https://vasp.at/wiki/index.php?action=history&feed=atom&title=Nos%C3%A9-Hoover_thermostat
Nosé-Hoover thermostat - Revision history
2026-04-18T18:22:45Z
Revision history for this page on the wiki
MediaWiki 1.43.8
https://vasp.at/wiki/index.php?title=Nos%C3%A9-Hoover_thermostat&diff=32315&oldid=prev
Singraber at 21:23, 17 October 2025
2025-10-17T21:23:22Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:23, 17 October 2025</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>where <math>m_{i}</math> and <math>k_{B}</math> are the mass of ion <math>i</math> and the Boltzmann constant, respectively. The first two terms are the kinetic and potential energy of the system. The third and fourth term represent the kinetic and potential energy of the fictitious coordinate <math>s</math>. These terms also ensure the energy conservation of the <del style="font-weight: bold; text-decoration: none;">Nose</del>-Hoover thermostat. The parameter <math>g</math> is usually equal to the number of degrees of freedom of the system <math>g=3N - N_{\mathrm{constraint}}</math>, where <math>N_{\mathrm{constraint}}</math> is equal to the number of constraint set (fixed coordinates in the {{TAG|POSCAR}} file). The parameter <math>Q</math> is an effective "mass" of <math>s</math>, which controls the coupling of the system to the heat bath. It is set by the {{TAG|INCAR}} tag {{TAG|SMASS}}. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>where <math>m_{i}</math> and <math>k_{B}</math> are the mass of ion <math>i</math> and the Boltzmann constant, respectively. The first two terms are the kinetic and potential energy of the system. The third and fourth term represent the kinetic and potential energy of the fictitious coordinate <math>s</math>. These terms also ensure the energy conservation of the <ins style="font-weight: bold; text-decoration: none;">Nosé</ins>-Hoover thermostat. The parameter <math>g</math> is usually equal to the number of degrees of freedom of the system <math>g=3N - N_{\mathrm{constraint}}</math>, where <math>N_{\mathrm{constraint}}</math> is equal to the number of constraint set (fixed coordinates in the {{TAG|POSCAR}} file). The parameter <math>Q</math> is an effective "mass" of <math>s</math>, which controls the coupling of the system to the heat bath. It is set by the {{TAG|INCAR}} tag {{TAG|SMASS}}. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The <del style="font-weight: bold; text-decoration: none;">Nose</del>-Hoover thermostat is selected by {{TAG|MDALGO}}=2.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The <ins style="font-weight: bold; text-decoration: none;">Nosé</ins>-Hoover thermostat is selected by {{TAG|MDALGO}}=2.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Related tags and articles==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Related tags and articles==</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Molecular dynamics calculations|Molecular-dynamics calculations]], [[Andersen thermostat]], [[Langevin thermostat]], [[CSVR thermostat]], [[<del style="font-weight: bold; text-decoration: none;">Nose</del>-Hoover<del style="font-weight: bold; text-decoration: none;">-</del>chain thermostat]], {{TAG|ISIF}}, {{TAG|MDALGO}}, {{TAG|SMASS}}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Molecular dynamics calculations|Molecular-dynamics calculations]], [[Andersen thermostat]], [[Langevin thermostat]], [[CSVR thermostat]], [[<ins style="font-weight: bold; text-decoration: none;">Nosé</ins>-Hoover chain thermostat]], {{TAG|ISIF}}, {{TAG|MDALGO}}, {{TAG|SMASS}}</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td></tr>
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Singraber
https://vasp.at/wiki/index.php?title=Nos%C3%A9-Hoover_thermostat&diff=32283&oldid=prev
Singraber: Singraber moved page Nose-Hoover thermostat to Nosé-Hoover thermostat: Misspelled title
2025-10-17T20:56:27Z
<p>Singraber moved page <a href="/wiki/Nose-Hoover_thermostat" class="mw-redirect" title="Nose-Hoover thermostat">Nose-Hoover thermostat</a> to <a href="/wiki/Nos%C3%A9-Hoover_thermostat" title="Nosé-Hoover thermostat">Nosé-Hoover thermostat</a>: Misspelled title</p>
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<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:56, 17 October 2025</td>
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Singraber
https://vasp.at/wiki/index.php?title=Nos%C3%A9-Hoover_thermostat&diff=31527&oldid=prev
Liebetreu at 14:30, 14 October 2025
2025-10-14T14:30:03Z
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\mathcal{L} = \sum\limits_{i=1}^{N} \frac{m_{i}}{2} s^{2} \dot{\<del style="font-weight: bold; text-decoration: none;">bold</del>{r}}_{i}^{2} - U(\<del style="font-weight: bold; text-decoration: none;">bold</del>{r}) + \frac{Q}{2} \dot{s}^{2}-g k_{B} T \mathrm{ln} \, s</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\mathcal{L} = \sum\limits_{i=1}^{N} \frac{m_{i}}{2} s^{2} \dot{\<ins style="font-weight: bold; text-decoration: none;">mathbf</ins>{r}}_{i}^{2} - U(\<ins style="font-weight: bold; text-decoration: none;">mathbf</ins>{r}) + \frac{Q}{2} \dot{s}^{2}-g k_{B} T \mathrm{ln} \, s</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td></tr>
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Liebetreu
https://vasp.at/wiki/index.php?title=Nos%C3%A9-Hoover_thermostat&diff=28566&oldid=prev
Jona at 10:28, 24 February 2025
2025-02-24T10:28:33Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:28, 24 February 2025</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The Nose-Hoover thermostat is selected by {{TAG|MDALGO}}=2.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The Nose-Hoover thermostat is selected by {{TAG|MDALGO}}=2.</div></td></tr>
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<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Related tags and articles==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Molecular dynamics calculations|Molecular-dynamics calculations]], [[Andersen thermostat]], [[Langevin thermostat]], [[CSVR thermostat]], [[Nose-Hoover-chain thermostat]], {{TAG|ISIF}}, {{TAG|MDALGO}}, {{TAG|SMASS}}</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td></tr>
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Jona
https://vasp.at/wiki/index.php?title=Nos%C3%A9-Hoover_thermostat&diff=20580&oldid=prev
Jona at 09:34, 13 July 2023
2023-07-13T09:34:51Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 09:34, 13 July 2023</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In the approach by Nosé and Hoover{{cite|nose:jcp:1984}}{{cite|nose:ptp:1991}}{{cite|hoover:pra:1985}}{{cite|frenkel:book:1996}}, an extra degree of freedom is introduced in the Hamiltonian. The heat bath is considered as an integral part of the system and has a fictious coordinate <math>s</math> which is introduced into the Lagrangian of the system. This Lagrangian for <del style="font-weight: bold; text-decoration: none;">an </del><math>N</math> is written as</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In the approach by Nosé and Hoover{{cite|nose:jcp:1984}}{{cite|nose:ptp:1991}}{{cite|hoover:pra:1985}}{{cite|frenkel:book:1996}}, an extra degree of freedom is introduced in the Hamiltonian. The heat bath is considered as an integral part of the system and has a fictious coordinate <math>s</math> which is introduced into the Lagrangian of the system. This Lagrangian for <ins style="font-weight: bold; text-decoration: none;">a </ins><math>N</math> <ins style="font-weight: bold; text-decoration: none;">particle system </ins>is written as</div></td></tr>
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Jona
https://vasp.at/wiki/index.php?title=Nos%C3%A9-Hoover_thermostat&diff=16060&oldid=prev
Huebsch at 14:09, 7 April 2022
2022-04-07T14:09:22Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:09, 7 April 2022</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In the approach by Nosé and Hoover{{cite|nose:jcp:1984}}{{cite|nose:ptp:1991}}{{cite|hoover:pra:1985}}{{cite|frenkel:book:1996}} an extra degree of freedom is introduced in the Hamiltonian. The heat bath is considered as an integral part of the system and has a fictious coordinate <math>s</math> which is introduced into the Lagrangian of the system. This Lagrangian for an <math>N</math> is written as</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In the approach by Nosé and Hoover{{cite|nose:jcp:1984}}{{cite|nose:ptp:1991}}{{cite|hoover:pra:1985}}{{cite|frenkel:book:1996}}<ins style="font-weight: bold; text-decoration: none;">, </ins>an extra degree of freedom is introduced in the Hamiltonian. The heat bath is considered as an integral part of the system and has a fictious coordinate <math>s</math> which is introduced into the Lagrangian of the system. This Lagrangian for an <math>N</math> is written as</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">::</ins><math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\mathcal{L} = \sum\limits_{i=1}^{N} \frac{m_{i}}{2} s^{2} \dot{\bold{r}}_{i}^{2} - U(\bold{r}) + \frac{Q}{2} \dot{s}^{2}-g k_{B} T \mathrm{ln} \, s</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\mathcal{L} = \sum\limits_{i=1}^{N} \frac{m_{i}}{2} s^{2} \dot{\bold{r}}_{i}^{2} - U(\bold{r}) + \frac{Q}{2} \dot{s}^{2}-g k_{B} T \mathrm{ln} \, s</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Molecular <del style="font-weight: bold; text-decoration: none;">Dynamics</del>]][[Category:Thermostats]][[Category:Theory]][[Category:Howto]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Molecular <ins style="font-weight: bold; text-decoration: none;">dynamics</ins>]][[Category:Thermostats]][[Category:Theory]][[Category:Howto]]</div></td></tr>
</table>
Huebsch
https://vasp.at/wiki/index.php?title=Nos%C3%A9-Hoover_thermostat&diff=8490&oldid=prev
Karsai at 11:47, 31 May 2019
2019-05-31T11:47:17Z
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td></tr>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">----</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Molecular Dynamics]][[Category:Thermostats]][[Category:Theory]][[Category:Howto]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Molecular Dynamics]][[Category:Thermostats]][[Category:Theory]][[Category:Howto]]</div></td></tr>
</table>
Karsai
https://vasp.at/wiki/index.php?title=Nos%C3%A9-Hoover_thermostat&diff=8489&oldid=prev
Karsai at 11:13, 31 May 2019
2019-05-31T11:13:44Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:13, 31 May 2019</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l5">Line 5:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>where <math>m_{i}</math> and <math>k_{B}</math> are the mass of ion <math>i</math> and the Boltzmann constant, respectively. The first two terms are the kinetic and potential energy of the system. The third and fourth term represent the kinetic and potential energy of the fictitious coordinate <math>s</math>. The parameter <math>g</math> is usually equal to the number of degrees of freedom of the system <math>g=3N - N_{\mathrm{constraint}}</math>, where <math>N_{\mathrm{constraint}}</math> is equal to the number of constraint set (fixed coordinates in the {{TAG|POSCAR}} file). The parameter <math>Q</math> is an effective "mass" of <math>s</math>, which controls the coupling of the system to the heat bath. It is set by the {{TAG|INCAR}} tag {{TAG|SMASS}}. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>where <math>m_{i}</math> and <math>k_{B}</math> are the mass of ion <math>i</math> and the Boltzmann constant, respectively. The first two terms are the kinetic and potential energy of the system. The third and fourth term represent the kinetic and potential energy of the fictitious coordinate <math>s</math><ins style="font-weight: bold; text-decoration: none;">. These terms also ensure the energy conservation of the Nose-Hoover thermostat</ins>. The parameter <math>g</math> is usually equal to the number of degrees of freedom of the system <math>g=3N - N_{\mathrm{constraint}}</math>, where <math>N_{\mathrm{constraint}}</math> is equal to the number of constraint set (fixed coordinates in the {{TAG|POSCAR}} file). The parameter <math>Q</math> is an effective "mass" of <math>s</math>, which controls the coupling of the system to the heat bath. It is set by the {{TAG|INCAR}} tag {{TAG|SMASS}}. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The Nose-Hoover thermostat is selected by {{TAG|MDALGO}}=2.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The Nose-Hoover thermostat is selected by {{TAG|MDALGO}}=2.</div></td></tr>
</table>
Karsai
https://vasp.at/wiki/index.php?title=Nos%C3%A9-Hoover_thermostat&diff=8482&oldid=prev
Karsai at 08:53, 31 May 2019
2019-05-31T08:53:10Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:53, 31 May 2019</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In the approach by Nosé and Hoover{{cite|nose:jcp:1984}}{{cite|nose:ptp:1991}}{{cite|hoover:pra:1985}} an extra degree of freedom is introduced in the Hamiltonian. The heat bath is considered as an integral part of the system and has a fictious coordinate <math>s</math> which is introduced into the Lagrangian of the system. This Lagrangian for an <math>N</math> is written as</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In the approach by Nosé and Hoover{{cite|nose:jcp:1984}}{{cite|nose:ptp:1991}}{{cite|hoover:pra:1985<ins style="font-weight: bold; text-decoration: none;">}}{{cite|frenkel:book:1996</ins>}} an extra degree of freedom is introduced in the Hamiltonian. The heat bath is considered as an integral part of the system and has a fictious coordinate <math>s</math> which is introduced into the Lagrangian of the system. This Lagrangian for an <math>N</math> is written as</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math></div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>where <math>m_{i}</math> and <math>k_{B}</math> are the mass of ion <math>i</math> and the Boltzmann constant, respectively. The first two terms are the kinetic and potential energy of the system. The third and fourth term represent the kinetic and potential energy of the fictitious coordinate <math>s</math>. The parameter <math>g</math> is usually equal to the number of degrees of freedom of the system <math>g=3N - N_{\mathrm{constraint}}</math>, where <math>N_{\mathrm{constraint}}</math> is equal to the number of constraint set (fixed coordinates in the {{TAG|POSCAR}} file). The parameter <math>Q</math> is an effective "mass" of <math>s</math>, which controls the coupling of the system to the heat bath. It is set by the {{TAG|INCAR}} tag {{TAG|SMASS}}. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>where <math>m_{i}</math> and <math>k_{B}</math> are the mass of ion <math>i</math> and the Boltzmann constant, respectively. The first two terms are the kinetic and potential energy of the system. The third and fourth term represent the kinetic and potential energy of the fictitious coordinate <math>s</math>. The parameter <math>g</math> is usually equal to the number of degrees of freedom of the system <math>g=3N - N_{\mathrm{constraint}}</math>, where <math>N_{\mathrm{constraint}}</math> is equal to the number of constraint set (fixed coordinates in the {{TAG|POSCAR}} file). The parameter <math>Q</math> is an effective "mass" of <math>s</math>, which controls the coupling of the system to the heat bath. It is set by the {{TAG|INCAR}} tag {{TAG|SMASS}}. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The Nose-Hoover thermostat is selected by {{TAG|MDALGO}}=2.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td></tr>
</table>
Karsai
https://vasp.at/wiki/index.php?title=Nos%C3%A9-Hoover_thermostat&diff=8481&oldid=prev
Karsai at 08:45, 31 May 2019
2019-05-31T08:45:50Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:45, 31 May 2019</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l2">Line 2:</td>
<td colspan="2" class="diff-lineno">Line 2:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\mathcal{L} = \sum\limits_{i=1}^{N} \frac{m_{i}}{2} s^{2} \dot{\bold{r}}_{i}^{2} - U(\bold{r}) + \frac{Q}{2} \dot{s}^{2}-<del style="font-weight: bold; text-decoration: none;">\frac{</del>g<del style="font-weight: bold; text-decoration: none;">}</del>{<del style="font-weight: bold; text-decoration: none;">\beta</del>}\mathrm{ln} \, s<del style="font-weight: bold; text-decoration: none;">.</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\mathcal{L} = \sum\limits_{i=1}^{N} \frac{m_{i}}{2} s^{2} \dot{\bold{r}}_{i}^{2} - U(\bold{r}) + \frac{Q}{2} \dot{s}^{2}-g <ins style="font-weight: bold; text-decoration: none;">k_</ins>{<ins style="font-weight: bold; text-decoration: none;">B</ins>} <ins style="font-weight: bold; text-decoration: none;">T </ins>\mathrm{ln} \, s</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">where <math>m_{i}</math> and <math>k_{B}</math> are the mass of ion <math>i</math> and the Boltzmann constant, respectively. The first two terms are the kinetic and potential energy of the system. The third and fourth term represent the kinetic and potential energy of the fictitious coordinate <math>s</math>. The parameter <math>g</math> is usually equal to the number of degrees of freedom of the system <math>g=3N - N_{\mathrm{constraint}}</math>, where <math>N_{\mathrm{constraint}}</math> is equal to the number of constraint set (fixed coordinates in the {{TAG|POSCAR}} file). The parameter <math>Q</math> is an effective "mass" of <math>s</math>, which controls the coupling of the system to the heat bath. It is set by the {{TAG|INCAR}} tag {{TAG|SMASS}}. </ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
</table>
Karsai