Thermodynamic integration with harmonic reference - Revision history

https://beta.vasp.at/wiki/index.php?action=history&feed=atom&title=Thermodynamic_integration_with_harmonic_reference Thermodynamic integration with harmonic reference - Revision history 2026-04-23T02:51:39Z Revision history for this page on the wiki MediaWiki 1.43.8 https://beta.vasp.at/wiki/index.php?title=Thermodynamic_integration_with_harmonic_reference&diff=24541&oldid=prev Huebsch at 06:30, 8 May 2024 2024-05-08T06:30:26Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 06:30, 8 May 2024</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l54">Line 54:</td> <td colspan="2" class="diff-lineno">Line 54:</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 TI calculations in internal coordinates are performed in NVT ensemble using any thermostat available in VASP. The coupling parameter <math>\lambda</math> is defined by setting the parameter {{TAG|TI_LAMBDA}} in the [[INCAR|INCAR]] file.</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 TI calculations in internal coordinates are performed in NVT ensemble using any thermostat available in VASP. The coupling parameter <math>\lambda</math> is defined by setting the parameter {{TAG|TI_LAMBDA}} in the [[INCAR|INCAR]] file.</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>The set of internal coordinates used in the TI calculation are defined via the {{FILE|ICONST}} file by setting the status to 3. The Hesse matrix <math>\mathbf{\underline{H}}^\mathbf{x}</math> is provided in the file {{FILE|HESSEMAT}} and its transformation into <math>\mathbf{\underline{H}}^\mathbf{q}</math> is performed by VASP. The potential energies of the system 1 and 0,<math>\mathbf{q}</math>, needed to compute <math>\langle V_1 -V_{0,\mathbf{q}} \rangle</math> used as integrant in the TI expression for <math>\Delta A_{0,\mathbf{q} \rightarrow 1} </math>, are written in the file {{FILE|REPORT}} in lines introduce by a string "e_ti>"</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 set of internal coordinates used in the TI calculation are defined via the {{FILE|ICONST}} file by setting the status to 3. The Hesse matrix <math>\mathbf{\underline{H}}^\mathbf{x}</math> is provided in the file {{FILE|HESSEMAT}} and its transformation into <math>\mathbf{\underline{H}}^\mathbf{q}</math> is performed by VASP. The potential energies of the system 1 and 0,<math>\mathbf{q}</math>, needed to compute <math>\langle V_1 -V_{0,\mathbf{q}} \rangle</math> used as integrant in the TI expression for <math>\Delta A_{0,\mathbf{q} \rightarrow 1} </math>, are written in the file {{FILE|REPORT}} in lines introduce by a string "e_ti>"</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;"></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;">== References ==</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;"></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;">[[Category:Molecular dynamics]]</ins></div></td></tr> </table>

Huebsch https://beta.vasp.at/wiki/index.php?title=Thermodynamic_integration_with_harmonic_reference&diff=22804&oldid=prev Huebsch: Huebsch moved page Category:Thermodynamic integration with harmonic reference to Thermodynamic integration with harmonic reference without leaving a redirect 2023-11-13T08:11:51Z

<p>Huebsch moved page <a href="/wiki/index.php?title=Category:Thermodynamic_integration_with_harmonic_reference&action=edit&redlink=1" class="new" title="Category:Thermodynamic integration with harmonic reference (page does not exist)">Category:Thermodynamic integration with harmonic reference</a> to <a href="/wiki/Thermodynamic_integration_with_harmonic_reference" title="Thermodynamic integration with harmonic reference">Thermodynamic integration with harmonic reference</a> without leaving a redirect</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <tr class="diff-title" lang="en"> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:11, 13 November 2023</td> </tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div> </td></tr></table>

Huebsch https://beta.vasp.at/wiki/index.php?title=Thermodynamic_integration_with_harmonic_reference&diff=22721&oldid=prev Tbucko at 11:45, 2 November 2023 2023-11-02T11:45:47Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:45, 2 November 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l32">Line 32:</td> <td colspan="2" class="diff-lineno">Line 32:</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># integrate <math>\langle V_1 -V_{0,\mathbf{x}} \rangle</math> over the <math>\lambda </math> grid and compute <math>\Delta A_{0,\mathbf{x}\rightarrow 1}</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># integrate <math>\langle V_1 -V_{0,\mathbf{x}} \rangle</math> over the <math>\lambda </math> grid and compute <math>\Delta A_{0,\mathbf{x}\rightarrow 1}</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>Unfortunately, there are several problems linked with such a straightforward approach. First, the systems with rotational and/or translational degrees of freedom cannot be treated in a straightforward manner because <math>V_{0,\mathbf{x}}(\mathbf{x})</math> is not invariant under rotations and translations. Conventional TI is thus unsuitable for simulations of gas phase molecules or adsorbate-substrate systems. and this problem also imposes restrictions on the choice of thermostat used in NVT simulation (Langevin thermostat, for instance, does not conserve position of the center of mass and is therefore unsuitable for the use in conventional TI). Furthermore, if the Hesse matrix of the harmonic system has one or more eigenvalues that nearly vanish, the simulations with <math>\lambda \rightarrow </math> 0 is likely to generate unphysical configurations causing serious convergence issues. These problems have been addressed in series of works by Amsler et al.<ref>[https://pubs.acs.org/doi/abs/10.1021/acs.jctc.0c01022 J Amsler, <del style="font-weight: bold; text-decoration: none;">PN </del>Plessow, F Studt, T Bucko, J. Chem. Theory Comput. 17, 1155-1169 (2021)]</ref> </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>Unfortunately, there are several problems linked with such a straightforward approach. First, the systems with rotational and/or translational degrees of freedom cannot be treated in a straightforward manner because <math>V_{0,\mathbf{x}}(\mathbf{x})</math> is not invariant under rotations and translations. Conventional TI is thus unsuitable for simulations of gas phase molecules or adsorbate-substrate systems. and this problem also imposes restrictions on the choice of thermostat used in NVT simulation (Langevin thermostat, for instance, does not conserve position of the center of mass and is therefore unsuitable for the use in conventional TI). Furthermore, if the Hesse matrix of the harmonic system has one or more eigenvalues that nearly vanish, the simulations with <math>\lambda \rightarrow </math> 0 is likely to generate unphysical configurations causing serious convergence issues. These problems have been addressed in series of works by Amsler et al.<ref>[https://pubs.acs.org/doi/abs/10.1021/acs.jctc.0c01022 J<ins style="font-weight: bold; text-decoration: none;">. </ins>Amsler, <ins style="font-weight: bold; text-decoration: none;">P. N. </ins>Plessow, F<ins style="font-weight: bold; text-decoration: none;">. </ins>Studt, T<ins style="font-weight: bold; text-decoration: none;">. </ins>Bucko, J. Chem. Theory Comput. 17, 1155-1169 (2021<ins style="font-weight: bold; text-decoration: none;">)]</ref><ref>[https://pubs.acs.org/doi/abs/10.1021/acs.jctc.3c00169 J. Amsler, P. N. Plessow, F. Studt, T. Bučko, J. Chem. Theory Comput. 19, 2455-2468 (2023</ins>)]</ref> </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>First, the method was formulated in terms of rotationally and translationally invariant internal coordinates <math>\mathbf{q}=\mathbf{q}(\mathbf{x})</math>, whereby the free energy of interacting system is repartitioned as follows:</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>First, the method was formulated in terms of rotationally and translationally invariant internal coordinates <math>\mathbf{q}=\mathbf{q}(\mathbf{x})</math>, whereby the free energy of interacting system is repartitioned as follows:</div></td></tr> </table>

Tbucko https://beta.vasp.at/wiki/index.php?title=Thermodynamic_integration_with_harmonic_reference&diff=22720&oldid=prev Tbucko at 11:43, 2 November 2023 2023-11-02T11:43:26Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:43, 2 November 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l32">Line 32:</td> <td colspan="2" class="diff-lineno">Line 32:</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># integrate <math>\langle V_1 -V_{0,\mathbf{x}} \rangle</math> over the <math>\lambda </math> grid and compute <math>\Delta A_{0,\mathbf{x}\rightarrow 1}</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># integrate <math>\langle V_1 -V_{0,\mathbf{x}} \rangle</math> over the <math>\lambda </math> grid and compute <math>\Delta A_{0,\mathbf{x}\rightarrow 1}</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>Unfortunately, there are several problems linked with such a straightforward approach. First, the systems with rotational and/or translational degrees of freedom cannot be treated in a straightforward manner because <math>V_{0,\mathbf{x}}(\mathbf{x})</math> is not invariant under rotations and translations. Conventional TI is thus unsuitable for simulations of gas phase molecules or adsorbate-substrate systems. and this problem also imposes restrictions on the choice of thermostat used in NVT simulation (Langevin thermostat, for instance, does not conserve position of the center of mass and is therefore unsuitable for the use in conventional TI). Furthermore, if the Hesse matrix of the harmonic system has one or more eigenvalues that nearly vanish, the simulations with <math>\lambda \rightarrow </math> 0 is likely to generate unphysical configurations causing serious convergence issues. These problems have been addressed in series of works by Amsler et al. </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>Unfortunately, there are several problems linked with such a straightforward approach. First, the systems with rotational and/or translational degrees of freedom cannot be treated in a straightforward manner because <math>V_{0,\mathbf{x}}(\mathbf{x})</math> is not invariant under rotations and translations. Conventional TI is thus unsuitable for simulations of gas phase molecules or adsorbate-substrate systems. and this problem also imposes restrictions on the choice of thermostat used in NVT simulation (Langevin thermostat, for instance, does not conserve position of the center of mass and is therefore unsuitable for the use in conventional TI). Furthermore, if the Hesse matrix of the harmonic system has one or more eigenvalues that nearly vanish, the simulations with <math>\lambda \rightarrow </math> 0 is likely to generate unphysical configurations causing serious convergence issues. These problems have been addressed in series of works by Amsler et al.<ins style="font-weight: bold; text-decoration: none;"><ref>[https://pubs.acs.org/doi/abs/10.1021/acs.jctc.0c01022 J Amsler, PN Plessow, F Studt, T Bucko, J. Chem. Theory Comput. 17, 1155-1169 (2021)]</ref> </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>First, the method was formulated in terms of rotationally and translationally invariant internal coordinates <math>\mathbf{q}=\mathbf{q}(\mathbf{x})</math>, whereby the free energy of interacting system is repartitioned as follows:</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>First, the method was formulated in terms of rotationally and translationally invariant internal coordinates <math>\mathbf{q}=\mathbf{q}(\mathbf{x})</math>, whereby the free energy of interacting system is repartitioned as follows:</div></td></tr> </table>

Tbucko https://beta.vasp.at/wiki/index.php?title=Thermodynamic_integration_with_harmonic_reference&diff=22714&oldid=prev Tbucko at 09:00, 2 November 2023 2023-11-02T09:00:07Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 09:00, 2 November 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l32">Line 32:</td> <td colspan="2" class="diff-lineno">Line 32:</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># integrate <math>\langle V_1 -V_{0,\mathbf{x}} \rangle</math> over the <math>\lambda </math> grid and compute <math>\Delta A_{0,\mathbf{x}\rightarrow 1}</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># integrate <math>\langle V_1 -V_{0,\mathbf{x}} \rangle</math> over the <math>\lambda </math> grid and compute <math>\Delta A_{0,\mathbf{x}\rightarrow 1}</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>Unfortunately, there are several problems linked with such a straightforward approach. First, the systems with rotational and/or translational degrees of freedom cannot be treated in a straightforward manner because <math>V_{0,\mathbf{x}}(\mathbf{x})</math> is not invariant under rotations and translations. Conventional TI is thus unsuitable for simulations of gas phase molecules or adsorbate-substrate systems. and this problem also imposes restrictions on the choice of thermostat used in NVT simulation (Langevin thermostat, for instance, does not conserve position of the center of mass and is therefore unsuitable for the use in conventional TI). Furthermore, if the Hesse matrix of the harmonic system has one or more eigenvalues that nearly vanish, the simulations with <math>\lambda \rightarrow </math> 0 is likely to generate unphysical configurations causing serious convergence issues. </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>Unfortunately, there are several problems linked with such a straightforward approach. First, the systems with rotational and/or translational degrees of freedom cannot be treated in a straightforward manner because <math>V_{0,\mathbf{x}}(\mathbf{x})</math> is not invariant under rotations and translations. Conventional TI is thus unsuitable for simulations of gas phase molecules or adsorbate-substrate systems. and this problem also imposes restrictions on the choice of thermostat used in NVT simulation (Langevin thermostat, for instance, does not conserve position of the center of mass and is therefore unsuitable for the use in conventional TI). Furthermore, if the Hesse matrix of the harmonic system has one or more eigenvalues that nearly vanish, the simulations with <math>\lambda \rightarrow </math> 0 is likely to generate unphysical configurations causing serious convergence issues<ins style="font-weight: bold; text-decoration: none;">. These problems have been addressed in series of works by Amsler et al</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" 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;">These problems have been addressed in series of works by Amsler et al.<ref>[https://pubs.acs.org/doi/abs/10.1021/acs.jctc.0c01022 J. Amsler</del>, <del style="font-weight: bold; text-decoration: none;">P.N. Plessow, F. Studt, T. Bučko, ''J. Chem. Theory Comput.'' 17, 1155 (2021)]</ref><ref>[https://pubs.acs.org/doi/abs/10.1021/acs.jctc.3c00169 J. Amsler, P.N. Plessow, F. Studt, T. Bučko, ''J. Chem. Theory Comput.'' 19, 2455 (2023)]</ref> </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><ins style="font-weight: bold; text-decoration: none;">First</ins>, the method was <ins style="font-weight: bold; text-decoration: none;">formulated </ins>in terms of rotationally and translationally invariant internal coordinates <math>\mathbf{q}=\mathbf{q}(\mathbf{x})</math>, whereby the free energy of interacting system is repartitioned as follows:</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><del style="font-weight: bold; text-decoration: none;">who reformulated </del>the method was in terms of rotationally and translationally invariant internal coordinates <math>\mathbf{q}=\mathbf{q}(\mathbf{x})</math>, whereby the free energy of interacting system is repartitioned as follows:</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>:<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;"><div>A_1 = A_{0,\mathbf{x}} + \Delta A_{0,\mathbf{x} \rightarrow 0,\mathbf{q}} + \Delta A_{0,\mathbf{q} \rightarrow 1} </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>A_1 = A_{0,\mathbf{x}} + \Delta A_{0,\mathbf{x} \rightarrow 0,\mathbf{q}} + \Delta A_{0,\mathbf{q} \rightarrow 1} </div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l54">Line 54:</td> <td colspan="2" class="diff-lineno">Line 53:</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 TI calculations in internal coordinates are performed in NVT ensemble using any thermostat available in VASP. The coupling parameter <math>\lambda</math> is defined by setting the parameter {{TAG|TI_LAMBDA}} in the [[INCAR|INCAR]] file.</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 TI calculations in internal coordinates are performed in NVT ensemble using any thermostat available in VASP. The coupling parameter <math>\lambda</math> is defined by setting the parameter {{TAG|TI_LAMBDA}} in the [[INCAR|INCAR]] file.</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>The set of internal coordinates used in the TI calculation are defined via the {{FILE|ICONST}} file by setting the status to 3. The Hesse matrix <math>\mathbf{\underline{H}}^\mathbf{x}</math> is provided in the file {{FILE|HESSEMAT}} and its transformation into <math>\mathbf{\underline{H}}^\mathbf{q}</math> is performed by VASP. The potential energies of the system 1 and 0,<math>\mathbf{q}</math>, needed to compute <math>\langle V_1 -V_{0,\mathbf{q}} \<del style="font-weight: bold; text-decoration: none;">rangle_{\lambda}</del></math> used as integrant in the TI expression for <math>\Delta A_{0,\mathbf{q} \rightarrow 1} </math>, are written in the file {{FILE|REPORT}} in lines introduce by a string "e_ti>"</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 set of internal coordinates used in the TI calculation are defined via the {{FILE|ICONST}} file by setting the status to 3. The Hesse matrix <math>\mathbf{\underline{H}}^\mathbf{x}</math> is provided in the file {{FILE|HESSEMAT}} and its transformation into <math>\mathbf{\underline{H}}^\mathbf{q}</math> is performed by VASP. The potential energies of the system 1 and 0,<math>\mathbf{q}</math>, needed to compute <math>\langle V_1 -V_{0,\mathbf{q}} \<ins style="font-weight: bold; text-decoration: none;">rangle</ins></math> used as integrant in the TI expression for <math>\Delta A_{0,\mathbf{q} \rightarrow 1} </math>, are written in the file {{FILE|REPORT}} in lines introduce by a string "e_ti>"</div></td></tr> </table>

Tbucko https://beta.vasp.at/wiki/index.php?title=Thermodynamic_integration_with_harmonic_reference&diff=22713&oldid=prev Tbucko at 08:52, 2 November 2023 2023-11-02T08:52:24Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:52, 2 November 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l34">Line 34:</td> <td colspan="2" class="diff-lineno">Line 34:</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>Unfortunately, there are several problems linked with such a straightforward approach. First, the systems with rotational and/or translational degrees of freedom cannot be treated in a straightforward manner because <math>V_{0,\mathbf{x}}(\mathbf{x})</math> is not invariant under rotations and translations. Conventional TI is thus unsuitable for simulations of gas phase molecules or adsorbate-substrate systems. and this problem also imposes restrictions on the choice of thermostat used in NVT simulation (Langevin thermostat, for instance, does not conserve position of the center of mass and is therefore unsuitable for the use in conventional TI). Furthermore, if the Hesse matrix of the harmonic system has one or more eigenvalues that nearly vanish, the simulations with <math>\lambda \rightarrow </math> 0 is likely to generate unphysical configurations causing serious convergence issues. </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>Unfortunately, there are several problems linked with such a straightforward approach. First, the systems with rotational and/or translational degrees of freedom cannot be treated in a straightforward manner because <math>V_{0,\mathbf{x}}(\mathbf{x})</math> is not invariant under rotations and translations. Conventional TI is thus unsuitable for simulations of gas phase molecules or adsorbate-substrate systems. and this problem also imposes restrictions on the choice of thermostat used in NVT simulation (Langevin thermostat, for instance, does not conserve position of the center of mass and is therefore unsuitable for the use in conventional TI). Furthermore, if the Hesse matrix of the harmonic system has one or more eigenvalues that nearly vanish, the simulations with <math>\lambda \rightarrow </math> 0 is likely to generate unphysical configurations causing serious convergence issues. </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>These problems have been addressed in series of works by Amsler et al. </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>These problems have been addressed in series of works by Amsler et al.<ins style="font-weight: bold; text-decoration: none;"><ref>[https://pubs.acs.org/doi/abs/10.1021/acs.jctc.0c01022 J. Amsler, P.N. Plessow, F. Studt, T. Bučko, ''J. Chem. Theory Comput.'' 17, 1155 (2021)]</ref><ref>[https://pubs.acs.org/doi/abs/10.1021/acs.jctc.3c00169 J. Amsler, P.N. Plessow, F. Studt, T. Bučko, ''J. Chem. Theory Comput.'' 19, 2455 (2023)]</ref> </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;"><div>who reformulated the method was in terms of rotationally and translationally invariant internal coordinates <math>\mathbf{q}=\mathbf{q}(\mathbf{x})</math>, whereby the free energy of interacting system is repartitioned as follows:</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>who reformulated the method was in terms of rotationally and translationally invariant internal coordinates <math>\mathbf{q}=\mathbf{q}(\mathbf{x})</math>, whereby the free energy of interacting system is repartitioned as follows:</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> </table>

Tbucko https://beta.vasp.at/wiki/index.php?title=Thermodynamic_integration_with_harmonic_reference&diff=22712&oldid=prev Tbucko at 08:48, 2 November 2023 2023-11-02T08:48:22Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:48, 2 November 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l32">Line 32:</td> <td colspan="2" class="diff-lineno">Line 32:</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># integrate <math>\langle V_1 -V_{0,\mathbf{x}} \rangle</math> over the <math>\lambda </math> grid and compute <math>\Delta A_{0,\mathbf{x}\rightarrow 1}</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># integrate <math>\langle V_1 -V_{0,\mathbf{x}} \rangle</math> over the <math>\lambda </math> grid and compute <math>\Delta A_{0,\mathbf{x}\rightarrow 1}</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>Unfortunately, there are several problems linked with such a straightforward approach. First, the systems with rotational and/or translational degrees of freedom cannot be treated in a straightforward manner because <math>V_{0,\mathbf{x}}(\mathbf{x})</math> is not invariant under rotations and translations. Conventional TI is thus unsuitable for simulations of gas phase molecules or adsorbate-substrate systems. and this problem also imposes restrictions on the choice of thermostat used in NVT simulation (Langevin thermostat, for instance, does not conserve position of the center of mass and is therefore unsuitable for the use in conventional TI). Furthermore, if the Hesse matrix of the harmonic system has one or more eigenvalues that nearly vanish, the simulations with <math>\lambda \rightarrow </math> 0 is likely to generate unphysical configurations causing serious convergence issues<del style="font-weight: bold; text-decoration: none;">. These problems have been addressed in series of works by Amsler et al</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>Unfortunately, there are several problems linked with such a straightforward approach. First, the systems with rotational and/or translational degrees of freedom cannot be treated in a straightforward manner because <math>V_{0,\mathbf{x}}(\mathbf{x})</math> is not invariant under rotations and translations. Conventional TI is thus unsuitable for simulations of gas phase molecules or adsorbate-substrate systems. and this problem also imposes restrictions on the choice of thermostat used in NVT simulation (Langevin thermostat, for instance, does not conserve position of the center of mass and is therefore unsuitable for the use in conventional TI). Furthermore, if the Hesse matrix of the harmonic system has one or more eigenvalues that nearly vanish, the simulations with <math>\lambda \rightarrow </math> 0 is likely to generate unphysical configurations causing serious convergence issues. </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><del style="font-weight: bold; text-decoration: none;">First, </del>the method was <del style="font-weight: bold; text-decoration: none;">formulated </del>in terms of rotationally and translationally invariant internal coordinates <math>\mathbf{q}=\mathbf{q}(\mathbf{x})</math>, whereby the free energy of interacting system is repartitioned as follows:</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;">These problems have been addressed in series of works by Amsler et al. </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;">who reformulated </ins>the method was in terms of rotationally and translationally invariant internal coordinates <math>\mathbf{q}=\mathbf{q}(\mathbf{x})</math>, whereby the free energy of interacting system is repartitioned as follows:</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;"><div>A_1 = A_{0,\mathbf{x}} + \Delta A_{0,\mathbf{x} \rightarrow 0,\mathbf{q}} + \Delta A_{0,\mathbf{q} \rightarrow 1} </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>A_1 = A_{0,\mathbf{x}} + \Delta A_{0,\mathbf{x} \rightarrow 0,\mathbf{q}} + \Delta A_{0,\mathbf{q} \rightarrow 1} </div></td></tr> </table>

Tbucko https://beta.vasp.at/wiki/index.php?title=Thermodynamic_integration_with_harmonic_reference&diff=22711&oldid=prev Tbucko at 08:47, 2 November 2023 2023-11-02T08:47:13Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:47, 2 November 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l53">Line 53:</td> <td colspan="2" class="diff-lineno">Line 53:</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 TI calculations in internal coordinates are performed in NVT ensemble using any thermostat available in VASP. The coupling parameter <math>\lambda</math> is defined by setting the parameter {{TAG|TI_LAMBDA}} in the [[INCAR|INCAR]] file.</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 TI calculations in internal coordinates are performed in NVT ensemble using any thermostat available in VASP. The coupling parameter <math>\lambda</math> is defined by setting the parameter {{TAG|TI_LAMBDA}} in the [[INCAR|INCAR]] file.</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>The set of internal coordinates used in the TI calculation are defined via the {{FILE|ICONST}} file by setting the status to 3. The Hesse matrix <math>\mathbf{\underline{H}}^\mathbf{x}</math> is provided in the file {{FILE|HESSEMAT}} and its transformation into <math>\mathbf{\underline{H}}^\mathbf{q}</math> is performed by VASP. The potential energies of the system 1 and 0,<math>\mathbf{q}</math>, needed to compute <math>\langle V_1 -V_{0,\mathbf{q}} \<del style="font-weight: bold; text-decoration: none;">rangle</del></math> used as integrant in the TI expression for <math>\Delta A_{0,\mathbf{q} \rightarrow 1} </math>, are written in the file {{FILE|REPORT}} in lines introduce by a string "e_ti>"</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 set of internal coordinates used in the TI calculation are defined via the {{FILE|ICONST}} file by setting the status to 3. The Hesse matrix <math>\mathbf{\underline{H}}^\mathbf{x}</math> is provided in the file {{FILE|HESSEMAT}} and its transformation into <math>\mathbf{\underline{H}}^\mathbf{q}</math> is performed by VASP. The potential energies of the system 1 and 0,<math>\mathbf{q}</math>, needed to compute <math>\langle V_1 -V_{0,\mathbf{q}} \<ins style="font-weight: bold; text-decoration: none;">rangle_{\lambda}</ins></math> used as integrant in the TI expression for <math>\Delta A_{0,\mathbf{q} \rightarrow 1} </math>, are written in the file {{FILE|REPORT}} in lines introduce by a string "e_ti>"</div></td></tr> </table>

Tbucko https://beta.vasp.at/wiki/index.php?title=Thermodynamic_integration_with_harmonic_reference&diff=22708&oldid=prev Tbucko at 08:36, 2 November 2023 2023-11-02T08:36:50Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:36, 2 November 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l53">Line 53:</td> <td colspan="2" class="diff-lineno">Line 53:</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 TI calculations in internal coordinates are performed in NVT ensemble using any thermostat available in VASP. The coupling parameter <math>\lambda</math> is defined by setting the parameter {{TAG|TI_LAMBDA}} in the [[INCAR|INCAR]] file.</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 TI calculations in internal coordinates are performed in NVT ensemble using any thermostat available in VASP. The coupling parameter <math>\lambda</math> is defined by setting the parameter {{TAG|TI_LAMBDA}} in the [[INCAR|INCAR]] file.</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>The set of internal coordinates used in the TI calculation are defined via the {{FILE|ICONST}} file by setting the status to 3. The Hesse matrix <math>\mathbf{\underline{H}}^\mathbf{x}</math> is provided in the file {{FILE|HESSEMAT}} and its transformation into <math>\mathbf{\underline{H}}^\mathbf{q}</math> is performed by VASP. The potential energies of the system 1 and 0,<math>\mathbf{q}</math>, needed to compute <math>\langle V_1 -V_{0,\mathbf{q}} \rangle</math> used as integrant in the TI expression for <math>\Delta A_{0,\mathbf{q} \rightarrow 1} </math> are written in the file {{FILE|REPORT}} in lines introduce by a string "e_ti>"</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 set of internal coordinates used in the TI calculation are defined via the {{FILE|ICONST}} file by setting the status to 3. The Hesse matrix <math>\mathbf{\underline{H}}^\mathbf{x}</math> is provided in the file {{FILE|HESSEMAT}} and its transformation into <math>\mathbf{\underline{H}}^\mathbf{q}</math> is performed by VASP. The potential energies of the system 1 and 0,<math>\mathbf{q}</math>, needed to compute <math>\langle V_1 -V_{0,\mathbf{q}} \rangle</math> used as integrant in the TI expression for <math>\Delta A_{0,\mathbf{q} \rightarrow 1} </math><ins style="font-weight: bold; text-decoration: none;">, </ins>are written in the file {{FILE|REPORT}} in lines introduce by a string "e_ti>"</div></td></tr> </table>

Tbucko https://beta.vasp.at/wiki/index.php?title=Thermodynamic_integration_with_harmonic_reference&diff=22707&oldid=prev Tbucko at 08:36, 2 November 2023 2023-11-02T08:36:22Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:36, 2 November 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l53">Line 53:</td> <td colspan="2" class="diff-lineno">Line 53:</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 TI calculations in internal coordinates are performed in NVT ensemble using any thermostat available in VASP. The coupling parameter <math>\lambda</math> is defined by setting the parameter {{TAG|TI_LAMBDA}} in the [[INCAR|INCAR]] file.</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 TI calculations in internal coordinates are performed in NVT ensemble using any thermostat available in VASP. The coupling parameter <math>\lambda</math> is defined by setting the parameter {{TAG|TI_LAMBDA}} in the [[INCAR|INCAR]] file.</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>The set of internal coordinates used in the TI calculation are defined via the {{FILE|ICONST}} file by setting the status to 3. The Hesse matrix <math>\mathbf{\underline{H}}^\mathbf{x}</math> is provided in the file {{FILE|HESSEMAT}} and its transformation into <math>\mathbf{\underline{H}}^\mathbf{q}</math> is performed by VASP. The potential energies of the system 1 and 0,<math>\mathbf{q}</math>, needed to compute <math>\langle V_1 -V_{0,\mathbf{q}} \rangle</math> used as integrant in the TI expression for <math>\Delta A_{0,\mathbf{q} \rightarrow 1} </math are written in the file {{FILE|REPORT}} in lines introduce by a string "e_ti>"</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 set of internal coordinates used in the TI calculation are defined via the {{FILE|ICONST}} file by setting the status to 3. The Hesse matrix <math>\mathbf{\underline{H}}^\mathbf{x}</math> is provided in the file {{FILE|HESSEMAT}} and its transformation into <math>\mathbf{\underline{H}}^\mathbf{q}</math> is performed by VASP. The potential energies of the system 1 and 0,<math>\mathbf{q}</math>, needed to compute <math>\langle V_1 -V_{0,\mathbf{q}} \rangle</math> used as integrant in the TI expression for <math>\Delta A_{0,\mathbf{q} \rightarrow 1} </math<ins style="font-weight: bold; text-decoration: none;">> </ins>are written in the file {{FILE|REPORT}} in lines introduce by a string "e_ti>"</div></td></tr> </table>

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