-Computational_costs_in_chemistry_algorithms-sublist" class="vector-toc-list"> <li id="toc-Algorithmic_complexity_examples" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Algorithmic_complexity_examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Algorithmic complexity examples</span> </div> </a> <ul id="toc-Algorithmic_complexity_examples-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Molecular_dynamics_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Molecular_dynamics_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Molecular dynamics</span> </div> </a> <ul id="toc-Molecular_dynamics_2-sublist" class="vector-toc-list"> <li id="toc-Algorithm" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Algorithm"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2.1</span> <span>Algorithm</span> </div> </a> <ul id="toc-Algorithm-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complexity" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Complexity"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2.2</span> <span>Complexity</span> </div> </a> <ul id="toc-Complexity-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Quantum_mechanics/molecular_mechanics_(QM/MM)_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quantum_mechanics/molecular_mechanics_(QM/MM)_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Quantum mechanics/molecular mechanics (QM/MM)</span> </div> </a> <ul id="toc-Quantum_mechanics/molecular_mechanics_(QM/MM)_2-sublist" class="vector-toc-list"> <li id="toc-Algorithm_2" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Algorithm_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3.1</span> <span>Algorithm</span> </div> </a> <ul id="toc-Algorithm_2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complexity_2" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Complexity_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3.2</span> <span>Complexity</span> </div> </a> <ul id="toc-Complexity_2-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Hartree-Fock_method" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hartree-Fock_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Hartree-Fock method</span> </div> </a> <ul id="toc-Hartree-Fock_method-sublist" class="vector-toc-list"> <li id="toc-Algorithm_3" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Algorithm_3"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4.1</span> <span>Algorithm</span> </div> </a> <ul id="toc-Algorithm_3-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complexity_3" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Complexity_3"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4.2</span> <span>Complexity</span> </div> </a> <ul id="toc-Complexity_3-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Density_functional_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Density_functional_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5</span> <span>Density functional theory</span> </div> </a> <ul id="toc-Density_functional_theory-sublist" class="vector-toc-list"> <li id="toc-Algorithm_4" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Algorithm_4"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5.1</span> <span>Algorithm</span> </div> </a> <ul id="toc-Algorithm_4-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complexity_4" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Complexity_4"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5.2</span> <span>Complexity</span> </div> </a> <ul id="toc-Complexity_4-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Standard_CCSD_and_CCSD(T)_method" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Standard_CCSD_and_CCSD(T)_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6</span> <span>Standard CCSD and CCSD(T) method</span> </div> </a> <ul id="toc-Standard_CCSD_and_CCSD(T)_method-sublist" class="vector-toc-list"> <li id="toc-Algorithm_5" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Algorithm_5"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6.1</span> <span>Algorithm</span> </div> </a> <ul id="toc-Algorithm_5-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complexity_5" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Complexity_5"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6.2</span> <span>Complexity</span> </div> </a> <ul id="toc-Complexity_5-sublist" class="vector-toc-list"> <li id="toc-CCSD" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#CCSD"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6.2.1</span> <span>CCSD</span> </div> </a> <ul id="toc-CCSD-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-CCSD(T)" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#CCSD(T)"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6.2.2</span> <span>CCSD(T)</span> </div> </a> <ul id="toc-CCSD(T)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Linear-scaling_CCSD(T)_method" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Linear-scaling_CCSD(T)_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.7</span> <span>Linear-scaling CCSD(T) method</span> </div> </a> <ul id="toc-Linear-scaling_CCSD(T)_method-sublist" class="vector-toc-list"> <li id="toc-Algorithm_6" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Algorithm_6"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.7.1</span> <span>Algorithm</span> </div> </a> <ul id="toc-Algorithm_6-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complexity_6" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Complexity_6"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.7.2</span> <span>Complexity</span> </div> </a> <ul id="toc-Complexity_6-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Accuracy" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Accuracy"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Accuracy</span> </div> </a> <ul id="toc-Accuracy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Software_packages" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Software_packages"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Software packages</span> </div> </a> <ul id="toc-Software_packages-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Specialized_journals_on_computational_chemistry" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Specialized_journals_on_computational_chemistry"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Specialized journals on computational chemistry</span> </div> </a> <ul id="toc-Specialized_journals_on_computational_chemistry-sublist" class="vector-toc-list"> </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">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-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">10</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">11</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" 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interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Qu%C3%ADmica_computacional" title="Química computacional – Asturian" lang="ast" hreflang="ast" data-title="Química computacional" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A6%B0%E0%A6%BF%E0%A6%97%E0%A6%A3%E0%A6%A8%E0%A6%BE%E0%A6%AE%E0%A7%82%E0%A6%B2%E0%A6%95_%E0%A6%B0%E0%A6%B8%E0%A6%BE%E0%A6%AF%E0%A6%BC%E0%A6%A8" title="পরিগণনামূলক রসায়ন – Bangla" lang="bn" hreflang="bn" data-title="পরিগণনামূলক রসায়ন" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/K%C3%A8-s%C7%B9g_ho%C3%A0-ha%CC%8Dk" title="Kè-sǹg hoà-ha̍k – Minnan" lang="nan" hreflang="nan" data-title="Kè-sǹg hoà-ha̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%98%D0%B7%D1%87%D0%B8%D1%81%D0%BB%D0%B8%D1%82%D0%B5%D0%BB%D0%BD%D0%B0_%D1%85%D0%B8%D0%BC%D0%B8%D1%8F" title="Изчислителна химия – Bulgarian" lang="bg" hreflang="bg" data-title="Изчислителна химия" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Qu%C3%ADmica_computacional" title="Química computacional – Catalan" lang="ca" hreflang="ca" data-title="Química computacional" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/V%C3%BDpo%C4%8Detn%C3%AD_chemie" title="Výpočetní chemie – Czech" lang="cs" hreflang="cs" data-title="Výpočetní chemie" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Arvutuskeemia" title="Arvutuskeemia – Estonian" lang="et" hreflang="et" data-title="Arvutuskeemia" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A5%CF%80%CE%BF%CE%BB%CE%BF%CE%B3%CE%B9%CF%83%CF%84%CE%B9%CE%BA%CE%AE_%CF%87%CE%B7%CE%BC%CE%B5%CE%AF%CE%B1" title="Υπολογιστική χημεία – Greek" lang="el" hreflang="el" data-title="Υπολογιστική χημεία" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Qu%C3%ADmica_computacional" title="Química computacional – Spanish" lang="es" hreflang="es" data-title="Química computacional" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Komputika_kemio" title="Komputika kemio – Esperanto" lang="eo" hreflang="eo" data-title="Komputika kemio" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Kimika_konputazional" title="Kimika konputazional – Basque" lang="eu" hreflang="eu" data-title="Kimika konputazional" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B4%DB%8C%D9%85%DB%8C_%D9%85%D8%AD%D8%A7%D8%B3%D8%A8%D8%A7%D8%AA%DB%8C" title="شیمی محاسباتی – Persian" lang="fa" hreflang="fa" data-title="شیمی محاسباتی" 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/Chimie_num%C3%A9rique" title="Chimie numérique – French" lang="fr" hreflang="fr" data-title="Chimie numérique" 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/%EA%B3%84%EC%82%B0%ED%99%94%ED%95%99" title="계산화학 – Korean" lang="ko" hreflang="ko" data-title="계산화학" 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%80%D5%A1%D5%B7%D5%BE%D5%B8%D5%B2%D5%A1%D5%AF%D5%A1%D5%B6_%D6%84%D5%AB%D5%B4%D5%AB%D5%A1" title="Հաշվողական քիմիա – Armenian" lang="hy" hreflang="hy" data-title="Հաշվողական քիմիա" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%AD%E0%A4%BF%E0%A4%95%E0%A4%B2%E0%A4%A8%E0%A4%BE%E0%A4%A4%E0%A5%8D%E0%A4%AE%E0%A4%95_%E0%A4%B0%E0%A4%B8%E0%A4%BE%E0%A4%AF%E0%A4%A8" title="अभिकलनात्मक रसायन – Hindi" lang="hi" hreflang="hi" data-title="अभिकलनात्मक रसायन" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Ra%C4%8Dunska_kemija" title="Računska kemija – Croatian" lang="hr" hreflang="hr" data-title="Računska kemija" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Informatikala_kemio" title="Informatikala kemio – Ido" lang="io" hreflang="io" data-title="Informatikala kemio" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kimia_komputasi" title="Kimia komputasi – Indonesian" lang="id" hreflang="id" data-title="Kimia komputasi" 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/Chimica_computazionale" title="Chimica computazionale – Italian" lang="it" hreflang="it" data-title="Chimica computazionale" 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%9B%D7%99%D7%9E%D7%99%D7%94_%D7%97%D7%99%D7%A9%D7%95%D7%91%D7%99%D7%AA" title="כימיה חישובית – Hebrew" lang="he" hreflang="he" data-title="כימיה חישובית" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Sz%C3%A1m%C3%ADt%C3%B3g%C3%A9pes_k%C3%A9mia" title="Számítógépes kémia – Hungarian" lang="hu" hreflang="hu" data-title="Számítógépes kémia" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BE%D1%86%D0%BE%D0%BE%D0%BB%D0%BB%D1%8B%D0%BD_%D1%85%D0%B8%D0%BC%D0%B8" title="Тооцооллын хими – Mongolian" lang="mn" hreflang="mn" data-title="Тооцооллын хими" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Computationele_chemie" title="Computationele chemie – Dutch" lang="nl" hreflang="nl" data-title="Computationele chemie" 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/%E8%A8%88%E7%AE%97%E5%8C%96%E5%AD%A6" title="計算化学 – Japanese" lang="ja" hreflang="ja" data-title="計算化学" 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-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Hisoblash_kimyosi" title="Hisoblash kimyosi – Uzbek" lang="uz" hreflang="uz" data-title="Hisoblash kimyosi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%95%E0%A9%B0%E0%A8%AA%E0%A8%BF%E0%A8%8A%E0%A8%9F%E0%A9%87%E0%A8%B8%E0%A8%BC%E0%A8%A8%E0%A8%B2_%E0%A8%B0%E0%A8%B8%E0%A8%BE%E0%A8%87%E0%A8%A3_%E0%A8%B5%E0%A8%BF%E0%A8%97%E0%A8%BF%E0%A8%86%E0%A8%A8" title="ਕੰਪਿਊਟੇਸ਼ਨਲ ਰਸਾਇਣ ਵਿਗਿਆਨ – Punjabi" lang="pa" hreflang="pa" data-title="ਕੰਪਿਊਟੇਸ਼ਨਲ ਰਸਾਇਣ ਵਿਗਿਆਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Chemia_obliczeniowa" title="Chemia obliczeniowa – Polish" lang="pl" hreflang="pl" data-title="Chemia obliczeniowa" 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/Qu%C3%ADmica_computacional" title="Química computacional – Portuguese" lang="pt" hreflang="pt" data-title="Química computacional" 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/Chimie_computa%C8%9Bional%C4%83" title="Chimie computațională – Romanian" lang="ro" hreflang="ro" data-title="Chimie computațională" 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%92%D1%8B%D1%87%D0%B8%D1%81%D0%BB%D0%B8%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D1%85%D0%B8%D0%BC%D0%B8%D1%8F" title="Вычислительная химия – Russian" lang="ru" hreflang="ru" data-title="Вычислительная химия" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Ch%C3%ACmica_cumputazziunali" title="Chìmica cumputazziunali – Sicilian" lang="scn" hreflang="scn" data-title="Chìmica cumputazziunali" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Computational_chemistry" title="Computational chemistry – Simple English" lang="en-simple" hreflang="en-simple" data-title="Computational chemistry" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Po%C4%8D%C3%ADta%C4%8Dov%C3%A1_ch%C3%A9mia" title="Počítačová chémia – Slovak" lang="sk" hreflang="sk" data-title="Počítačová chémia" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Ra%C4%8Dunska_kemija" title="Računska kemija – Slovenian" lang="sl" hreflang="sl" data-title="Računska kemija" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Ra%C4%8Dunarska_hemija" title="Računarska hemija – Serbian" lang="sr" hreflang="sr" data-title="Računarska hemija" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Ra%C4%8Dunarska_hemija" title="Računarska hemija – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Računarska hemija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Laskennallinen_kemia" title="Laskennallinen kemia – Finnish" lang="fi" hreflang="fi" data-title="Laskennallinen kemia" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Ber%C3%A4kningskemi" title="Beräkningskemi – Swedish" lang="sv" hreflang="sv" data-title="Beräkningskemi" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Kimikang_pangkomputasyon" title="Kimikang pangkomputasyon – Tagalog" lang="tl" hreflang="tl" data-title="Kimikang pangkomputasyon" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%84%E0%B8%A1%E0%B8%B5%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%84%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%93" title="เคมีการคำนวณ – Thai" lang="th" hreflang="th" data-title="เคมีการคำนวณ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Hesaplamal%C4%B1_kimya" title="Hesaplamalı kimya – Turkish" lang="tr" hreflang="tr" data-title="Hesaplamalı kimya" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9E%D0%B1%D1%87%D0%B8%D1%81%D0%BB%D1%8E%D0%B2%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0_%D1%85%D1%96%D0%BC%D1%96%D1%8F" title="Обчислювальна хімія – Ukrainian" lang="uk" hreflang="uk" data-title="Обчислювальна хімія" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%C3%B3a_h%E1%BB%8Dc_t%C3%ADnh_to%C3%A1n" title="Hóa học tính toán – Vietnamese" lang="vi" hreflang="vi" data-title="Hóa học tính toán" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Kimika_kompyutasyunal" title="Kimika kompyutasyunal – Waray" lang="war" hreflang="war" data-title="Kimika kompyutasyunal" 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id="mw-indicator-good-star" class="mw-indicator"><div class="mw-parser-output"><span typeof="mw:File"><a href="/wiki/Wikipedia:Good_articles*" title="This is a good article. Click here for more information."><img alt="This is a good article. Click here for more information." src="//upload.wikimedia.org/wikipedia/en/thumb/9/94/Symbol_support_vote.svg/19px-Symbol_support_vote.svg.png" decoding="async" width="19" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/94/Symbol_support_vote.svg/29px-Symbol_support_vote.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/94/Symbol_support_vote.svg/39px-Symbol_support_vote.svg.png 2x" data-file-width="180" data-file-height="185" /></a></span></div></div> </div> <div id="siteSub" class="noprint">From Wikipedia, the 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">Branch of chemistry</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:C60_isosurface.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a7/C60_isosurface.png/220px-C60_isosurface.png" decoding="async" width="220" height="203" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a7/C60_isosurface.png/330px-C60_isosurface.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a7/C60_isosurface.png/440px-C60_isosurface.png 2x" data-file-width="734" data-file-height="676" /></a><figcaption><a href="/wiki/Fullerene" title="Fullerene">C<sub>60</sub> molecule</a> with <a href="/wiki/Isosurface" title="Isosurface">isosurface</a> of ground-state electron density as calculated with <a href="/wiki/Density_functional_theory" title="Density functional theory">density functional theory</a></figcaption></figure> <p><b>Computational chemistry</b> is a branch of <a href="/wiki/Chemistry" title="Chemistry">chemistry</a> that uses <a href="/wiki/Computer_simulation" title="Computer simulation">computer simulations</a> to assist in solving chemical problems.<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> It uses methods of <a href="/wiki/Theoretical_chemistry" title="Theoretical chemistry">theoretical chemistry</a> incorporated into <a href="/wiki/Computer_program" title="Computer program">computer programs</a> to calculate the structures and properties of <a href="/wiki/Molecule" title="Molecule">molecules</a>, groups of molecules, and solids.<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> The importance of this subject stems from the fact that, with the exception of some relatively recent findings related to the hydrogen molecular ion (<a href="/wiki/Dihydrogen_cation" title="Dihydrogen cation">dihydrogen cation</a>), achieving an accurate quantum mechanical depiction of chemical systems analytically, or in a closed form, is not feasible.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The complexity inherent in the <a href="/wiki/Many-body_problem" title="Many-body problem">many-body problem</a> exacerbates the challenge of providing detailed descriptions of quantum mechanical systems.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> While computational results normally complement information obtained by chemical <a href="/wiki/Experiment" title="Experiment">experiments</a>, it can occasionally predict unobserved chemical <a href="/wiki/Phenomena" class="mw-redirect" title="Phenomena">phenomena</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Computational chemistry differs from <a href="/wiki/Theoretical_chemistry" title="Theoretical chemistry">theoretical chemistry</a>, which involves a mathematical description of chemistry. However, computational chemistry involves the usage of computer programs and additional mathematical skills in order to accurately model various chemical problems. In theoretical chemistry, chemists, physicists, and mathematicians develop <a href="/wiki/Algorithm" title="Algorithm">algorithms</a> and computer programs to predict atomic and molecular properties and reaction paths for <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reactions.</a> Computational chemists, in contrast, may simply apply existing computer programs and methodologies to specific chemical questions.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Historically, computational chemistry has had two different aspects: </p> <ul><li>Computational studies, used to find a starting point for a laboratory synthesis or to assist in understanding experimental data, such as the position and source of spectroscopic peaks.<sup id="cite_ref-Patel-2021_7-0" class="reference"><a href="#cite_note-Patel-2021-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></li> <li>Computational studies, used to predict the possibility of so far entirely unknown molecules or to explore reaction mechanisms not readily studied via experiments.<sup id="cite_ref-Patel-2021_7-1" class="reference"><a href="#cite_note-Patel-2021-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></li></ul> <p>These aspects, along with computational chemistry's purpose, have resulted in a whole host of algorithms. </p> <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=Computational_chemistry&action=edit&section=2" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Building on the founding discoveries and theories in the <a href="/wiki/History_of_quantum_mechanics" title="History of quantum mechanics">history of quantum mechanics</a>, the first theoretical calculations in chemistry were those of <a href="/wiki/Walter_Heitler" title="Walter Heitler">Walter Heitler</a> and <a href="/wiki/Fritz_London" title="Fritz London">Fritz London</a> in 1927, using <a href="/wiki/Valence_bond_theory" title="Valence bond theory">valence bond theory</a>.<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> The books that were influential in the early development of computational quantum chemistry include <a href="/wiki/Linus_Pauling" title="Linus Pauling">Linus Pauling</a> and <a href="/wiki/Edgar_Bright_Wilson" title="Edgar Bright Wilson">E. Bright Wilson</a>'s 1935 <i>Introduction to Quantum Mechanics – with Applications to Chemistry</i>,<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> <a href="/wiki/Henry_Eyring_(chemist)" title="Henry Eyring (chemist)">Eyring</a>, Walter and Kimball's 1944 <i>Quantum Chemistry</i>,<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> Heitler's 1945 <i>Elementary Wave Mechanics – with Applications to Quantum Chemistry</i>,<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> and later <a href="/wiki/Charles_Coulson" title="Charles Coulson">Coulson</a>'s 1952 textbook <i>Valence</i>, each of which served as primary references for chemists in the decades to follow.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>With the development of efficient computer technology in the 1940s, the solutions of elaborate <a href="/wiki/Wave_equation" title="Wave equation">wave equations</a> for complex <a href="/wiki/Atom" title="Atom">atomic</a> systems began to be a realizable objective. In the early 1950s, the first semi-empirical atomic orbital calculations were performed. Theoretical chemists became extensive users of the early digital computers. One significant advancement was marked by Clemens C. J. Roothaan's 1951 paper in the Reviews of Modern Physics.<sup id="cite_ref-Roothaan-1951_13-0" class="reference"><a href="#cite_note-Roothaan-1951-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Ruedenberg-1954_14-0" class="reference"><a href="#cite_note-Ruedenberg-1954-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> This paper focused largely on the "LCAO MO" approach (Linear Combination of Atomic Orbitals Molecular Orbitals). For many years, it was the second-most cited paper in that journal.<sup id="cite_ref-Roothaan-1951_13-1" class="reference"><a href="#cite_note-Roothaan-1951-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Ruedenberg-1954_14-1" class="reference"><a href="#cite_note-Ruedenberg-1954-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> A very detailed account of such use in the United Kingdom is given by Smith and Sutcliffe.<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> The first <i>ab initio</i> <a href="/wiki/Hartree%E2%80%93Fock_method" title="Hartree–Fock method">Hartree–Fock method</a> calculations on diatomic molecules were performed in 1956 at MIT, using a <a href="/wiki/Basis_set_(chemistry)" title="Basis set (chemistry)">basis set</a> of <a href="/wiki/Slater_orbital" class="mw-redirect" title="Slater orbital">Slater orbitals</a>.<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> For diatomic molecules, a systematic study using a minimum basis set and the first calculation with a larger basis set were published by Ransil and Nesbet respectively in 1960.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> The first polyatomic calculations using <a href="/wiki/Gaussian_orbital" title="Gaussian orbital">Gaussian orbitals</a> were performed in the late 1950s. The first <a href="/wiki/Configuration_interaction" title="Configuration interaction">configuration interaction</a> calculations were performed in Cambridge on the <a href="/wiki/EDSAC" title="EDSAC">EDSAC</a> computer in the 1950s using Gaussian orbitals by <a href="/wiki/Francis_Boys" class="mw-redirect" title="Francis Boys">Boys</a> and coworkers.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> By 1971, when a bibliography of <i>ab initio</i> calculations was published,<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> the largest molecules included were <a href="/wiki/Naphthalene" title="Naphthalene">naphthalene</a> and <a href="/wiki/Azulene" title="Azulene">azulene</a>.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> Abstracts of many earlier developments in <i>ab initio</i> theory have been published by Schaefer.<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> </p><p>In 1964, <a href="/wiki/H%C3%BCckel_method" title="Hückel method">Hückel method</a> calculations (using a simple <a href="/wiki/Linear_combination_of_atomic_orbitals" title="Linear combination of atomic orbitals">linear combination of atomic orbitals</a> (LCAO) method to determine electron energies of molecular orbitals of π electrons in conjugated hydrocarbon systems) of molecules, ranging in complexity from <a href="/wiki/Butadiene" title="Butadiene">butadiene</a> and <a href="/wiki/Benzene" title="Benzene">benzene</a> to <a href="/wiki/Ovalene" title="Ovalene">ovalene</a>, were generated on computers at Berkeley and Oxford.<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> These empirical methods were replaced in the 1960s by <a href="/wiki/Semi-empirical_quantum_chemistry_method" title="Semi-empirical quantum chemistry method">semi-empirical methods</a> such as <a href="/wiki/CNDO/2" title="CNDO/2">CNDO</a>.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p><p>In the early 1970s, efficient <i>ab initio</i> computer programs such as ATMOL, <a href="/wiki/Gaussian_(software)" title="Gaussian (software)">Gaussian</a>, IBMOL, and POLYAYTOM, began to be used to speed <i>ab initio</i> calculations of molecular orbitals.<sup id="cite_ref-Ma-2022_25-0" class="reference"><a href="#cite_note-Ma-2022-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> Of these four programs, only Gaussian, now vastly expanded, is still in use, but many other programs are now in use.<sup id="cite_ref-Ma-2022_25-1" class="reference"><a href="#cite_note-Ma-2022-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> At the same time, the methods of <a href="/wiki/Molecular_mechanics" title="Molecular mechanics">molecular mechanics</a>, such as MM2 <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force field</a>, were developed, primarily by <a href="/wiki/Norman_Allinger" title="Norman Allinger">Norman Allinger</a>.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p><p>One of the first mentions of the term <i>computational chemistry</i> can be found in the 1970 book <i>Computers and Their Role in the Physical Sciences</i> by Sidney Fernbach and Abraham Haskell Taub, where they state "It seems, therefore, that 'computational chemistry' can finally be more and more of a reality."<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> During the 1970s, widely different methods began to be seen as part of a new emerging discipline of <i>computational chemistry</i>.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> The <i><a href="/wiki/Journal_of_Computational_Chemistry" title="Journal of Computational Chemistry">Journal of Computational Chemistry</a></i> was first published in 1980. </p><p>Computational chemistry has featured in several Nobel Prize awards, most notably in 1998 and 2013. <a href="/wiki/Walter_Kohn" title="Walter Kohn">Walter Kohn</a>, "for his development of the density-functional theory", and <a href="/wiki/John_Pople" title="John Pople">John Pople</a>, "for his development of computational methods in quantum chemistry", received the 1998 <a href="/wiki/Nobel_Prize" title="Nobel Prize">Nobel Prize</a> in Chemistry.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Martin_Karplus" title="Martin Karplus">Martin Karplus</a>, <a href="/wiki/Michael_Levitt_(biophysicist)" title="Michael Levitt (biophysicist)">Michael Levitt</a> and <a href="/wiki/Arieh_Warshel" title="Arieh Warshel">Arieh Warshel</a> received the 2013 <a href="/wiki/Nobel_Prize" title="Nobel Prize">Nobel Prize</a> in Chemistry for "the development of multiscale models for complex chemical systems".<sup id="cite_ref-bio_30-0" class="reference"><a href="#cite_note-bio-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=3" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are several fields within computational chemistry. </p> <ul><li>The prediction of the molecular structure of molecules by the use of the simulation of forces, or more accurate quantum chemical methods, to find stationary points on the energy surface as the position of the nuclei is varied.<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></li> <li>Storing and searching for data on chemical entities (see <a href="/wiki/Chemical_database" title="Chemical database">chemical databases</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></li> <li>Identifying <a href="/wiki/Correlation" title="Correlation">correlations</a> between <a href="/wiki/Chemical_structure" title="Chemical structure">chemical structures</a> and properties (see <i>quantitative structure–property relationship</i> (QSPR) and <i><a href="/wiki/Quantitative_structure%E2%80%93activity_relationship" title="Quantitative structure–activity relationship">quantitative structure–activity relationship</a></i> (QSAR)).<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></li> <li>Computational approaches to help in the efficient synthesis of compounds.<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></li> <li>Computational approaches to design molecules that interact in specific ways with other molecules (e.g. <a href="/wiki/Drug_design" title="Drug design">drug design</a> and <a href="/wiki/Catalysis" title="Catalysis">catalysis</a>).<sup id="cite_ref-doi.org_35-0" class="reference"><a href="#cite_note-doi.org-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup></li></ul> <p>These fields can give rise to several applications as shown below. </p> <div class="mw-heading mw-heading3"><h3 id="Catalysis">Catalysis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=4" title="Edit section: Catalysis"><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:CatalysisScheme.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/CatalysisScheme.png/220px-CatalysisScheme.png" decoding="async" width="220" height="129" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/CatalysisScheme.png/330px-CatalysisScheme.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/CatalysisScheme.png/440px-CatalysisScheme.png 2x" data-file-width="1159" data-file-height="681" /></a><figcaption>Computational chemistry can help predict values like activation energy from catalysis. The presence of the catalyst opens a different reaction pathway (shown in red) with lower activation energy. The final result and the overall thermodynamics are the same.</figcaption></figure> <p>Computational chemistry is a tool for analyzing catalytic systems without doing experiments. Modern <a href="/wiki/Electronic_structure" class="mw-redirect" title="Electronic structure">electronic structure theory</a> and <a href="/wiki/Density_functional_theory" title="Density functional theory">density functional theory</a> has allowed researchers to discover and understand <a href="/wiki/Catalysis" title="Catalysis">catalysts</a>.<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> Computational studies apply theoretical chemistry to catalysis research. Density functional theory methods calculate the energies and orbitals of molecules to give models of those structures.<sup id="cite_ref-Patel-2020_37-0" class="reference"><a href="#cite_note-Patel-2020-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> Using these methods, researchers can predict values like <a href="/wiki/Activation_energy" title="Activation energy">activation energy</a>, <a href="/wiki/Active_site" title="Active site">site reactivity</a><sup id="cite_ref-van_Santen-1996_38-0" class="reference"><a href="#cite_note-van_Santen-1996-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> and other thermodynamic properties.<sup id="cite_ref-Patel-2020_37-1" class="reference"><a href="#cite_note-Patel-2020-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p><p>Data that is difficult to obtain experimentally can be found using computational methods to model the mechanisms of catalytic cycles.<sup id="cite_ref-van_Santen-1996_38-1" class="reference"><a href="#cite_note-van_Santen-1996-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> Skilled computational chemists provide predictions that are close to experimental data with proper considerations of methods and basis sets. With good computational data, researchers can predict how catalysts can be improved to lower the cost and increase the efficiency of these reactions.<sup id="cite_ref-Patel-2020_37-2" class="reference"><a href="#cite_note-Patel-2020-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Drug_development">Drug development</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=5" title="Edit section: Drug development"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Computational chemistry is used in <a href="/wiki/Drug_development" title="Drug development">drug development</a> to model potentially useful drug molecules and help companies save time and cost in drug development. The drug discovery process involves analyzing data, finding ways to improve current molecules, finding synthetic routes, and testing those molecules.<sup id="cite_ref-doi.org_35-1" class="reference"><a href="#cite_note-doi.org-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> Computational chemistry helps with this process by giving predictions of which experiments would be best to do without conducting other experiments. Computational methods can also find values that are difficult to find experimentally like <a href="/wiki/Acid_dissociation_constant" title="Acid dissociation constant">pKa</a>'s of compounds.<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> Methods like density functional theory can be used to model drug molecules and find their properties, like their <a href="/wiki/HOMO_and_LUMO" title="HOMO and LUMO">HOMO and LUMO energies</a> and molecular orbitals. Computational chemists also help companies with developing informatics, infrastructure and designs of drugs.<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> </p><p>Aside from drug synthesis, <a href="/wiki/Drug_carrier" title="Drug carrier">drug carriers</a> are also researched by computational chemists for <a href="/wiki/Nanomaterials" title="Nanomaterials">nanomaterials</a>. It allows researchers to simulate environments to test the effectiveness and stability of drug carriers. Understanding how water interacts with these nanomaterials ensures stability of the material in human bodies. These computational simulations help researchers optimize the material find the best way to structure these nanomaterials before making them.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Computational_chemistry_databases">Computational chemistry databases</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=6" title="Edit section: Computational chemistry databases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Database" title="Database">Databases</a> are useful for both computational and non computational chemists in research and verifying the validity of computational methods. Empirical data is used to analyze the error of computational methods against experimental data. Empirical data helps researchers with their methods and basis sets to have greater confidence in the researchers results. Computational chemistry databases are also used in testing software or hardware for computational chemistry.<sup id="cite_ref-Muresan-2012_42-0" class="reference"><a href="#cite_note-Muresan-2012-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p><p>Databases can also use purely calculated data. Purely calculated data uses calculated values over experimental values for databases. Purely calculated data avoids dealing with these adjusting for different experimental conditions like zero-point energy. These calculations can also avoid experimental errors for difficult to test molecules. Though purely calculated data is often not perfect, identifying issues is often easier for calculated data than experimental.<sup id="cite_ref-Muresan-2012_42-1" class="reference"><a href="#cite_note-Muresan-2012-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p><p>Databases also give public access to information for researchers to use. They contain data that other researchers have found and uploaded to these databases so that anyone can search for them. Researchers use these databases to find information on molecules of interest and learn what can be done with those molecules. Some publicly available chemistry databases include the following.<sup id="cite_ref-Muresan-2012_42-2" class="reference"><a href="#cite_note-Muresan-2012-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p> <ul><li><a href="/wiki/BindingDB" title="BindingDB">BindingDB</a>: Contains experimental information about protein-small molecule interactions.<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></li> <li><a href="/wiki/Protein_Data_Bank" title="Protein Data Bank">RCSB</a>: Stores publicly available 3D models of macromolecules (proteins, nucleic acids) and small molecules (drugs, inhibitors)<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></li> <li><a href="/wiki/ChEMBL" title="ChEMBL">ChEMBL</a>: Contains data from research on drug development such as assay results.<sup id="cite_ref-Muresan-2012_42-3" class="reference"><a href="#cite_note-Muresan-2012-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/DrugBank" title="DrugBank">DrugBank</a>: Data about mechanisms of drugs can be found here.<sup id="cite_ref-Muresan-2012_42-4" class="reference"><a href="#cite_note-Muresan-2012-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Methods">Methods</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=7" title="Edit section: Methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Ab_initio_method"><i>Ab initio</i> method</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=8" title="Edit section: Ab initio method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Ab_initio_quantum_chemistry_methods" title="Ab initio quantum chemistry methods">Ab initio quantum chemistry methods</a></div> <p>The programs used in computational chemistry are based on many different <a href="/wiki/Quantum_chemistry" title="Quantum chemistry">quantum-chemical</a> methods that solve the molecular <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a> associated with the <a href="/wiki/Molecular_Hamiltonian" title="Molecular Hamiltonian">molecular Hamiltonian</a>.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> Methods that do not include any empirical or semi-empirical parameters in their equations – being derived directly from theory, with no inclusion of experimental data – are called <i><a href="/wiki/Ab_initio_quantum_chemistry_methods" title="Ab initio quantum chemistry methods">ab initio methods</a></i>.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> A theoretical approximation is rigorously defined on first principles and then solved within an error margin that is qualitatively known beforehand. If numerical iterative methods must be used, the aim is to iterate until full machine accuracy is obtained (the best that is possible with a finite <a href="/wiki/Word_length" class="mw-redirect" title="Word length">word length</a> on the computer, and within the mathematical and/or physical approximations made).<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p><p>Ab initio methods need to define a level of theory (the method) and a <a href="/wiki/Basis_set_(chemistry)" title="Basis set (chemistry)">basis set.</a><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> A basis set consists of functions centered on the molecule's atoms. These sets are then used to describe molecular orbitals via the <a href="/wiki/Linear_combination_of_atomic_orbitals" title="Linear combination of atomic orbitals">linear combination of atomic orbitals</a> (LCAO) molecular orbital method <a href="/wiki/Ansatz" title="Ansatz">ansatz</a>.<sup id="cite_ref-Hinchliffe-2001_49-0" class="reference"><a href="#cite_note-Hinchliffe-2001-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Electron_correlation.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Electron_correlation.svg/300px-Electron_correlation.svg.png" decoding="async" width="300" height="173" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Electron_correlation.svg/450px-Electron_correlation.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Electron_correlation.svg/600px-Electron_correlation.svg.png 2x" data-file-width="428" data-file-height="247" /></a><figcaption>Diagram illustrating various <i>ab initio</i> electronic structure methods in terms of energy. Spacings are not to scale.</figcaption></figure> <p>A common type of <i>ab initio</i> electronic structure calculation is the <a href="/wiki/Hartree%E2%80%93Fock_method" title="Hartree–Fock method">Hartree–Fock method</a> (HF), an extension of <a href="/wiki/Molecular_orbital_theory" title="Molecular orbital theory">molecular orbital theory</a>, where electron-electron repulsions in the molecule are not specifically taken into account; only the electrons' average effect is included in the calculation. As the basis set size increases, the energy and wave function tend towards a limit called the Hartree–Fock limit.<sup id="cite_ref-Hinchliffe-2001_49-1" class="reference"><a href="#cite_note-Hinchliffe-2001-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> </p><p>Many types of calculations begin with a Hartree–Fock calculation and subsequently correct for electron-electron repulsion, referred to also as <a href="/wiki/Electronic_correlation" title="Electronic correlation">electronic correlation</a>.<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> These types of calculations are termed <a href="/wiki/Post-Hartree%E2%80%93Fock" class="mw-redirect" title="Post-Hartree–Fock">post-Hartree–Fock</a> methods. By continually improving these methods, scientists can get increasingly closer to perfectly predicting the behavior of atomic and molecular systems under the framework of quantum mechanics, as defined by the Schrödinger equation.<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> To obtain exact agreement with the experiment, it is necessary to include specific terms, some of which are far more important for heavy atoms than lighter ones.<sup id="cite_ref-Matveeva-2023_52-0" class="reference"><a href="#cite_note-Matveeva-2023-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> </p><p>In most cases, the Hartree–Fock wave function occupies a single configuration or determinant.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> In some cases, particularly for bond-breaking processes, this is inadequate, and several <a href="/wiki/Multi-configurational_self-consistent_field" title="Multi-configurational self-consistent field">configurations</a> must be used.<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> </p><p>The total molecular energy can be evaluated as a function of the <a href="/wiki/Molecular_geometry" title="Molecular geometry">molecular geometry</a>; in other words, the <a href="/wiki/Potential_energy_surface" title="Potential energy surface">potential energy surface</a>.<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> Such a surface can be used for reaction dynamics. The stationary points of the surface lead to predictions of different <a href="/wiki/Isomer" title="Isomer">isomers</a> and the <a href="/wiki/Transition_state_theory" title="Transition state theory">transition structures</a> for conversion between isomers, but these can be determined without full knowledge of the complete surface.<sup id="cite_ref-Matveeva-2023_52-1" class="reference"><a href="#cite_note-Matveeva-2023-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Diazomethane-pi-system.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Diazomethane-pi-system.png/220px-Diazomethane-pi-system.png" decoding="async" width="220" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Diazomethane-pi-system.png/330px-Diazomethane-pi-system.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/12/Diazomethane-pi-system.png/440px-Diazomethane-pi-system.png 2x" data-file-width="2150" data-file-height="1654" /></a><figcaption>Molecular orbital diagram of the conjugated pi systems of the diazomethane molecule using Hartree-Fock Method, CH<sub>2</sub>N<sub>2</sub></figcaption></figure> <div class="mw-heading mw-heading4"><h4 id="Computational_thermochemistry">Computational thermochemistry</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=9" title="Edit section: Computational thermochemistry"><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/Computational_chemical_methods_in_solid-state_physics" title="Computational chemical methods in solid-state physics">Computational chemical methods in solid-state physics</a> and <a href="/wiki/Thermochemistry" title="Thermochemistry">Thermochemistry</a></div> <p>A particularly important objective, called computational <a href="/wiki/Thermochemistry" title="Thermochemistry">thermochemistry</a>, is to calculate thermochemical quantities such as the <a href="/wiki/Standard_enthalpy_change_of_formation" class="mw-redirect" title="Standard enthalpy change of formation">enthalpy of formation</a> to chemical accuracy. Chemical accuracy is the accuracy required to make realistic chemical predictions and is generally considered to be 1 kcal/mol or 4 kJ/mol. To reach that accuracy in an economic way, it is necessary to use a series of post-Hartree–Fock methods and combine the results. These methods are called <a href="/wiki/Quantum_chemistry_composite_methods" title="Quantum chemistry composite methods">quantum chemistry composite methods</a>.<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> </p> <div class="mw-heading mw-heading4"><h4 id="Chemical_dynamics">Chemical dynamics</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=10" title="Edit section: Chemical dynamics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>After the electronic and <a href="/wiki/Molecular_geometry" title="Molecular geometry">nuclear</a> variables are <a href="/wiki/Separation_of_variables" title="Separation of variables">separated</a> within the Born–Oppenheimer representation), the <a href="/wiki/Wave_packet" title="Wave packet">wave packet</a> corresponding to the nuclear <a href="/wiki/Degrees_of_freedom_(physics_and_chemistry)" title="Degrees of freedom (physics and chemistry)">degrees of freedom</a> is propagated via the <a href="/wiki/Time_evolution" title="Time evolution">time evolution</a> <a href="/wiki/Operator_(physics)" title="Operator (physics)">operator (physics)</a> associated to the time-dependent <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a> (for the full <a href="/wiki/Molecular_Hamiltonian" title="Molecular Hamiltonian">molecular Hamiltonian</a>).<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> In the <a href="/wiki/Complementarity_(physics)" title="Complementarity (physics)">complementary</a> energy-dependent approach, the time-independent <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a> is solved using the <a href="/wiki/Scattering_theory" class="mw-redirect" title="Scattering theory">scattering theory</a> formalism. The potential representing the interatomic interaction is given by the <a href="/wiki/Potential_energy_surface" title="Potential energy surface">potential energy surfaces</a>. In general, the <a href="/wiki/Potential_energy_surface" title="Potential energy surface">potential energy surfaces</a> are coupled via the <a href="/wiki/Vibronic_coupling" title="Vibronic coupling">vibronic coupling</a> terms.<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> </p><p>The most popular methods for propagating the <a href="/wiki/Wave_packet" title="Wave packet">wave packet</a> associated to the <a href="/wiki/Molecular_geometry" title="Molecular geometry">molecular geometry</a> are: </p> <ul><li>the <a href="/wiki/Chebyshev_polynomials" title="Chebyshev polynomials">Chebyshev (real) polynomial</a>,<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup></li> <li>the <a href="/wiki/Multi-configuration_time-dependent_Hartree" title="Multi-configuration time-dependent Hartree">multi-configuration time-dependent Hartree</a> method (MCTDH),<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup></li> <li>the semiclassical method</li> <li>and the split operator technique explained below.<sup id="cite_ref-Lukassen-2018_61-0" class="reference"><a href="#cite_note-Lukassen-2018-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading5"><h5 id="Split_operator_technique">Split operator technique</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=11" title="Edit section: Split operator technique"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>How a computational method solves quantum equations impacts the accuracy and efficiency of the method. The split operator technique is one of these methods for solving differential equations. In computational chemistry, split operator technique reduces computational costs of simulating chemical systems. Computational costs are about how much time it takes for computers to calculate these chemical systems, as it can take days for more complex systems. Quantum systems are difficult and time-consuming to solve for humans. Split operator methods help computers calculate these systems quickly by solving the sub problems in a quantum <a href="/wiki/Differential_equation" title="Differential equation">differential equation</a>. The method does this by separating the differential equation into two different equations, like when there are more than two operators. Once solved, the split equations are combined into one equation again to give an easily calculable solution.<sup id="cite_ref-Lukassen-2018_61-1" class="reference"><a href="#cite_note-Lukassen-2018-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> </p><p>This method is used in many fields that require solving differential equations, such as <a href="/wiki/Mathematical_biology" class="mw-redirect" title="Mathematical biology">biology</a>. However, the technique comes with a splitting error. For example, with the following solution for a differential equation.<sup id="cite_ref-Lukassen-2018_61-2" class="reference"><a href="#cite_note-Lukassen-2018-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle e^{h(A+B)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo>+</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle e^{h(A+B)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dda126c3235e69c1a79287eebe0f361857e79296" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.3ex; height:2.676ex;" alt="{\textstyle e^{h(A+B)}}"></span> </p><p>The equation can be split, but the solutions will not be exact, only similar. This is an example of first order splitting.<sup id="cite_ref-Lukassen-2018_61-3" class="reference"><a href="#cite_note-Lukassen-2018-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle e^{h(A+B)}\approx e^{hA}e^{hB}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo>+</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mo>≈</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>A</mi> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>B</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle e^{h(A+B)}\approx e^{hA}e^{hB}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d958ea3979d344d79c1c9566a42b9b7167bacde9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:17.404ex; height:2.676ex;" alt="{\textstyle e^{h(A+B)}\approx e^{hA}e^{hB}}"></span> </p><p>There are ways to reduce this error, which include taking an average of two split equations.<sup id="cite_ref-Lukassen-2018_61-4" class="reference"><a href="#cite_note-Lukassen-2018-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> </p><p>Another way to increase accuracy is to use higher order splitting. Usually, second order splitting is the most that is done because higher order splitting requires much more time to calculate and is not worth the cost. Higher order methods become too difficult to implement, and are not useful for solving differential equations despite the higher accuracy.<sup id="cite_ref-Lukassen-2018_61-5" class="reference"><a href="#cite_note-Lukassen-2018-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> </p><p>Computational chemists spend much time making systems calculated with split operator technique more accurate while minimizing the computational cost. Calculating methods is a massive challenge for many chemists trying to simulate molecules or chemical environments.<sup id="cite_ref-Lukassen-2018_61-6" class="reference"><a href="#cite_note-Lukassen-2018-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Density_functional_methods">Density functional methods</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=12" title="Edit section: Density functional 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 article: <a href="/wiki/Density_functional_theory" title="Density functional theory">Density functional theory</a></div> <p>Density functional theory (DFT) methods are often considered to be <i><a href="/wiki/Ab_initio_quantum_chemistry_methods" title="Ab initio quantum chemistry methods">ab initio methods</a></i> for determining the molecular electronic structure, even though many of the most common <a href="/wiki/Functional_(mathematics)" title="Functional (mathematics)">functionals</a> use parameters derived from empirical data, or from more complex calculations. In DFT, the total energy is expressed in terms of the total one-<a href="/wiki/Electronic_density" class="mw-redirect" title="Electronic density">electron density</a> rather than the wave function. In this type of calculation, there is an approximate <a href="/wiki/Hamiltonian_(quantum_mechanics)" title="Hamiltonian (quantum mechanics)">Hamiltonian</a> and an approximate expression for the total electron density. DFT methods can be very accurate for little computational cost. Some methods combine the density functional exchange functional with the Hartree–Fock exchange term and are termed <a href="/wiki/Hybrid_functional" title="Hybrid functional">hybrid functional</a> methods.<sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Semi-empirical_methods">Semi-empirical methods</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=13" title="Edit section: Semi-empirical 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 article: <a href="/wiki/Semi-empirical_quantum_chemistry_methods" class="mw-redirect" title="Semi-empirical quantum chemistry methods">Semi-empirical quantum chemistry methods</a></div> <p>Semi-empirical <a href="/wiki/Quantum_chemistry" title="Quantum chemistry">quantum chemistry</a> methods are based on the <a href="/wiki/Hartree%E2%80%93Fock_method" title="Hartree–Fock method">Hartree–Fock method</a> formalism, but make many approximations and obtain some parameters from empirical data. They were very important in computational chemistry from the 60s to the 90s, especially for treating large molecules where the full Hartree–Fock method without the approximations were too costly. The use of empirical parameters appears to allow some inclusion of correlation effects into the methods.<sup id="cite_ref-Ramachandran-2008_63-0" class="reference"><a href="#cite_note-Ramachandran-2008-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> </p><p>Primitive semi-empirical methods were designed even before, where the two-electron part of the <a href="/wiki/Hamiltonian_(quantum_mechanics)" title="Hamiltonian (quantum mechanics)">Hamiltonian</a> is not explicitly included. For π-electron systems, this was the <a href="/wiki/H%C3%BCckel_method" title="Hückel method">Hückel method</a> proposed by <a href="/wiki/Erich_H%C3%BCckel" title="Erich Hückel">Erich Hückel</a>, and for all valence electron systems, the <a href="/wiki/Extended_H%C3%BCckel_method" title="Extended Hückel method">extended Hückel method</a> proposed by <a href="/wiki/Roald_Hoffmann" title="Roald Hoffmann">Roald Hoffmann</a>. Sometimes, Hückel methods are referred to as "completely empirical" because they do not derive from a Hamiltonian.<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> Yet, the term "empirical methods", or "empirical force fields" is usually used to describe molecular mechanics.<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> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:MM_PEF_3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/MM_PEF_3.png/220px-MM_PEF_3.png" decoding="async" width="220" height="153" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/MM_PEF_3.png/330px-MM_PEF_3.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/MM_PEF_3.png/440px-MM_PEF_3.png 2x" data-file-width="3360" data-file-height="2342" /></a><figcaption>Molecular mechanics potential energy function with continuum solvent</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Molecular_mechanics">Molecular mechanics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=14" title="Edit section: Molecular mechanics"><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/Molecular_mechanics" title="Molecular mechanics">Molecular mechanics</a></div> <p>In many cases, large molecular systems can be modeled successfully while avoiding quantum mechanical calculations entirely. <a href="/wiki/Molecular_mechanics" title="Molecular mechanics">Molecular mechanics</a> simulations, for example, use one classical expression for the energy of a compound, for instance, the <a href="/wiki/Harmonic_oscillator" title="Harmonic oscillator">harmonic oscillator</a>. All constants appearing in the equations must be obtained beforehand from experimental data or <i>ab initio</i> calculations.<sup id="cite_ref-Ramachandran-2008_63-1" class="reference"><a href="#cite_note-Ramachandran-2008-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> </p><p> The database of compounds used for parameterization, i.e. the resulting set of parameters and functions is called the <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force field</a>, is crucial to the success of molecular mechanics calculations. A force field parameterized against a specific class of molecules, for instance, proteins, would be expected to only have any relevance when describing other molecules of the same class.<sup id="cite_ref-Ramachandran-2008_63-2" class="reference"><a href="#cite_note-Ramachandran-2008-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> These methods can be applied to proteins and other large biological molecules, and allow studies of the approach and interaction (docking) of potential drug molecules.<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><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><figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/A_molecular_dynamics_simulation_of_argon_gas.webm/220px--A_molecular_dynamics_simulation_of_argon_gas.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="220" data-durationhint="40" data-mwtitle="A_molecular_dynamics_simulation_of_argon_gas.webm" data-mwprovider="wikimediacommons" resource="/wiki/File:A_molecular_dynamics_simulation_of_argon_gas.webm"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/A_molecular_dynamics_simulation_of_argon_gas.webm/A_molecular_dynamics_simulation_of_argon_gas.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="480" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/A_molecular_dynamics_simulation_of_argon_gas.webm/A_molecular_dynamics_simulation_of_argon_gas.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="720" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/5/55/A_molecular_dynamics_simulation_of_argon_gas.webm" type="video/webm; codecs="vp8"" data-width="1000" data-height="1000" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/A_molecular_dynamics_simulation_of_argon_gas.webm/A_molecular_dynamics_simulation_of_argon_gas.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="144" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/A_molecular_dynamics_simulation_of_argon_gas.webm/A_molecular_dynamics_simulation_of_argon_gas.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="240" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/A_molecular_dynamics_simulation_of_argon_gas.webm/A_molecular_dynamics_simulation_of_argon_gas.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="360" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/55/A_molecular_dynamics_simulation_of_argon_gas.webm/A_molecular_dynamics_simulation_of_argon_gas.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="360" data-height="360" /></video></span><figcaption>Molecular Dynamics for Argon Gas</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Molecular_dynamics">Molecular dynamics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=15" title="Edit section: Molecular dynamics"><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/Molecular_dynamics" title="Molecular dynamics">Molecular dynamics</a></div> <p>Molecular dynamics (MD) use either <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>, <a href="/wiki/Molecular_mechanics" title="Molecular mechanics">molecular mechanics</a> or a <a href="/wiki/QM/MM" title="QM/MM">mixture of both</a> to calculate forces which are then used to solve <a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's laws of motion</a> to examine the time-dependent behavior of systems. The result of a molecular dynamics simulation is a trajectory that describes how the position and velocity of particles varies with time. The phase point of a system described by the positions and momenta of all its particles on a previous time point will determine the next phase point in time by integrating over Newton's laws of motion.<sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Monte_Carlo">Monte Carlo</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=16" title="Edit section: Monte Carlo"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Monte_Carlo_method" title="Monte Carlo method">Monte Carlo</a> (MC) generates configurations of a system by making random changes to the positions of its particles, together with their orientations and conformations where appropriate.<sup id="cite_ref-69" class="reference"><a href="#cite_note-69"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> It is a random sampling method, which makes use of the so-called <i>importance sampling</i>. Importance sampling methods are able to generate low energy states, as this enables properties to be calculated accurately. The potential energy of each configuration of the system can be calculated, together with the values of other properties, from the positions of the atoms.<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> <div class="mw-heading mw-heading3"><h3 id="Quantum_mechanics/molecular_mechanics_(QM/MM)"><span id="Quantum_mechanics.2Fmolecular_mechanics_.28QM.2FMM.29"></span>Quantum mechanics/molecular mechanics (QM/MM)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=17" title="Edit section: Quantum mechanics/molecular mechanics (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/MM is a hybrid method that attempts to combine the accuracy of quantum mechanics with the speed of molecular mechanics. It is useful for simulating very large molecules such as <a href="/wiki/Enzyme" title="Enzyme">enzymes</a>.<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> </p> <div class="mw-heading mw-heading3"><h3 id="Quantum_Computational_Chemistry">Quantum Computational Chemistry</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=18" title="Edit section: Quantum Computational Chemistry"><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/Quantum_computational_chemistry" title="Quantum computational chemistry">Quantum computational chemistry</a></div> <p><a href="/wiki/Quantum_computational_chemistry" title="Quantum computational chemistry">Quantum computational chemistry</a> aims to exploit <a href="/wiki/Quantum_computing" title="Quantum computing">quantum computing</a> to simulate chemical systems, distinguishing itself from the QM/MM (Quantum Mechanics/Molecular Mechanics) approach.<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> While QM/MM uses a hybrid approach, combining quantum mechanics for a portion of the system with classical mechanics for the remainder, quantum computational chemistry exclusively uses quantum computing methods to represent and process information, such as Hamiltonian operators.<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> </p><p>Conventional computational chemistry methods often struggle with the complex quantum mechanical equations, particularly due to the exponential growth of a quantum system's wave function. Quantum computational chemistry addresses these challenges using <a href="/wiki/Quantum_computing" title="Quantum computing">quantum computing methods</a>, such as qubitization and <a href="/wiki/Quantum_phase_estimation" class="mw-redirect" title="Quantum phase estimation">quantum phase estimation</a>, which are believed to offer scalable solutions.<sup id="cite_ref-Nielsen-2010_75-0" class="reference"><a href="#cite_note-Nielsen-2010-75"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup> </p><p>Qubitization involves adapting the Hamiltonian operator for more efficient processing on quantum computers, enhancing the simulation's efficiency. Quantum phase estimation, on the other hand, assists in accurately determining energy eigenstates, which are critical for understanding the quantum system's behavior.<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> </p><p>While these techniques have advanced the field of computational chemistry, especially in the simulation of chemical systems, their practical application is currently limited mainly to smaller systems due to technological constraints. Nevertheless, these developments may lead to significant progress towards achieving more precise and resource-efficient quantum chemistry simulations.<sup id="cite_ref-Nielsen-2010_75-1" class="reference"><a href="#cite_note-Nielsen-2010-75"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Computational_costs_in_chemistry_algorithms">Computational costs in chemistry algorithms</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=19" title="Edit section: Computational costs in chemistry algorithms"><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/Computational_complexity" title="Computational complexity">Computational complexity</a> and <a href="/wiki/List_of_complexity_classes" title="List of complexity classes">List of complexity classes</a></div> <p>The computational cost and algorithmic complexity in chemistry are used to help understand and predict chemical phenomena. They help determine which algorithms/computational methods to use when solving chemical problems. This section focuses on the scaling of computational complexity with molecule size and details the algorithms commonly used in both domains.<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> </p><p>In quantum chemistry, particularly, the complexity can grow exponentially with the number of electrons involved in the system. This exponential growth is a significant barrier to simulating large or complex systems accurately.<sup id="cite_ref-78" class="reference"><a href="#cite_note-78"><span class="cite-bracket">[</span>78<span class="cite-bracket">]</span></a></sup> </p><p>Advanced algorithms in both fields strive to balance accuracy with computational efficiency. For instance, in MD, methods like <a href="/wiki/Verlet_integration" title="Verlet integration">Verlet integration</a> or <a href="/wiki/Beeman%27s_algorithm" title="Beeman's algorithm">Beeman's algorithm</a> are employed for their computational efficiency. In quantum chemistry, hybrid methods combining different computational approaches (like QM/MM) are increasingly used to tackle large biomolecular systems.<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> </p> <div class="mw-heading mw-heading3"><h3 id="Algorithmic_complexity_examples">Algorithmic complexity examples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=20" title="Edit section: Algorithmic complexity examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The following list illustrates the impact of computational complexity on algorithms used in chemical computations. It is important to note that while this list provides key examples, it is not comprehensive and serves as a guide to understanding how computational demands influence the selection of specific computational methods in chemistry. </p> <div class="mw-heading mw-heading3"><h3 id="Molecular_dynamics_2">Molecular dynamics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=21" title="Edit section: Molecular dynamics"><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">See also: <a href="/wiki/Molecular_dynamics" title="Molecular dynamics">Molecular dynamics</a></div> <div class="mw-heading mw-heading4"><h4 id="Algorithm">Algorithm</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=22" title="Edit section: Algorithm"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Solves Newton's equations of motion for atoms and molecules.<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> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_1" poster="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/A_Molecular_Dynamics_Simulation_of_Liquid_Water_at_298_K.webm/220px--A_Molecular_Dynamics_Simulation_of_Liquid_Water_at_298_K.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="40" data-mwtitle="A_Molecular_Dynamics_Simulation_of_Liquid_Water_at_298_K.webm" data-mwprovider="wikimediacommons" resource="/wiki/File:A_Molecular_Dynamics_Simulation_of_Liquid_Water_at_298_K.webm"><source src="//upload.wikimedia.org/wikipedia/commons/6/6d/A_Molecular_Dynamics_Simulation_of_Liquid_Water_at_298_K.webm" type="video/webm; codecs="vp8"" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/6d/A_Molecular_Dynamics_Simulation_of_Liquid_Water_at_298_K.webm/A_Molecular_Dynamics_Simulation_of_Liquid_Water_at_298_K.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/6d/A_Molecular_Dynamics_Simulation_of_Liquid_Water_at_298_K.webm/A_Molecular_Dynamics_Simulation_of_Liquid_Water_at_298_K.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/6d/A_Molecular_Dynamics_Simulation_of_Liquid_Water_at_298_K.webm/A_Molecular_Dynamics_Simulation_of_Liquid_Water_at_298_K.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/6d/A_Molecular_Dynamics_Simulation_of_Liquid_Water_at_298_K.webm/A_Molecular_Dynamics_Simulation_of_Liquid_Water_at_298_K.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/6/6d/A_Molecular_Dynamics_Simulation_of_Liquid_Water_at_298_K.webm/A_Molecular_Dynamics_Simulation_of_Liquid_Water_at_298_K.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /></video></span><figcaption>Molecular dynamics simulation of liquid water at 298 K</figcaption></figure> <div class="mw-heading mw-heading4"><h4 id="Complexity">Complexity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=23" title="Edit section: Complexity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The standard pairwise interaction calculation in MD leads to an <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 {\mathcal {O}}(N^{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> </mrow> </mrow> <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 {\mathcal {O}}(N^{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58b124da561cf34f2121e39eaff8e84ef4592c98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.836ex; height:3.176ex;" alt="{\displaystyle {\mathcal {O}}(N^{2})}"></span>complexity for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> particles. This is because each particle interacts with every other particle, resulting in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {N(N-1)}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>N</mi> <mo stretchy="false">(</mo> <mi>N</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {N(N-1)}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f30b6021696cd9c86c48fb4471088974f6c42b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.776ex; height:5.676ex;" alt="{\displaystyle {\frac {N(N-1)}{2}}}"></span> interactions.<sup id="cite_ref-81" class="reference"><a href="#cite_note-81"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup> Advanced algorithms, such as the Ewald summation or Fast Multipole Method, reduce this to <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 {\mathcal {O}}(N\log N)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>N</mi> <mi>log</mi> <mo>⁡</mo> <mi>N</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {O}}(N\log N)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8658b7724f2492980eab8528378dc975a9a072ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.532ex; height:2.843ex;" alt="{\displaystyle {\mathcal {O}}(N\log N)}"></span> or even <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 {\mathcal {O}}(N)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>N</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {O}}(N)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d707ed387b83504adae2f6b5af62901c87cd545" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.723ex; height:2.843ex;" alt="{\displaystyle {\mathcal {O}}(N)}"></span> by grouping distant particles and treating them as a single entity or using clever mathematical approximations.<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><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> </p> <div class="mw-heading mw-heading3"><h3 id="Quantum_mechanics/molecular_mechanics_(QM/MM)_2"><span id="Quantum_mechanics.2Fmolecular_mechanics_.28QM.2FMM.29_2"></span>Quantum mechanics/molecular mechanics (QM/MM)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=24" title="Edit section: Quantum mechanics/molecular mechanics (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">See also: <a href="/wiki/QM/MM" title="QM/MM">QM/MM</a></div> <div class="mw-heading mw-heading4"><h4 id="Algorithm_2">Algorithm</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=25" title="Edit section: Algorithm"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Combines quantum mechanical calculations for a small region with molecular mechanics for the larger environment.<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> </p> <div class="mw-heading mw-heading4"><h4 id="Complexity_2">Complexity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=26" title="Edit section: Complexity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The complexity of QM/MM methods depends on both the size of the quantum region and the method used for quantum calculations. For example, if a Hartree-Fock method is used for the quantum part, the complexity can be approximated 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 {\mathcal {O}}(M^{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {O}}(M^{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56d4e54472d20728432dfd8cb45a89a7d2d508b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.212ex; height:3.176ex;" alt="{\displaystyle {\mathcal {O}}(M^{2})}"></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 M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> is the number of basis functions in the quantum region. This complexity arises from the need to solve a set of coupled equations iteratively until self-consistency is achieved.<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> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hartree-Fock.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Hartree-Fock.png/220px-Hartree-Fock.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Hartree-Fock.png/330px-Hartree-Fock.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Hartree-Fock.png/440px-Hartree-Fock.png 2x" data-file-width="720" data-file-height="540" /></a><figcaption>Algorithmic flowchart illustrating the Hartree–Fock method</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Hartree-Fock_method">Hartree-Fock method</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=27" title="Edit section: Hartree-Fock method"><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">See also: <a href="/wiki/Hartree%E2%80%93Fock_method" title="Hartree–Fock method">Hartree–Fock method</a></div> <div class="mw-heading mw-heading4"><h4 id="Algorithm_3">Algorithm</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=28" title="Edit section: Algorithm"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Finds a single Fock state that minimizes the energy.<sup id="cite_ref-Lucas-2014_86-0" class="reference"><a href="#cite_note-Lucas-2014-86"><span class="cite-bracket">[</span>86<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Complexity_3">Complexity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=29" title="Edit section: Complexity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>NP-hard or NP-complete as demonstrated by embedding instances of the <a href="/wiki/Ising_model" title="Ising model">Ising model</a> into Hartree-Fock calculations. The Hartree-Fock method involves solving the Roothaan-Hall equations, which scales 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 {\mathcal {O}}(N^{3})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {O}}(N^{3})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee918a334c66ee3d432e63d5d61273888234e9a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.836ex; height:3.176ex;" alt="{\displaystyle {\mathcal {O}}(N^{3})}"></span> to <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 {\mathcal {O}}(N)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>N</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {O}}(N)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d707ed387b83504adae2f6b5af62901c87cd545" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.723ex; height:2.843ex;" alt="{\displaystyle {\mathcal {O}}(N)}"></span> depending on implementation, with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> being the number of basis functions. The computational cost mainly comes from evaluating and transforming the two-electron integrals. This proof of NP-hardness or NP-completeness comes from embedding problems like the Ising model into the Hartree-Fock formalism.<sup id="cite_ref-Lucas-2014_86-1" class="reference"><a href="#cite_note-Lucas-2014-86"><span class="cite-bracket">[</span>86<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Acrolein-s-trans-GED-MW-3D-sf.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Acrolein-s-trans-GED-MW-3D-sf.png/220px-Acrolein-s-trans-GED-MW-3D-sf.png" decoding="async" width="220" height="167" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Acrolein-s-trans-GED-MW-3D-sf.png/330px-Acrolein-s-trans-GED-MW-3D-sf.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Acrolein-s-trans-GED-MW-3D-sf.png/440px-Acrolein-s-trans-GED-MW-3D-sf.png 2x" data-file-width="2913" data-file-height="2208" /></a><figcaption>An <a href="/wiki/Acrolein" title="Acrolein">acrolein</a> molecule. DFT gives good results in the prediction of sensitivity of some nanostructures to environmental pollutants such as Acrolein.<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></figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Density_functional_theory">Density functional theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=30" title="Edit section: Density functional theory"><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">See also: <a href="/wiki/Density_functional_theory" title="Density functional theory">Density functional theory</a></div> <div class="mw-heading mw-heading4"><h4 id="Algorithm_4">Algorithm</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=31" title="Edit section: Algorithm"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Investigates the <a href="/wiki/Electronic_structure" class="mw-redirect" title="Electronic structure">electronic structure</a> or <a href="/wiki/Nuclear_structure" title="Nuclear structure">nuclear structure</a> of <a href="/wiki/Many-body_problem" title="Many-body problem">many-body systems</a> such as atoms, molecules, and the <a href="/wiki/Condensed_phase" class="mw-redirect" title="Condensed phase">condensed phases</a>.<sup id="cite_ref-88" class="reference"><a href="#cite_note-88"><span class="cite-bracket">[</span>88<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Complexity_4">Complexity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=32" title="Edit section: Complexity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Traditional implementations of DFT typically scale 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 {\mathcal {O}}(N^{3})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {O}}(N^{3})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee918a334c66ee3d432e63d5d61273888234e9a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.836ex; height:3.176ex;" alt="{\displaystyle {\mathcal {O}}(N^{3})}"></span>, mainly due to the need to diagonalize the <a href="/wiki/Kohn%E2%80%93Sham_equations" title="Kohn–Sham equations">Kohn-Sham matrix</a>.<sup id="cite_ref-89" class="reference"><a href="#cite_note-89"><span class="cite-bracket">[</span>89<span class="cite-bracket">]</span></a></sup> The diagonalization step, which finds the eigenvalues and eigenvectors of the matrix, contributes most to this scaling. Recent advances in DFT aim to reduce this complexity through various approximations and algorithmic improvements.<sup id="cite_ref-90" class="reference"><a href="#cite_note-90"><span class="cite-bracket">[</span>90<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Standard_CCSD_and_CCSD(T)_method"><span id="Standard_CCSD_and_CCSD.28T.29_method"></span>Standard CCSD and CCSD(T) method</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=33" title="Edit section: Standard CCSD and CCSD(T) method"><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">See also: <a href="/wiki/Coupled_cluster" title="Coupled cluster">Coupled cluster</a></div> <div class="mw-heading mw-heading4"><h4 id="Algorithm_5">Algorithm</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=34" title="Edit section: Algorithm"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>CCSD and CCSD(T) methods are advanced electronic structure techniques involving single, double, and in the case of CCSD(T), perturbative triple excitations for calculating electronic correlation effects.<sup id="cite_ref-Sengupta-2016_91-0" class="reference"><a href="#cite_note-Sengupta-2016-91"><span class="cite-bracket">[</span>91<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Complexity_5">Complexity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=35" title="Edit section: Complexity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading5"><h5 id="CCSD">CCSD</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=36" title="Edit section: CCSD"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Scales 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 {\mathcal {O}}(M^{6})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {O}}(M^{6})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47b9bdbd6c1b68cb014ae0990df1a54d006673f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.212ex; height:3.176ex;" alt="{\displaystyle {\mathcal {O}}(M^{6})}"></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 M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> is the number of basis functions. This intense computational demand arises from the inclusion of single and double excitations in the electron correlation calculation.<sup id="cite_ref-Sengupta-2016_91-1" class="reference"><a href="#cite_note-Sengupta-2016-91"><span class="cite-bracket">[</span>91<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading5"><h5 id="CCSD(T)"><span id="CCSD.28T.29"></span>CCSD(T)</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=37" title="Edit section: CCSD(T)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>With the addition of perturbative triples, the complexity increases to <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 {\mathcal {O}}(M^{7})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {O}}(M^{7})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5972317c40430064fdae1e244af6644bbea7f13" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.212ex; height:3.176ex;" alt="{\displaystyle {\mathcal {O}}(M^{7})}"></span>. This elevated complexity restricts practical usage to smaller systems, typically up to 20-25 atoms in conventional implementations.<sup id="cite_ref-Sengupta-2016_91-2" class="reference"><a href="#cite_note-Sengupta-2016-91"><span class="cite-bracket">[</span>91<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Methan_2a1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Methan_2a1.png/220px-Methan_2a1.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Methan_2a1.png/330px-Methan_2a1.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Methan_2a1.png/440px-Methan_2a1.png 2x" data-file-width="1300" data-file-height="1300" /></a><figcaption><a href="/wiki/Electron_density" title="Electron density">Electron density</a> plot of the 2a1 molecular orbital of <a href="/wiki/Methane" title="Methane">methane</a> at the CCSD(T)/cc-pVQZ level. Graphic created with <a href="/wiki/Molden" title="Molden">Molden</a> based on correlated geometry optimization with CFOUR at the CCSD(T) level in cc-pVQZ basis.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Linear-scaling_CCSD(T)_method"><span id="Linear-scaling_CCSD.28T.29_method"></span>Linear-scaling CCSD(T) method</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=38" title="Edit section: Linear-scaling CCSD(T) method"><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">See also: <a href="/wiki/Coupled_cluster" title="Coupled cluster">Coupled cluster</a></div> <div class="mw-heading mw-heading4"><h4 id="Algorithm_6">Algorithm</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=39" title="Edit section: Algorithm"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An adaptation of the standard CCSD(T) method using local natural orbitals (NOs) to significantly reduce the computational burden and enable application to larger systems.<sup id="cite_ref-Sengupta-2016_91-3" class="reference"><a href="#cite_note-Sengupta-2016-91"><span class="cite-bracket">[</span>91<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Complexity_6">Complexity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=40" title="Edit section: Complexity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Achieves linear scaling with the system size, a major improvement over the traditional fifth-power scaling of CCSD. This advancement allows for practical applications to molecules of up to 100 atoms with reasonable basis sets, marking a significant step forward in computational chemistry's capability to handle larger systems with high accuracy.<sup id="cite_ref-Sengupta-2016_91-4" class="reference"><a href="#cite_note-Sengupta-2016-91"><span class="cite-bracket">[</span>91<span class="cite-bracket">]</span></a></sup> </p><p>Proving the complexity classes for algorithms involves a combination of mathematical proof and computational experiments. For example, in the case of the Hartree-Fock method, the proof of NP-hardness is a theoretical result derived from complexity theory, specifically through reductions from known <a href="/wiki/NP-hardness" title="NP-hardness">NP-hard</a> problems.<sup id="cite_ref-xlink.rsc.org_92-0" class="reference"><a href="#cite_note-xlink.rsc.org-92"><span class="cite-bracket">[</span>92<span class="cite-bracket">]</span></a></sup> </p><p>For other methods like MD or DFT, the computational complexity is often empirically observed and supported by algorithm analysis. In these cases, the proof of correctness is less about formal mathematical proofs and more about consistently observing the computational behaviour across various systems and implementations.<sup id="cite_ref-xlink.rsc.org_92-1" class="reference"><a href="#cite_note-xlink.rsc.org-92"><span class="cite-bracket">[</span>92<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Accuracy">Accuracy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=41" title="Edit section: Accuracy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Computational chemistry is not an <i>exact</i> description of real-life chemistry, as the mathematical and physical models of nature can only provide an approximation. However, the majority of chemical phenomena can be described to a certain degree in a qualitative or approximate quantitative computational scheme.<sup id="cite_ref-93" class="reference"><a href="#cite_note-93"><span class="cite-bracket">[</span>93<span class="cite-bracket">]</span></a></sup> </p><p>Molecules consist of nuclei and electrons, so the methods of <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> apply. Computational chemists often attempt to solve the non-relativistic <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a>, with relativistic corrections added, although some progress has been made in solving the fully relativistic <a href="/wiki/Dirac_equation" title="Dirac equation">Dirac equation</a>. In principle, it is possible to solve the Schrödinger equation in either its time-dependent or time-independent form, as appropriate for the problem in hand; in practice, this is not possible except for very small systems. Therefore, a great number of approximate methods strive to achieve the best trade-off between accuracy and computational cost.<sup id="cite_ref-94" class="reference"><a href="#cite_note-94"><span class="cite-bracket">[</span>94<span class="cite-bracket">]</span></a></sup> </p><p>Accuracy can always be improved with greater computational cost. Significant errors can present themselves in <a href="/wiki/Ab_initio" title="Ab initio">ab initio</a> models comprising many electrons, due to the computational cost of full relativistic-inclusive methods.<sup id="cite_ref-Sengupta-2016_91-5" class="reference"><a href="#cite_note-Sengupta-2016-91"><span class="cite-bracket">[</span>91<span class="cite-bracket">]</span></a></sup> This complicates the study of molecules interacting with high atomic mass unit atoms, such as transitional metals and their catalytic properties. Present algorithms in computational chemistry can routinely calculate the properties of small molecules that contain up to about 40 electrons with errors for energies less than a few kJ/mol. For geometries, bond lengths can be predicted within a few picometers and bond angles within 0.5 degrees. The treatment of larger molecules that contain a few dozen atoms is computationally tractable by more approximate methods such as <a href="/wiki/Density_functional_theory" title="Density functional theory">density functional theory</a> (DFT).<sup id="cite_ref-95" class="reference"><a href="#cite_note-95"><span class="cite-bracket">[</span>95<span class="cite-bracket">]</span></a></sup> </p><p>There is some dispute within the field whether or not the latter methods are sufficient to describe complex chemical reactions, such as those in biochemistry. Large molecules can be studied by semi-empirical approximate methods. Even larger molecules are treated by <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical mechanics</a> methods that use what are called <a href="/wiki/Molecular_mechanics" title="Molecular mechanics">molecular mechanics</a> (MM).In QM-MM methods, small parts of large complexes are treated quantum mechanically (QM), and the remainder is treated approximately (MM).<sup id="cite_ref-96" class="reference"><a href="#cite_note-96"><span class="cite-bracket">[</span>96<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Software_packages">Software packages</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=42" title="Edit section: Software packages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Many self-sufficient <a href="/wiki/Category:Computational_chemistry_software" title="Category:Computational chemistry software">computational chemistry software packages</a> exist. Some include many methods covering a wide range, while others concentrate on a very specific range or even on one method. Details of most of them can be found in: </p> <ul><li><a href="/wiki/Biomolecular" class="mw-redirect" title="Biomolecular">Biomolecular</a> modelling programs: <a href="/wiki/List_of_protein_structure_prediction_software" title="List of protein structure prediction software">proteins</a>, <a href="/wiki/Comparison_of_nucleic_acid_simulation_software" title="Comparison of nucleic acid simulation software">nucleic acid</a>.</li> <li><a href="/wiki/Comparison_of_software_for_molecular_mechanics_modeling" title="Comparison of software for molecular mechanics modeling">Molecular mechanics</a> programs.</li> <li><a href="/wiki/List_of_quantum_chemistry_and_solid-state_physics_software" title="List of quantum chemistry and solid-state physics software">Quantum chemistry and solid state-physics software</a> supporting several methods.</li> <li><a href="/wiki/Molecular_design_software" title="Molecular design software">Molecular design software</a></li> <li><a href="/wiki/Semi-empirical_quantum_chemistry_methods" class="mw-redirect" title="Semi-empirical quantum chemistry methods">Semi-empirical</a> programs.</li> <li><a href="/wiki/Valence_bond_programs" title="Valence bond programs">Valence bond programs</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Specialized_journals_on_computational_chemistry">Specialized journals on computational chemistry</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_chemistry&action=edit&section=43" title="Edit section: Specialized journals on computational chemistry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i><a rel="nofollow" class="external text" href="http://www.sciencedirect.com/science/bookseries/15741400">Annual Reports in Computational Chemistry</a></i></li> <li><i><a href="/wiki/Computational_and_Theoretical_Chemistry" title="Computational and Theoretical Chemistry">Computational and Theoretical Chemistry</a></i></li> <li><i><a rel="nofollow" class="external text" href="http://www.sciencedirect.com/science/journal/10893156">Computational and Theoretical Polymer Science</a></i></li> <li><a href="/wiki/Computers_%26_Chemical_Engineering" title="Computers & Chemical Engineering">Computers & Chemical Engineering</a></li> <li><i><a href="/wiki/Journal_of_Chemical_Information_and_Modeling" title="Journal of Chemical Information and Modeling">Journal of Chemical Information and Modeling</a></i></li> <li><i><a rel="nofollow" class="external text" href="https://www.jstage.jst.go.jp/browse/jchemsoft">Journal of Chemical Software</a></i></li> <li><i><a href="/wiki/Journal_of_Chemical_Theory_and_Computation" title="Journal of Chemical Theory and Computation">Journal of Chemical Theory and Computation</a></i></li> <li><i><a href="/wiki/Journal_of_Cheminformatics" title="Journal of Cheminformatics">Journal of Cheminformatics</a></i></li> <li><i><a href="/wiki/Journal_of_Computational_Chemistry" title="Journal of Computational Chemistry">Journal of Computational Chemistry</a></i></li> <li><i><a rel="nofollow" class="external text" href="https://www.jstage.jst.go.jp/browse/jcac">Journal of Computer Aided Chemistry</a></i></li> <li><i><a rel="nofollow" class="external text" href="https://www.jstage.jst.go.jp/browse/jccj">Journal of Computer Chemistry Japan</a></i></li> <li><i><a rel="nofollow" class="external text" href="https://www.springer.com/chemistry/physical+chemistry/journal/10822">Journal of Computer-aided Molecular Design</a></i></li> <li><i><a href="/wiki/Journal_of_Theoretical_and_Computational_Chemistry" class="mw-redirect" title="Journal of Theoretical and Computational Chemistry">Journal of Theoretical and Computational Chemistry</a></i></li> <li><i><a href="/wiki/Molecular_Informatics" title="Molecular Informatics">Molecular Informatics</a></i></li> <li><i><a href="/wiki/Theoretical_Chemistry_Accounts" 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.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="CITEREFParrillLipkowitz2018" class="citation book cs1">Parrill, Abby L.; Lipkowitz, Kenny B., eds. 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Phys</i>. <b>15</b> (2): 397–411. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1208.3334">1208.3334</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013PCCP...15..397W">2013PCCP...15..397W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FC2CP42695A">10.1039/C2CP42695A</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1463-9076">1463-9076</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/23172634">23172634</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:12351374">12351374</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Chem.+Chem.+Phys.&rft.atitle=Computational+complexity+in+electronic+structure&rft.volume=15&rft.issue=2&rft.pages=397-411&rft.date=2013&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A12351374%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2013PCCP...15..397W&rft_id=info%3Aarxiv%2F1208.3334&rft.issn=1463-9076&rft_id=info%3Adoi%2F10.1039%2FC2CP42695A&rft_id=info%3Apmid%2F23172634&rft.aulast=Whitfield&rft.aufirst=James+Daniel&rft.au=Love%2C+Peter+John&rft.au=Aspuru-Guzik%2C+Al%C3%A1n&rft_id=http%3A%2F%2Fxlink.rsc.org%2F%3FDOI%3DC2CP42695A&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComputational+chemistry" class="Z3988"></span></span> </li> <li id="cite_note-93"><span class="mw-cite-backlink"><b><a href="#cite_ref-93">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="http://www.nap.edu/catalog/4886"><i>Mathematical Challenges from Theoretical/Computational Chemistry</i></a>. 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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" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <b><a href="/wiki/Category:Chemistry" title="Category:Chemistry">Category</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Chemistry" class="extiw" title="commons:Category:Chemistry">Commons</a></b></li> <li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Symbol_portal_class.svg" class="mw-file-description" title="Portal"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/23px-Symbol_portal_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/31px-Symbol_portal_class.svg.png 2x" data-file-width="180" data-file-height="185" /></a></span> <b><a href="/wiki/Portal:Chemistry" title="Portal:Chemistry">Portal</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="WikiProject"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/16px-People_icon.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/24px-People_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/32px-People_icon.svg.png 2x" data-file-width="100" data-file-height="100" /></span></span> <b><a href="/wiki/Wikipedia:WikiProject_Chemistry" title="Wikipedia:WikiProject Chemistry">WikiProject</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Computational_science" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Computational_science" title="Template:Computational science"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Template_talk:Computational_science&action=edit&redlink=1" class="new" title="Template talk:Computational science (page does not exist)"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Computational_science" title="Special:EditPage/Template:Computational science"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Computational_science" style="font-size:114%;margin:0 4em"><a href="/wiki/Computational_science" title="Computational science">Computational science</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computational_biology" title="Computational biology">Biology</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/Computational_anatomy" title="Computational anatomy">Anatomy</a></li> <li><a href="/wiki/Modelling_biological_systems" title="Modelling biological systems">Biological systems</a></li> <li><a href="/wiki/Computational_cognition" title="Computational cognition">Cognition</a></li> <li><a href="/wiki/Computational_genomics" title="Computational genomics">Genomics</a></li> <li><a href="/wiki/Computational_neuroscience" title="Computational neuroscience">Neuroscience</a></li> <li><a href="/wiki/Computational_phylogenetics" title="Computational phylogenetics">Phylogenetics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">Chemistry</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/Electronic_structure" class="mw-redirect" title="Electronic structure">Electronic structure</a></li> <li><a href="/wiki/Molecular_mechanics" title="Molecular mechanics">Molecular mechanics</a></li> <li><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computational_physics" title="Computational physics">Physics</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/Computational_astrophysics" title="Computational astrophysics">Astrophysics</a></li> <li><a href="/wiki/Computational_electromagnetics" title="Computational electromagnetics">Electromagnetics</a></li> <li><a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">Fluid dynamics</a></li> <li><a href="/wiki/Computational_geophysics" title="Computational geophysics">Geophysics</a></li> <li><a href="/wiki/Computational_mechanics" title="Computational mechanics">Mechanics</a></li> <li><a href="/wiki/Computational_particle_physics" title="Computational particle physics">Particle physics</a></li> <li><a href="/wiki/Computational_thermodynamics" title="Computational thermodynamics">Thermodynamics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computational_linguistics" title="Computational linguistics">Linguistics</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/Computational_semantics" title="Computational semantics">Semantics</a></li> <li><a href="/wiki/Computational_lexicology" title="Computational lexicology">Lexicology</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computational_social_science" title="Computational social science">Social science</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/Computational_politics" title="Computational politics">Politics</a></li> <li><a href="/wiki/Computational_sociology" title="Computational sociology">Sociology</a></li> <li><a href="/wiki/Computational_economics" title="Computational economics">Economics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Computational_finance" title="Computational finance">Finance</a></li> <li><a href="/wiki/Computational_materials_science" title="Computational materials science">Materials science</a></li> <li><a href="/wiki/Computational_mathematics" title="Computational mathematics">Mathematics</a></li> <li><a href="/wiki/Computational_statistics" title="Computational statistics">Statistics</a></li> <li><a href="/wiki/Computational_engineering" title="Computational engineering">Engineering</a></li> <li><a href="/wiki/Computational_semiotics" title="Computational semiotics">Semiotics</a></li> <li><a href="/wiki/Computational_transportation_science" title="Computational transportation science">Transportation science</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Computer_science" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Computer_science" title="Template:Computer science"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Computer_science" title="Template talk:Computer science"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Computer_science" title="Special:EditPage/Template:Computer science"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Computer_science" style="font-size:114%;margin:0 4em"><a href="/wiki/Computer_science" title="Computer science">Computer science</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div>Note: This template roughly follows the 2012 <a href="/wiki/ACM_Computing_Classification_System" title="ACM Computing Classification System">ACM Computing Classification System</a>.</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computer_hardware" title="Computer hardware">Hardware</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/Printed_circuit_board" title="Printed circuit board">Printed circuit board</a></li> <li><a href="/wiki/Peripheral" title="Peripheral">Peripheral</a></li> <li><a href="/wiki/Integrated_circuit" title="Integrated circuit">Integrated circuit</a></li> <li><a href="/wiki/Very_Large_Scale_Integration" class="mw-redirect" title="Very Large Scale Integration">Very Large Scale Integration</a></li> <li><a href="/wiki/System_on_a_chip" title="System on a chip">Systems on Chip (SoCs)</a></li> <li><a href="/wiki/Green_computing" title="Green computing">Energy consumption (Green computing)</a></li> <li><a href="/wiki/Electronic_design_automation" title="Electronic design automation">Electronic design automation</a></li> <li><a href="/wiki/Hardware_acceleration" title="Hardware acceleration">Hardware acceleration</a></li> <li><a href="/wiki/Processor_(computing)" title="Processor (computing)">Processor</a></li> <li><a href="/wiki/List_of_computer_size_categories" title="List of computer size categories">Size</a> / <a href="/wiki/Form_factor_(design)" title="Form factor (design)">Form</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Computer systems organization</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/Computer_architecture" title="Computer architecture">Computer architecture</a></li> <li><a href="/wiki/Computational_complexity" title="Computational complexity">Computational complexity</a></li> <li><a href="/wiki/Dependability" title="Dependability">Dependability</a></li> <li><a href="/wiki/Embedded_system" title="Embedded system">Embedded system</a></li> <li><a href="/wiki/Real-time_computing" title="Real-time computing">Real-time computing</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computer_network" title="Computer network">Networks</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/Network_architecture" title="Network architecture">Network architecture</a></li> <li><a href="/wiki/Network_protocol" class="mw-redirect" title="Network protocol">Network protocol</a></li> <li><a href="/wiki/Networking_hardware" title="Networking hardware">Network components</a></li> <li><a href="/wiki/Network_scheduler" title="Network scheduler">Network scheduler</a></li> <li><a href="/wiki/Network_performance" title="Network performance">Network performance evaluation</a></li> <li><a href="/wiki/Network_service" title="Network service">Network service</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Software organization</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/Interpreter_(computing)" title="Interpreter (computing)">Interpreter</a></li> <li><a href="/wiki/Middleware" title="Middleware">Middleware</a></li> <li><a href="/wiki/Virtual_machine" title="Virtual machine">Virtual machine</a></li> <li><a href="/wiki/Operating_system" title="Operating system">Operating system</a></li> <li><a href="/wiki/Software_quality" title="Software quality">Software quality</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Programming_language_theory" title="Programming language theory">Software notations</a> and <a href="/wiki/Programming_tool" title="Programming tool">tools</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/Programming_paradigm" title="Programming paradigm">Programming paradigm</a></li> <li><a href="/wiki/Programming_language" title="Programming language">Programming language</a></li> <li><a href="/wiki/Compiler_construction" class="mw-redirect" title="Compiler construction">Compiler</a></li> <li><a href="/wiki/Domain-specific_language" title="Domain-specific language">Domain-specific language</a></li> <li><a href="/wiki/Modeling_language" title="Modeling language">Modeling language</a></li> <li><a href="/wiki/Software_framework" title="Software framework">Software framework</a></li> <li><a href="/wiki/Integrated_development_environment" title="Integrated development environment">Integrated development environment</a></li> <li><a href="/wiki/Software_configuration_management" title="Software configuration management">Software configuration management</a></li> <li><a href="/wiki/Library_(computing)" title="Library (computing)">Software library</a></li> <li><a href="/wiki/Software_repository" title="Software repository">Software repository</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Software_development" title="Software development">Software development</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/Control_variable_(programming)" class="mw-redirect" title="Control variable (programming)">Control variable</a></li> <li><a href="/wiki/Software_development_process" title="Software development process">Software development process</a></li> <li><a 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style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Model_of_computation" title="Model of computation">Model of computation</a> <ul><li><a href="/wiki/Stochastic_computing" title="Stochastic computing">Stochastic</a></li></ul></li> <li><a href="/wiki/Formal_language" title="Formal language">Formal language</a></li> <li><a href="/wiki/Automata_theory" title="Automata theory">Automata theory</a></li> <li><a href="/wiki/Computability_theory" title="Computability theory">Computability theory</a></li> <li><a href="/wiki/Computational_complexity_theory" title="Computational complexity theory">Computational complexity theory</a></li> <li><a href="/wiki/Logic_in_computer_science" title="Logic in computer science">Logic</a></li> <li><a href="/wiki/Semantics_(computer_science)" title="Semantics (computer science)">Semantics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Algorithm" title="Algorithm">Algorithms</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/Algorithm_design" class="mw-redirect" title="Algorithm design">Algorithm design</a></li> <li><a href="/wiki/Analysis_of_algorithms" title="Analysis of algorithms">Analysis of algorithms</a></li> <li><a href="/wiki/Algorithmic_efficiency" title="Algorithmic efficiency">Algorithmic efficiency</a></li> <li><a href="/wiki/Randomized_algorithm" title="Randomized algorithm">Randomized algorithm</a></li> <li><a href="/wiki/Computational_geometry" title="Computational geometry">Computational geometry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mathematics of <a href="/wiki/Computing" title="Computing">computing</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/Discrete_mathematics" title="Discrete mathematics">Discrete mathematics</a></li> <li><a href="/wiki/Probability" title="Probability">Probability</a></li> <li><a href="/wiki/Statistics" title="Statistics">Statistics</a></li> <li><a href="/wiki/Mathematical_software" title="Mathematical software">Mathematical software</a></li> <li><a href="/wiki/Information_theory" title="Information theory">Information theory</a></li> <li><a href="/wiki/Mathematical_analysis" title="Mathematical analysis">Mathematical analysis</a></li> <li><a href="/wiki/Numerical_analysis" title="Numerical analysis">Numerical analysis</a></li> <li><a href="/wiki/Theoretical_computer_science" title="Theoretical computer science">Theoretical computer science</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Information_system" title="Information system">Information systems</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/Database" title="Database">Database management system</a></li> <li><a href="/wiki/Computer_data_storage" title="Computer data storage">Information storage systems</a></li> <li><a href="/wiki/Enterprise_information_system" title="Enterprise information system">Enterprise information system</a></li> <li><a href="/wiki/Social_software" title="Social software">Social information systems</a></li> <li><a href="/wiki/Geographic_information_system" title="Geographic information system">Geographic information system</a></li> <li><a href="/wiki/Decision_support_system" title="Decision support system">Decision support system</a></li> <li><a href="/wiki/Process_control" class="mw-redirect" title="Process control">Process control system</a></li> <li><a href="/wiki/Multimedia_database" title="Multimedia database">Multimedia information system</a></li> <li><a href="/wiki/Data_mining" title="Data mining">Data mining</a></li> <li><a href="/wiki/Digital_library" title="Digital library">Digital library</a></li> <li><a href="/wiki/Computing_platform" title="Computing platform">Computing platform</a></li> <li><a href="/wiki/Digital_marketing" title="Digital marketing">Digital marketing</a></li> <li><a href="/wiki/World_Wide_Web" title="World Wide Web">World Wide Web</a></li> <li><a href="/wiki/Information_retrieval" title="Information retrieval">Information retrieval</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computer_security" title="Computer security">Security</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/Cryptography" title="Cryptography">Cryptography</a></li> <li><a href="/wiki/Formal_methods" title="Formal methods">Formal methods</a></li> <li><a href="/wiki/Security_hacker" title="Security hacker">Security hacker</a></li> <li><a href="/wiki/Security_service_(telecommunication)" title="Security service (telecommunication)">Security services</a></li> <li><a href="/wiki/Intrusion_detection_system" title="Intrusion detection system">Intrusion detection system</a></li> <li><a href="/wiki/Hardware_security" title="Hardware security">Hardware security</a></li> <li><a href="/wiki/Network_security" title="Network security">Network security</a></li> <li><a href="/wiki/Information_security" title="Information security">Information security</a></li> <li><a href="/wiki/Application_security" title="Application security">Application security</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Human%E2%80%93computer_interaction" title="Human–computer interaction">Human–computer interaction</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/Interaction_design" title="Interaction design">Interaction design</a></li> <li><a href="/wiki/Social_computing" title="Social computing">Social computing</a></li> <li><a href="/wiki/Ubiquitous_computing" title="Ubiquitous computing">Ubiquitous computing</a></li> <li><a href="/wiki/Visualization_(graphics)" title="Visualization (graphics)">Visualization</a></li> <li><a href="/wiki/Computer_accessibility" title="Computer accessibility">Accessibility</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Concurrency_(computer_science)" title="Concurrency (computer science)">Concurrency</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/Concurrent_computing" title="Concurrent computing">Concurrent computing</a></li> <li><a href="/wiki/Parallel_computing" title="Parallel computing">Parallel computing</a></li> <li><a href="/wiki/Distributed_computing" title="Distributed computing">Distributed computing</a></li> <li><a href="/wiki/Multithreading_(computer_architecture)" title="Multithreading (computer architecture)">Multithreading</a></li> <li><a href="/wiki/Multiprocessing" title="Multiprocessing">Multiprocessing</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Artificial_intelligence" title="Artificial intelligence">Artificial intelligence</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/Natural_language_processing" title="Natural language processing">Natural language processing</a></li> <li><a href="/wiki/Knowledge_representation_and_reasoning" title="Knowledge representation and reasoning">Knowledge representation and reasoning</a></li> <li><a href="/wiki/Computer_vision" title="Computer vision">Computer vision</a></li> <li><a href="/wiki/Automated_planning_and_scheduling" title="Automated planning and scheduling">Automated planning and scheduling</a></li> <li><a href="/wiki/Mathematical_optimization" title="Mathematical optimization">Search methodology</a></li> <li><a href="/wiki/Control_theory" title="Control theory">Control method</a></li> <li><a href="/wiki/Philosophy_of_artificial_intelligence" title="Philosophy of artificial intelligence">Philosophy of artificial intelligence</a></li> <li><a href="/wiki/Distributed_artificial_intelligence" title="Distributed artificial intelligence">Distributed artificial intelligence</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Machine_learning" title="Machine learning">Machine learning</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/Supervised_learning" title="Supervised learning">Supervised learning</a></li> <li><a href="/wiki/Unsupervised_learning" title="Unsupervised learning">Unsupervised learning</a></li> <li><a href="/wiki/Reinforcement_learning" title="Reinforcement learning">Reinforcement learning</a></li> <li><a href="/wiki/Multi-task_learning" title="Multi-task learning">Multi-task learning</a></li> <li><a href="/wiki/Cross-validation_(statistics)" title="Cross-validation (statistics)">Cross-validation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computer_graphics" title="Computer graphics">Graphics</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/Computer_animation" title="Computer animation">Animation</a></li> <li><a href="/wiki/Rendering_(computer_graphics)" title="Rendering (computer graphics)">Rendering</a></li> <li><a href="/wiki/Photograph_manipulation" title="Photograph manipulation">Photograph manipulation</a></li> <li><a href="/wiki/Graphics_processing_unit" title="Graphics processing unit">Graphics processing unit</a></li> <li><a href="/wiki/Mixed_reality" title="Mixed reality">Mixed reality</a></li> <li><a href="/wiki/Virtual_reality" title="Virtual reality">Virtual reality</a></li> <li><a href="/wiki/Image_compression" title="Image compression">Image compression</a></li> <li><a href="/wiki/Solid_modeling" title="Solid modeling">Solid modeling</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Applied computing</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/Quantum_Computing" class="mw-redirect" title="Quantum Computing">Quantum Computing</a></li> <li><a href="/wiki/E-commerce" title="E-commerce">E-commerce</a></li> <li><a href="/wiki/Enterprise_software" title="Enterprise software">Enterprise software</a></li> <li><a href="/wiki/Computational_mathematics" title="Computational mathematics">Computational 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