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interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Mec%C3%A0nica_molecular" title="Mecànica molecular – Catalan" lang="ca" hreflang="ca" data-title="Mecànica molecular" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Molekulare_Mechanik" title="Molekulare Mechanik – German" lang="de" hreflang="de" data-title="Molekulare Mechanik" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Mec%C3%A1nica_molecular" title="Mecánica molecular – Spanish" lang="es" hreflang="es" data-title="Mecánica molecular" 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/Molekula_mekaniko" title="Molekula mekaniko – Esperanto" lang="eo" hreflang="eo" data-title="Molekula mekaniko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%DA%A9%D8%A7%D9%86%DB%8C%DA%A9_%D9%85%D9%88%D9%84%DA%A9%D9%88%D9%84%DB%8C" title="مکانیک مولکولی – Persian" lang="fa" hreflang="fa" data-title="مکانیک مولکولی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/M%C3%A9canique_mol%C3%A9culaire" title="Mécanique moléculaire – French" lang="fr" hreflang="fr" data-title="Mécanique moléculaire" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B6%84%EC%9E%90%EC%97%AD%ED%95%99" title="분자역학 – Korean" lang="ko" hreflang="ko" data-title="분자역학" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Mekanika_molekul" title="Mekanika molekul – Indonesian" lang="id" hreflang="id" data-title="Mekanika molekul" 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/Meccanica_molecolare" title="Meccanica molecolare – Italian" lang="it" hreflang="it" data-title="Meccanica molecolare" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D1%8B%D0%BD_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA" title="Молекулын механик – Mongolian" lang="mn" hreflang="mn" data-title="Молекулын механик" 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/Moleculaire_mechanica" title="Moleculaire mechanica – Dutch" lang="nl" hreflang="nl" data-title="Moleculaire mechanica" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%88%86%E5%AD%90%E5%8A%9B%E5%AD%A6%E6%B3%95" title="分子力学法 – Japanese" lang="ja" hreflang="ja" data-title="分子力学法" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Mechanika_molekularna" title="Mechanika molekularna – Polish" lang="pl" hreflang="pl" data-title="Mechanika molekularna" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Molekulov%C3%A1_mechanika" title="Molekulová mechanika – Slovak" lang="sk" hreflang="sk" data-title="Molekulová mechanika" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Molekulska_mehanika" title="Molekulska mehanika – Serbian" lang="sr" hreflang="sr" data-title="Molekulska mehanika" 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-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Molekylmekanik" title="Molekylmekanik – Swedish" lang="sv" hreflang="sv" data-title="Molekylmekanik" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Molek%C3%BCler_mekanik" title="Moleküler mekanik – Turkish" lang="tr" hreflang="tr" data-title="Moleküler mekanik" data-language-autonym="Türkçe" data-language-local-name="Turkish" 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searchaux" style="display:none">Use of classical mechanics to model molecular systems</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Bond_stretching_energy.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Bond_stretching_energy.svg/220px-Bond_stretching_energy.svg.png" decoding="async" width="220" height="286" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Bond_stretching_energy.svg/330px-Bond_stretching_energy.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Bond_stretching_energy.svg/440px-Bond_stretching_energy.svg.png 2x" data-file-width="515" data-file-height="669" /></a><figcaption>A <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force field</a> is used to minimize the bond stretching energy of this ethane molecule.</figcaption></figure> <p><b>Molecular mechanics</b> uses <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical mechanics</a> to model <a href="/wiki/Molecular" class="mw-redirect" title="Molecular">molecular</a> systems. The <a href="/wiki/Born%E2%80%93Oppenheimer" class="mw-redirect" title="Born–Oppenheimer">Born–Oppenheimer</a> approximation is assumed valid and the potential energy of all systems is calculated as a function of the nuclear coordinates using <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force fields</a>. Molecular mechanics can be used to study molecule systems ranging in size and complexity from small to large biological systems or material assemblies with many thousands to millions of atoms. </p><p>All-atomistic molecular mechanics methods have the following properties: </p> <ul><li>Each atom is simulated as one particle</li> <li>Each particle is assigned a radius (typically the <a href="/wiki/Van_der_Waals_radius" title="Van der Waals radius">van der Waals radius</a>), polarizability, and a constant net charge (generally derived from quantum calculations and/or experiment)</li> <li>Bonded interactions are treated as <i>springs</i> with an equilibrium distance equal to the experimental or calculated bond length</li></ul> <p>Variants on this theme are possible. For example, many simulations have historically used a <i>united-atom</i> representation in which each terminal <a href="/wiki/Methyl_group" title="Methyl group">methyl group</a> or intermediate <a href="/wiki/Methylene_bridge" title="Methylene bridge">methylene unit</a> was considered one particle, and large protein systems are commonly simulated using a <i>bead</i> model that assigns two to four particles per <a href="/wiki/Amino_acid" title="Amino acid">amino acid</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Functional_form">Functional form</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_mechanics&action=edit&section=1" title="Edit section: Functional form"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Molecular_mechanics" title="Special:EditPage/Molecular mechanics">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">December 2017</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:MM_PEF.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/MM_PEF.png/220px-MM_PEF.png" decoding="async" width="220" height="168" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/MM_PEF.png/330px-MM_PEF.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/MM_PEF.png/440px-MM_PEF.png 2x" data-file-width="2880" data-file-height="2200" /></a><figcaption>Molecular mechanics potential energy function with continuum solvent.</figcaption></figure> <p>The following functional abstraction, termed an <a href="/wiki/Interatomic_potential" title="Interatomic potential">interatomic potential</a> function or <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force field</a> in chemistry, calculates the molecular system's potential energy (E) in a given conformation as a sum of individual energy terms. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ E=E_{\text{covalent}}+E_{\text{noncovalent}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>E</mi> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>covalent</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>noncovalent</mtext> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ E=E_{\text{covalent}}+E_{\text{noncovalent}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f26dc12a2680bb31ebf5e2f4437d99a9cd72c81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:27.193ex; height:2.509ex;" alt="{\displaystyle \ E=E_{\text{covalent}}+E_{\text{noncovalent}}\,}"></span></dd></dl> <p>where the components of the covalent and noncovalent contributions are given by the following summations: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ E_{\text{covalent}}=E_{\text{bond}}+E_{\text{angle}}+E_{\text{dihedral}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>covalent</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>bond</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>angle</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>dihedral</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ E_{\text{covalent}}=E_{\text{bond}}+E_{\text{angle}}+E_{\text{dihedral}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c2653635cf629a4d64834c1b2813169f5a79c8a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:36.295ex; height:2.843ex;" alt="{\displaystyle \ E_{\text{covalent}}=E_{\text{bond}}+E_{\text{angle}}+E_{\text{dihedral}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ E_{\text{noncovalent}}=E_{\text{electrostatic}}+E_{\text{van der Waals}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>noncovalent</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>electrostatic</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>van der Waals</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ E_{\text{noncovalent}}=E_{\text{electrostatic}}+E_{\text{van der Waals}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b80b37c32f20c4b911f3cdcf98ba88369ea9197" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:40.177ex; height:2.509ex;" alt="{\displaystyle \ E_{\text{noncovalent}}=E_{\text{electrostatic}}+E_{\text{van der Waals}}}"></span></dd></dl> <p>The <a href="/wiki/Potential_energy_of_protein" class="mw-redirect" title="Potential energy of protein">exact functional form of the potential function</a>, or force field, depends on the particular simulation program being used. Generally the bond and angle terms are modeled as <a href="/wiki/Harmonic_oscillator" title="Harmonic oscillator">harmonic potentials</a> centered around equilibrium bond-length values derived from experiment or theoretical calculations of electronic structure performed with software which does <i>ab-initio</i> type calculations such as <a href="/wiki/Gaussian_(software)" title="Gaussian (software)">Gaussian</a>. For accurate reproduction of vibrational spectra, the <a href="/wiki/Morse_potential" title="Morse potential">Morse potential</a> can be used instead, at computational cost. The dihedral or torsional terms typically have multiple minima and thus cannot be modeled as harmonic oscillators, though their specific functional form varies with the implementation. This class of terms may include <i>improper</i> dihedral terms, which function as correction factors for out-of-plane deviations (for example, they can be used to keep <a href="/wiki/Benzene" title="Benzene">benzene</a> rings planar, or correct geometry and chirality of tetrahedral atoms in a united-atom representation). </p><p>The non-bonded terms are much more computationally costly to calculate in full, since a typical atom is bonded to only a few of its neighbors, but interacts with every other atom in the molecule. Fortunately the <a href="/wiki/Van_der_Waals_force" title="Van der Waals force">van der Waals</a> term falls off rapidly. It is typically modeled using a <i>6–12 <a href="/wiki/Lennard-Jones_potential" title="Lennard-Jones potential">Lennard-Jones potential</a></i>, which means that attractive forces fall off with distance as <i>r</i><sup>−6</sup> and repulsive forces as <i>r</i><sup>−12</sup>, where r represents the distance between two atoms. The repulsive part <i>r</i><sup>−12</sup> is however unphysical, because repulsion increases exponentially. Description of van der Waals forces by the Lennard-Jones 6–12 potential introduces inaccuracies, which become significant at short distances.<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> Generally a cutoff radius is used to speed up the calculation so that atom pairs which distances are greater than the cutoff have a van der Waals interaction energy of zero. </p><p>The electrostatic terms are notoriously difficult to calculate well because they do not fall off rapidly with distance, and long-range electrostatic interactions are often important features of the system under study (especially for <a href="/wiki/Protein" title="Protein">proteins</a>). The basic functional form is the <a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb potential</a>, which only falls off as <i>r</i><sup>−1</sup>. A variety of methods are used to address this problem, the simplest being a cutoff radius similar to that used for the van der Waals terms. However, this introduces a sharp discontinuity between atoms inside and atoms outside the radius. Switching or scaling functions that modulate the apparent electrostatic energy are somewhat more accurate methods that multiply the calculated energy by a smoothly varying scaling factor from 0 to 1 at the outer and inner cutoff radii. Other more sophisticated but computationally intensive methods are <a href="/wiki/Ewald_summation#Particle_mesh_Ewald_(PME)_method" title="Ewald summation">particle mesh Ewald</a> (PME) and the <a href="/wiki/Fast_multipole_method" title="Fast multipole method">multipole algorithm</a>. </p><p>In addition to the functional form of each energy term, a useful energy function must be assigned parameters for force constants, van der Waals multipliers, and other constant terms. These terms, together with the equilibrium bond, angle, and dihedral values, partial charge values, atomic masses and radii, and energy function definitions, are collectively termed a <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force field</a>. Parameterization is typically done through agreement with experimental values and theoretical calculations results. <a href="/wiki/Norman_L._Allinger" class="mw-redirect" title="Norman L. Allinger">Norman L. Allinger</a>'s force field in the last MM4 version calculate for hydrocarbons heats of formation with a <a href="/wiki/Root-mean-square_error" class="mw-redirect" title="Root-mean-square error">RMS error</a> of 0.35 kcal/mol, vibrational spectra with a RMS error of 24 cm<sup>−1</sup>, rotational barriers with a RMS error of 2.2°, <style data-mw-deduplicate="TemplateStyles:r1123817410">.mw-parser-output .template-chem2-su{display:inline-block;font-size:80%;line-height:1;vertical-align:-0.35em}.mw-parser-output .template-chem2-su>span{display:block;text-align:left}.mw-parser-output sub.template-chem2-sub{font-size:80%;vertical-align:-0.35em}.mw-parser-output sup.template-chem2-sup{font-size:80%;vertical-align:0.65em}</style><span class="chemf nowrap">C−C</span> bond lengths within 0.004 Å and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C−C−C</span> angles within 1°.<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> Later MM4 versions cover also compounds with heteroatoms such as aliphatic amines.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Each force field is parameterized to be internally consistent, but the parameters are generally not transferable from one force field to another. </p> <div class="mw-heading mw-heading2"><h2 id="Areas_of_application">Areas of application</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_mechanics&action=edit&section=2" title="Edit section: Areas of application"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The main use of molecular mechanics is in the field of <a href="/wiki/Molecular_dynamics" title="Molecular dynamics">molecular dynamics</a>. This uses the <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force field</a> to calculate the forces acting on each particle and a suitable integrator to model the dynamics of the particles and predict trajectories. Given enough sampling and subject to the <a href="/wiki/Ergodic_hypothesis" title="Ergodic hypothesis">ergodic hypothesis</a>, molecular dynamics trajectories can be used to estimate thermodynamic parameters of a system or probe kinetic properties, such as reaction rates and mechanisms. </p><p>Molecular mechanics is also used within <a href="/wiki/QM/MM" title="QM/MM">QM/MM</a>, which allows study of proteins and enzyme kinetics. The system is divided into two regions—one of which is treated with <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> (QM) allowing breaking and formation of bonds and the rest of the protein is modeled using molecular mechanics (MM). MM alone does not allow the study of mechanisms of enzymes, which QM allows. QM also produces more exact energy calculation of the system although it is much more computationally expensive. </p><p>Another application of molecular mechanics is energy minimization, whereby the <a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">force field</a> is used as an <a href="/wiki/Optimization_(mathematics)" class="mw-redirect" title="Optimization (mathematics)">optimization</a> criterion. This method uses an appropriate algorithm (e.g. <a href="/wiki/Gradient_descent" title="Gradient descent">steepest descent</a>) to find the molecular structure of a local energy minimum. These minima correspond to stable conformers of the molecule (in the chosen force field) and molecular motion can be modelled as vibrations around and interconversions between these stable conformers. It is thus common to find local energy minimization methods combined with global energy optimization, to find the global energy minimum (and other low energy states). At finite temperature, the molecule spends most of its time in these low-lying states, which thus dominate the molecular properties. Global optimization can be accomplished using <a href="/wiki/Simulated_annealing" title="Simulated annealing">simulated annealing</a>, the <a href="/wiki/Metropolis%E2%80%93Hastings_algorithm" title="Metropolis–Hastings algorithm">Metropolis algorithm</a> and other <a href="/wiki/Monte_Carlo_method" title="Monte Carlo method">Monte Carlo methods</a>, or using different deterministic methods of discrete or continuous optimization. While the force field represents only the <a href="/wiki/Enthalpy" title="Enthalpy">enthalpic</a> component of <a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">free energy</a> (and only this component is included during energy minimization), it is possible to include the <a href="/wiki/Entropy" title="Entropy">entropic</a> component through the use of additional methods, such as <a href="/wiki/Normal_mode" title="Normal mode">normal mode</a> analysis. </p><p>Molecular mechanics potential energy functions have been used to calculate binding constants,<sup id="cite_ref-Kuhn_4-0" class="reference"><a href="#cite_note-Kuhn-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-huo_5-0" class="reference"><a href="#cite_note-huo-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Mobley_6-0" class="reference"><a href="#cite_note-Mobley-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Wang_7-0" class="reference"><a href="#cite_note-Wang-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kollman_8-0" class="reference"><a href="#cite_note-Kollman-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> protein folding kinetics,<sup id="cite_ref-Snow_9-0" class="reference"><a href="#cite_note-Snow-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> protonation equilibria,<sup id="cite_ref-Barth_10-0" class="reference"><a href="#cite_note-Barth-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Docking_(molecular)" title="Docking (molecular)">active site coordinates</a>,<sup id="cite_ref-Mobley_6-1" class="reference"><a href="#cite_note-Mobley-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Chakrabarti_11-0" class="reference"><a href="#cite_note-Chakrabarti-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> and to <a href="/wiki/Protein_design" title="Protein design">design binding sites</a>.<sup id="cite_ref-Boas_12-0" class="reference"><a href="#cite_note-Boas-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Environment_and_solvation">Environment and solvation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_mechanics&action=edit&section=3" title="Edit section: Environment and solvation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Molecular_mechanics" title="Special:EditPage/Molecular mechanics">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">December 2017</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>In molecular mechanics, several ways exist to define the environment surrounding a molecule or molecules of interest. A system can be simulated in vacuum (termed a gas-phase simulation) with no surrounding environment, but this is usually undesirable because it introduces artifacts in the molecular geometry, especially in charged molecules. Surface charges that would ordinarily interact with solvent molecules instead interact with each other, producing molecular conformations that are unlikely to be present in any other environment. The most accurate way to solvate a system is to place explicit water molecules in the simulation box with the molecules of interest and treat the water molecules as interacting particles like those in the other molecule(s). A variety of <a href="/wiki/Water_model" title="Water model">water models</a> exist with increasing levels of complexity, representing water as a simple hard sphere (a united-atom model), as three separate particles with fixed bond angle, or even as four or five separate interaction centers to account for unpaired electrons on the oxygen atom. As water models grow more complex, related simulations grow more computationally intensive. A compromise method has been found in <a href="/wiki/Implicit_solvation" title="Implicit solvation">implicit solvation</a>, which replaces the explicitly represented water molecules with a mathematical expression that reproduces the average behavior of water molecules (or other solvents such as lipids). This method is useful to prevent artifacts that arise from vacuum simulations and reproduces bulk solvent properties well, but cannot reproduce situations in which individual water molecules create specific interactions with a solute that are not well captured by the solvent model, such as water molecules that are part of the hydrogen bond network within a protein.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Software_packages">Software packages</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_mechanics&action=edit&section=4" title="Edit section: Software packages"><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/Comparison_of_software_for_molecular_mechanics_modeling" title="Comparison of software for molecular mechanics modeling">Comparison of software for molecular mechanics modeling</a></div> <p>This is a limited list; many more packages are available. </p> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 22em;"> <ul><li><a href="/wiki/Abalone_(molecular_mechanics)" title="Abalone (molecular mechanics)">Abalone</a></li> <li>ACEMD - GPU MD<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/AMBER" title="AMBER">AMBER</a></li> <li><a href="/wiki/Ascalaph_Designer" title="Ascalaph Designer">Ascalaph Designer</a><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/BOSS_(molecular_mechanics)" title="BOSS (molecular mechanics)">BOSS</a></li> <li><a href="/wiki/CHARMM" title="CHARMM">CHARMM</a></li> <li>COSMOS<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></li> <li><a href="/wiki/CP2K" title="CP2K">CP2K</a></li> <li><a href="/wiki/Ghemical" title="Ghemical">Ghemical</a></li> <li><a href="/wiki/GROMACS" title="GROMACS">GROMACS</a></li> <li><a href="/wiki/GROMOS" title="GROMOS">GROMOS</a></li> <li><a href="/wiki/Internal_Coordinate_Mechanics" title="Internal Coordinate Mechanics">Internal Coordinate Mechanics</a> (ICM)</li> <li><a href="/wiki/LAMMPS" title="LAMMPS">LAMMPS</a></li> <li><a href="/wiki/MacroModel" title="MacroModel">MacroModel</a></li> <li><a href="/wiki/MDynaMix" title="MDynaMix">MDynaMix</a></li> <li><a href="/wiki/Molecular_Operating_Environment" title="Molecular Operating Environment">Molecular Operating Environment</a> (MOE)</li> <li><a href="/wiki/NAMD" title="NAMD">NAMD</a></li> <li><a href="/wiki/Q_(software)" title="Q (software)">Q</a></li> <li><a href="/wiki/Q-Chem" title="Q-Chem">Q-Chem</a></li> <li><a href="/wiki/Spartan_(chemistry_software)" title="Spartan (chemistry software)">Spartan</a></li> <li>StruMM3D (STR3DI32)<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></li> <li><a href="/wiki/Tinker_(software)" title="Tinker (software)">Tinker</a></li> <li><a href="/wiki/X-PLOR" title="X-PLOR">X-PLOR</a></li> <li><a href="/wiki/Yasara" class="mw-redirect" title="Yasara">Yasara</a></li> <li>Zodiac<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></li></ul></div> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_mechanics&action=edit&section=5" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col" style="column-width: 30em;"> <ul><li><a href="/wiki/Molecular_graphics" title="Molecular graphics">Molecular graphics</a></li> <li><a href="/wiki/Molecular_dynamics" title="Molecular dynamics">Molecular dynamics</a></li> <li><a href="/wiki/Molecule_editor" title="Molecule editor">Molecule editor</a></li> <li><a href="/wiki/Force_field_(chemistry)" title="Force field (chemistry)">Force field (chemistry)</a></li> <li><a href="/wiki/Comparison_of_force_field_implementations" class="mw-redirect" title="Comparison of force field implementations">Comparison of force field implementations</a></li> <li><a href="/wiki/Molecular_design_software" title="Molecular design software">Molecular design software</a></li> <li><a href="/wiki/Molecular_modeling_on_GPU" class="mw-redirect" title="Molecular modeling on GPU">Molecular modeling on GPU</a></li> <li><a href="/wiki/Comparison_of_software_for_molecular_mechanics_modeling" title="Comparison of software for molecular mechanics modeling">Comparison of software for molecular mechanics modeling</a></li> <li><a href="/wiki/List_of_software_for_Monte_Carlo_molecular_modeling" title="List of software for Monte Carlo molecular modeling">List of software for Monte Carlo molecular modeling</a></li></ul></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_mechanics&action=edit&section=6" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output 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Chichester, West Sussex, England: Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-470-09182-7" title="Special:BookSources/0-470-09182-7"><bdi>0-470-09182-7</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/55887497">55887497</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Essentials+of+computational+chemistry+%3A+theories+and+models&rft.place=Chichester%2C+West+Sussex%2C+England&rft.edition=2nd&rft.pub=Wiley&rft.date=2004&rft_id=info%3Aoclcnum%2F55887497&rft.isbn=0-470-09182-7&rft.aulast=Cramer&rft.aufirst=Christopher+J.&rft_id=https%3A%2F%2Fwww.worldcat.org%2Foclc%2F55887497&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+mechanics" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20081121103813/http://multiscalelab.org/acemd">ACEMD - GPU MD</a></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.biomolecular-modeling.com/Products.html">Ascalaph</a></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.cosmos-software.de/ce_intro.html">COSMOS</a></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.exorga.com/">StruMM3D (STR3DI32)</a></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.zeden.org/">Zodiac</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20091216074609/http://www.zeden.org/">Archived</a> 2009-12-16 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Literature">Literature</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_mechanics&action=edit&section=7" title="Edit section: Literature"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAllingerBurkert1982" class="citation book cs1">Allinger NL, Burkert U (1982). <i>Molecular Mechanics</i>. American Chemical Society. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8412-0885-8" title="Special:BookSources/978-0-8412-0885-8"><bdi>978-0-8412-0885-8</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/987878077">987878077</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Molecular+Mechanics&rft.pub=American+Chemical+Society&rft.date=1982&rft_id=info%3Aoclcnum%2F987878077&rft.isbn=978-0-8412-0885-8&rft.aulast=Allinger&rft.aufirst=NL&rft.au=Burkert%2C+U&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBox_VG1997" class="citation journal cs1">Box VG (March 1997). "The Molecular Mechanics of Quantized Valence Bonds". <i>J Mol Model</i>. <b>3</b> (3): 124–41. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs008940050026">10.1007/s008940050026</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:93821090">93821090</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J+Mol+Model.&rft.atitle=The+Molecular+Mechanics+of+Quantized+Valence+Bonds&rft.volume=3&rft.issue=3&rft.pages=124-41&rft.date=1997-03&rft_id=info%3Adoi%2F10.1007%2Fs008940050026&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A93821090%23id-name%3DS2CID&rft.au=Box+VG&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBox_VG1998" class="citation journal cs1">Box VG (12 November 1998). <a rel="nofollow" class="external text" href="https://triggered.stanford.clockss.org/ServeContent?doi=10.3987%2Frev-98-504">"The anomeric effect of monosaccharides and their derivatives. Insights from the new QVBMM molecular mechanics force field"</a>. <i>Heterocycles</i>. <b>48</b> (11): 2389–417. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3987%2FREV-98-504">10.3987/REV-98-504</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Heterocycles&rft.atitle=The+anomeric+effect+of+monosaccharides+and+their+derivatives.+Insights+from+the+new+QVBMM+molecular+mechanics+force+field&rft.volume=48&rft.issue=11&rft.pages=2389-417&rft.date=1998-11-12&rft_id=info%3Adoi%2F10.3987%2FREV-98-504&rft.au=Box+VG&rft_id=https%3A%2F%2Ftriggered.stanford.clockss.org%2FServeContent%3Fdoi%3D10.3987%252Frev-98-504&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBox_VG2004" class="citation journal cs1">Box VG (2004). "Stereo-electronic effects in polynucleotides and their double helices". <i>J. Mol. Struct</i>. <b>689</b> (1–2): 33–41. <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/2004JMoSt.689...33B">2004JMoSt.689...33B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.molstruc.2003.10.019">10.1016/j.molstruc.2003.10.019</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Mol.+Struct.&rft.atitle=Stereo-electronic+effects+in+polynucleotides+and+their+double+helices&rft.volume=689&rft.issue=1%E2%80%932&rft.pages=33-41&rft.date=2004&rft_id=info%3Adoi%2F10.1016%2Fj.molstruc.2003.10.019&rft_id=info%3Abibcode%2F2004JMoSt.689...33B&rft.au=Box+VG&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBecker_OM2001" class="citation book cs1">Becker OM (2001). <i>Computational biochemistry and biophysics</i>. Marcel Dekker. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8247-0455-1" title="Special:BookSources/978-0-8247-0455-1"><bdi>978-0-8247-0455-1</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/54078278">54078278</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computational+biochemistry+and+biophysics&rft.pub=Marcel+Dekker&rft.date=2001&rft_id=info%3Aoclcnum%2F54078278&rft.isbn=978-0-8247-0455-1&rft.au=Becker+OM&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMackerell_AD2004" class="citation journal cs1">Mackerell AD (October 2004). "Empirical force fields for biological macromolecules: overview and issues". <i>J Comput Chem</i>. <b>25</b> (13): 1584–1604. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fjcc.20082">10.1002/jcc.20082</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/15264253">15264253</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:9162620">9162620</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J+Comput+Chem&rft.atitle=Empirical+force+fields+for+biological+macromolecules%3A+overview+and+issues&rft.volume=25&rft.issue=13&rft.pages=1584-1604&rft.date=2004-10&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A9162620%23id-name%3DS2CID&rft_id=info%3Apmid%2F15264253&rft_id=info%3Adoi%2F10.1002%2Fjcc.20082&rft.au=Mackerell+AD&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchlick_T2010" class="citation book cs1">Schlick T (2010). <i>Molecular modeling and simulation: an interdisciplinary guide</i> (2nd ed.). Springer. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-1-4419-6351-2">10.1007/978-1-4419-6351-2</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-95404-2" title="Special:BookSources/978-0-387-95404-2"><bdi>978-0-387-95404-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Molecular+modeling+and+simulation%3A+an+interdisciplinary+guide&rft.edition=2nd&rft.pub=Springer&rft.date=2010&rft_id=info%3Adoi%2F10.1007%2F978-1-4419-6351-2&rft.isbn=978-0-387-95404-2&rft.au=Schlick+T&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+mechanics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNambooriRamachandranGopakumar2008" class="citation book cs1">Namboori, Krishnan; Ramachandran, K.S.; Gopakumar, Deepa (2008). <a rel="nofollow" class="external text" href="http://www.amrita.edu/publication/computational-chemistry-and-molecular-modeling"><i>Computational Chemistry and Molecular Modeling: Principles and Applications</i></a>. Springer. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-540-77304-7">10.1007/978-3-540-77304-7</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-77302-3" title="Special:BookSources/978-3-540-77302-3"><bdi>978-3-540-77302-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computational+Chemistry+and+Molecular+Modeling%3A+Principles+and+Applications&rft.pub=Springer&rft.date=2008&rft_id=info%3Adoi%2F10.1007%2F978-3-540-77304-7&rft.isbn=978-3-540-77302-3&rft.aulast=Namboori&rft.aufirst=Krishnan&rft.au=Ramachandran%2C+K.S.&rft.au=Gopakumar%2C+Deepa&rft_id=http%3A%2F%2Fwww.amrita.edu%2Fpublication%2Fcomputational-chemistry-and-molecular-modeling&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolecular+mechanics" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molecular_mechanics&action=edit&section=8" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20130715003803/http://dissertations.ub.rug.nl/faculties/science/1996/h.bekker/">Molecular dynamics simulation methods revised</a></li> <li><a rel="nofollow" class="external text" href="http://www.layruoru.com/dokuwiki/doku.php/molecular_mechanics_-_it_is_simple">Molecular mechanics - it is simple</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist 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of inorganic compounds">List of inorganic compounds</a></li> <li><a href="/wiki/Periodic_table" title="Periodic table">Periodic table</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Analytical_chemistry" title="Analytical chemistry">Analytical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Instrumental_chemistry" title="Instrumental chemistry">Instrumental chemistry</a></li> <li><a href="/wiki/Electroanalytical_methods" title="Electroanalytical methods">Electroanalytical methods</a></li> <li><a href="/wiki/Spectroscopy" title="Spectroscopy">Spectroscopy</a> <ul><li><a href="/wiki/Infrared_spectroscopy" title="Infrared spectroscopy">IR</a></li> <li><a href="/wiki/Raman_spectroscopy" title="Raman spectroscopy">Raman</a></li> <li><a href="/wiki/Ultraviolet%E2%80%93visible_spectroscopy" title="Ultraviolet–visible 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href="/wiki/Crystallography" title="Crystallography">Crystallography</a></li> <li><a href="/wiki/Characterization_(materials_science)" title="Characterization (materials science)">Characterization</a></li> <li><a href="/wiki/Titration" title="Titration">Titration</a></li> <li><a href="/wiki/Wet_chemistry" title="Wet chemistry">Wet chemistry</a></li> <li><a href="/wiki/Calorimetry" title="Calorimetry">Calorimetry</a></li> <li><a href="/wiki/Elemental_analysis" title="Elemental analysis">Elemental analysis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Theoretical_chemistry" title="Theoretical chemistry">Theoretical</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_chemistry" title="Quantum chemistry">Quantum chemistry</a></li> <li><a href="/wiki/Computational_chemistry" title="Computational chemistry">Computational chemistry</a> <ul><li><a href="/wiki/Mathematical_chemistry" title="Mathematical chemistry">Mathematical chemistry</a></li></ul></li> <li><a href="/wiki/Molecular_modelling" title="Molecular modelling">Molecular modelling</a></li> <li><a class="mw-selflink selflink">Molecular mechanics</a></li> <li><a href="/wiki/Molecular_dynamics" title="Molecular dynamics">Molecular dynamics</a></li> <li><a href="/wiki/Molecular_geometry" title="Molecular geometry">Molecular geometry</a> <ul><li><a href="/wiki/VSEPR_theory" title="VSEPR theory">VSEPR theory</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Physical_chemistry" title="Physical chemistry">Physical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Electrochemistry" title="Electrochemistry">Electrochemistry</a> <ul><li><a href="/wiki/Spectroelectrochemistry" title="Spectroelectrochemistry">Spectroelectrochemistry</a></li> <li><a href="/wiki/Photoelectrochemistry" title="Photoelectrochemistry">Photoelectrochemistry</a></li></ul></li> <li><a href="/wiki/Thermochemistry" title="Thermochemistry">Thermochemistry</a></li> <li><a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">Chemical thermodynamics</a></li> <li><a href="/wiki/Surface_science" title="Surface science">Surface science</a></li> <li><a href="/wiki/Interface_and_colloid_science" title="Interface and colloid science">Interface and colloid science</a> <ul><li><a href="/wiki/Micromeritics" title="Micromeritics">Micromeritics</a></li></ul></li> <li><a href="/wiki/Cryochemistry" title="Cryochemistry">Cryochemistry</a></li> <li><a href="/wiki/Sonochemistry" title="Sonochemistry">Sonochemistry</a></li> <li><a href="/wiki/Structural_chemistry" title="Structural chemistry">Structural chemistry</a></li> <li><a href="/wiki/Chemical_physics" title="Chemical physics">Chemical physics</a> <ul><li><a href="/wiki/Molecular_physics" title="Molecular physics">Molecular physics</a></li></ul></li> <li><a href="/wiki/Femtochemistry" title="Femtochemistry">Femtochemistry</a></li> <li><a href="/wiki/Chemical_kinetics" title="Chemical kinetics">Chemical kinetics</a></li> <li><a href="/wiki/Spectroscopy" title="Spectroscopy">Spectroscopy</a></li> <li><a href="/wiki/Photochemistry" title="Photochemistry">Photochemistry</a></li> <li><a href="/wiki/Spin_chemistry" title="Spin chemistry">Spin chemistry</a></li> <li><a href="/wiki/Microwave_chemistry" title="Microwave chemistry">Microwave chemistry</a></li> <li><a href="/wiki/Equilibrium_chemistry" title="Equilibrium chemistry">Equilibrium chemistry</a></li> <li><a href="/wiki/Mechanochemistry" title="Mechanochemistry">Mechanochemistry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Inorganic_chemistry" title="Inorganic chemistry">Inorganic</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Coordination_complex" title="Coordination complex">Coordination chemistry</a></li> <li><a href="/wiki/Magnetochemistry" title="Magnetochemistry">Magnetochemistry</a></li> <li><a href="/wiki/Organometallic_chemistry" title="Organometallic chemistry">Organometallic chemistry</a> <ul><li><a href="/wiki/Organolanthanide_chemistry" title="Organolanthanide chemistry">Organolanthanide chemistry</a></li></ul></li> <li><a href="/wiki/Atom_cluster" class="mw-redirect" title="Atom cluster">Cluster chemistry</a></li> <li><a href="/wiki/Solid-state_chemistry" title="Solid-state chemistry">Solid-state chemistry</a></li> <li><a href="/wiki/Ceramic_chemistry" class="mw-redirect" title="Ceramic chemistry">Ceramic chemistry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Organic_chemistry" title="Organic chemistry">Organic</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Stereochemistry" title="Stereochemistry">Stereochemistry</a> <ul><li><a href="/wiki/Alkane_stereochemistry" class="mw-redirect" title="Alkane stereochemistry">Alkane stereochemistry</a></li></ul></li> <li><a href="/wiki/Physical_organic_chemistry" title="Physical organic chemistry">Physical organic chemistry</a></li> <li><a href="/wiki/Organic_reactions" class="mw-redirect" title="Organic reactions">Organic reactions</a></li> <li><a href="/wiki/Organic_synthesis" title="Organic synthesis">Organic synthesis</a></li> <li><a href="/wiki/Retrosynthetic_analysis" title="Retrosynthetic analysis">Retrosynthetic analysis</a></li> <li><a href="/wiki/Enantioselective_synthesis" title="Enantioselective synthesis">Enantioselective synthesis</a></li> <li><a href="/wiki/Total_synthesis" title="Total synthesis">Total synthesis</a> / <a href="/wiki/Semisynthesis" title="Semisynthesis">Semisynthesis</a></li> <li><a href="/wiki/Fullerene_chemistry" title="Fullerene chemistry">Fullerene chemistry</a></li> <li><a href="/wiki/Polymer_chemistry" title="Polymer chemistry">Polymer chemistry</a></li> <li><a href="/wiki/Petrochemistry" class="mw-redirect" title="Petrochemistry">Petrochemistry</a></li> <li><a href="/wiki/Dynamic_covalent_chemistry" title="Dynamic covalent chemistry">Dynamic covalent chemistry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Biochemistry" title="Biochemistry">Biological</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biochemistry" title="Biochemistry">Biochemistry</a> <ul><li><a href="/wiki/Molecular_biology" title="Molecular biology">Molecular biology</a></li> <li><a href="/wiki/Cell_biology" title="Cell biology">Cell biology</a></li></ul></li> <li><a href="/wiki/Chemical_biology" title="Chemical biology">Chemical biology</a> <ul><li><a href="/wiki/Bioorthogonal_chemistry" title="Bioorthogonal chemistry">Bioorthogonal chemistry</a></li></ul></li> <li><a href="/wiki/Medicinal_chemistry" title="Medicinal chemistry">Medicinal chemistry</a> <ul><li><a href="/wiki/Pharmacology" title="Pharmacology">Pharmacology</a></li></ul></li> <li><a href="/wiki/Clinical_chemistry" title="Clinical chemistry">Clinical chemistry</a></li> <li><a href="/wiki/Neurochemistry" title="Neurochemistry">Neurochemistry</a></li> <li><a href="/wiki/Bioorganic_chemistry" title="Bioorganic chemistry">Bioorganic chemistry</a></li> <li><a href="/wiki/Bioorganometallic_chemistry" title="Bioorganometallic chemistry">Bioorganometallic chemistry</a></li> <li><a href="/wiki/Bioinorganic_chemistry" title="Bioinorganic chemistry">Bioinorganic chemistry</a></li> <li><a href="/wiki/Biophysical_chemistry" title="Biophysical chemistry">Biophysical chemistry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Interdisciplinarity" title="Interdisciplinarity">Interdisciplinarity</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nuclear_chemistry" title="Nuclear chemistry">Nuclear chemistry</a> <ul><li><a href="/wiki/Radiochemistry" title="Radiochemistry">Radiochemistry</a></li> <li><a href="/wiki/Radiation_chemistry" title="Radiation chemistry">Radiation chemistry</a></li> <li><a href="/wiki/Actinide_chemistry" title="Actinide chemistry">Actinide chemistry</a></li></ul></li> <li><a href="/wiki/Cosmochemistry" title="Cosmochemistry">Cosmochemistry</a> / <a href="/wiki/Astrochemistry" title="Astrochemistry">Astrochemistry</a> / <a href="/wiki/Stellar_chemistry" title="Stellar chemistry">Stellar chemistry</a></li> <li><a href="/wiki/Geochemistry" title="Geochemistry">Geochemistry</a> <ul><li><a href="/wiki/Biogeochemistry" title="Biogeochemistry">Biogeochemistry</a></li> <li><a href="/wiki/Photogeochemistry" title="Photogeochemistry">Photogeochemistry</a></li></ul></li></ul> <ul><li><a href="/wiki/Environmental_chemistry" title="Environmental chemistry">Environmental chemistry</a> <ul><li><a href="/wiki/Atmospheric_chemistry" title="Atmospheric chemistry">Atmospheric chemistry</a></li> <li><a href="/wiki/Ocean_chemistry" class="mw-redirect" title="Ocean chemistry">Ocean chemistry</a></li></ul></li> <li><a href="/wiki/Clay_chemistry" title="Clay chemistry">Clay chemistry</a></li> <li><a href="/wiki/Carbochemistry" title="Carbochemistry">Carbochemistry</a></li> <li><a href="/wiki/Food_chemistry" title="Food chemistry">Food chemistry</a> <ul><li><a href="/wiki/Carbohydrate_chemistry" class="mw-redirect" title="Carbohydrate chemistry">Carbohydrate chemistry</a></li> <li><a href="/wiki/Food_physical_chemistry" title="Food physical chemistry">Food physical chemistry</a></li></ul></li> <li><a href="/wiki/Agricultural_chemistry" title="Agricultural chemistry">Agricultural chemistry</a> <ul><li><a href="/wiki/Soil_chemistry" title="Soil chemistry">Soil chemistry</a></li></ul></li></ul> <ul><li><a href="/wiki/Chemistry_education" title="Chemistry education">Chemistry education</a> <ul><li><a href="/wiki/Amateur_chemistry" title="Amateur chemistry">Amateur chemistry</a></li> <li><a href="/wiki/General_chemistry" title="General chemistry">General chemistry</a></li></ul></li> <li><a href="/wiki/Clandestine_chemistry" title="Clandestine chemistry">Clandestine chemistry</a></li> <li><a href="/wiki/Forensic_chemistry" title="Forensic chemistry">Forensic chemistry</a> <ul><li><a href="/wiki/Forensic_toxicology" title="Forensic toxicology">Forensic toxicology</a></li> <li><a href="/wiki/Post-mortem_chemistry" title="Post-mortem chemistry">Post-mortem chemistry</a></li></ul></li></ul> <ul><li><a href="/wiki/Nanochemistry" title="Nanochemistry">Nanochemistry</a> <ul><li><a href="/wiki/Supramolecular_chemistry" title="Supramolecular chemistry">Supramolecular chemistry</a></li></ul></li> <li><a href="/wiki/Chemical_synthesis" title="Chemical synthesis">Chemical synthesis</a> <ul><li><a href="/wiki/Green_chemistry" title="Green chemistry">Green chemistry</a></li> <li><a href="/wiki/Click_chemistry" title="Click chemistry">Click chemistry</a></li> <li><a href="/wiki/Combinatorial_chemistry" title="Combinatorial chemistry">Combinatorial chemistry</a></li> <li><a href="/wiki/Biosynthesis" title="Biosynthesis">Biosynthesis</a></li></ul></li> <li><a href="/wiki/Chemical_engineering" title="Chemical engineering">Chemical engineering</a> <ul><li><a href="/wiki/Stoichiometry" title="Stoichiometry">Stoichiometry</a></li></ul></li> <li><a href="/wiki/Materials_science" title="Materials science">Materials science</a> <ul><li><a href="/wiki/Metallurgy" title="Metallurgy">Metallurgy</a></li> <li><a href="/wiki/Ceramic_engineering" title="Ceramic engineering">Ceramic engineering</a></li> <li><a href="/wiki/Polymer_science" title="Polymer science">Polymer science</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">See also</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/History_of_chemistry" title="History of chemistry">History of chemistry</a></li> <li><a href="/wiki/Nobel_Prize_in_Chemistry" title="Nobel Prize in Chemistry">Nobel Prize in Chemistry</a></li> <li><a href="/wiki/Timeline_of_chemistry" title="Timeline of chemistry">Timeline of chemistry</a> <ul><li><a href="/wiki/Discovery_of_chemical_elements" title="Discovery of chemical elements">of element discoveries</a></li></ul></li> <li>"<a href="/wiki/The_central_science" title="The central science">The central science</a>"</li> <li><a href="/wiki/Chemical_reaction" title="Chemical reaction">Chemical reaction</a> <ul><li><a href="/wiki/Catalysis" title="Catalysis">Catalysis</a></li></ul></li> <li><a href="/wiki/Chemical_element" title="Chemical element">Chemical element</a></li> <li><a href="/wiki/Chemical_compound" title="Chemical compound">Chemical compound</a></li> <li><a href="/wiki/Atom" title="Atom">Atom</a></li> <li><a href="/wiki/Molecule" title="Molecule">Molecule</a></li> <li><a href="/wiki/Ion" title="Ion">Ion</a></li> <li><a href="/wiki/Chemical_substance" title="Chemical substance">Chemical substance</a></li> <li><a href="/wiki/Chemical_bond" title="Chemical bond">Chemical bond</a></li> <li><a href="/wiki/Alchemy" title="Alchemy">Alchemy</a></li> <li><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" 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