Metadynamics: Difference between revisions

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In metadynamics,<ref name="Laio02"/><ref name="Iannuzzi03"/> the bias potential
#REDIRECT [[Category:Metadynamics]]
that acts on a selected number of geometric parameters (collective variables) &xi;={&xi;<sub>1</sub>, &xi;<sub>2</sub>, ...,&xi;<sub>''m''</sub>} is constructed on-the-fly during the simulation. The Hamiltonian for the metadynamics <math>\tilde{H}(q,p)</math> can be written as:
:<math>
\tilde{H}(q,p,t) = H(q,p) + \tilde{V}(t,\xi),
</math>
where <math>H(q,p)</math> is the Hamiltonian for the original (unbiased) system, and <math>\tilde{V}(t,\xi)</math> is the time-dependent bias potential. The latter term is usually defined as a sum of Gaussian hills with height ''h'' and width ''w'':
:<math>
\tilde{V}(t,\xi) = h \sum_{i=1}^{\lfloor t/t_G \rfloor} \exp{\left\{ -\frac{|\xi^{(t)}-\xi^{(i \cdot t_G)}|^2}{2
w^2} \right\}}.
</math>
In practice, <math>\tilde{V}(t,\xi)</math> is updated by adding a new Gaussian with a time increment ''t''<sub>G</sub>, which is typically one or two orders of magnitude greater than the time step used in the MD simulation.
 
In the limit of infinite simulation time, the bias potential is related to the free energy via:
:<math>
A(\xi) = - \lim_{t \to \infty} \tilde{V}(t,\xi) + const.
</math>
Practical hints as how to adjust the parameters used in metadynamics (''h'', ''w'', ''t''<sub>G</sub>) are given in Refs.<ref name="Ensing05"/><ref name="Laio05"/>.
 
The error estimation in free-energy calculations with metadynamics is discussed in Ref.<ref name="Laio05"/>.
 
== Anderson thermostat ==
 
* For a metadynamics run with Andersen thermostat, one has to:
#Set the standard MD-related tags: {{TAG|IBRION}}=0, {{TAG|TEBEG}}, {{TAG|POTIM}}, and {{TAG|NSW}}
#Set {{TAG|MDALGO}}=1 ({{TAG|MDALGO}}=11 in VASP 5.x), and choose an appropriate setting for {{TAG|ANDERSEN_PROB}}
#Set the parameters {{TAG|HILLS_H}}, {{TAG|HILLS_W}}, and {{TAG|HILLS_BIN}}
#Define collective variables in the {{FILE|ICONST}}-file, and set the {{TAG|STATUS}} parameter for the collective variables to 5
#If needed, define the bias potential in the {{FILE|PENALTYPOT}}-file
 
The actual time-dependent bias potential is written to the {{FILE|HILLSPOT}}-file, which is updated after adding a new Gaussian. At the beginning of the simulation, VASP attempts to read the initial bias potential from the {{FILE|PENALTYPOT}}-file. For the continuation of a metadynamics run, copy {{FILE|HILLSPOT}} to {{FILE|PENALTYPOT}}. The values of all collective variables for each MD step are listed in {{FILE|REPORT}}-file, check the lines after the string <tt>Metadynamics</tt>.
 
== Nose-Hoover thermostat ==
* For a metadynamics run with Nose-Hoover thermostat, one has to:
#Set the standard MD-related tags: {{TAG|IBRION}}=0, {{TAG|TEBEG}}, {{TAG|POTIM}}, and {{TAG|NSW}}
#Set {{TAG|MDALGO}}=2 ({{TAG|MDALGO}}=21 in VASP 5.x), and choose an appropriate setting for {{TAG|SMASS}}
#Set the parameters {{TAG|HILLS_H}}, {{TAG|HILLS_W}}, and {{TAG|HILLS_BIN}}
#Define collective variables in the {{FILE|ICONST}}-file, and set the <tt>STATUS</tt> parameter for the collective variables to 5
#If needed, define the bias potential in the {{FILE|PENALTYPOT}}-file
 
The actual time-dependent bias potential is written to the {{FILE|HILLSPOT}}-file, which is updated after adding a new Gaussian. At the beginning of the simulation, VASP attempts to read the initial bias potential from the {{FILE|PENALTYPOT}}-file. For the continuation of a metadynamics run, copy {{FILE|HILLSPOT}} to {{FILE|PENALTYPOT}}. The values of all collective variables for each MD step are listed in {{FILE|REPORT}}-file, check the lines after the string <tt>Metadynamics</tt>.
 
<div id="BiasedMD"></div>
 
== References ==
<references>
<ref name="Laio02">[http://dx.doi.org/10.1073/pnas.202427399 A. Laio and M. Parrinello, Proc. Natl. Acad, Sci. USA 99, 12562 (2002).]</ref>
<ref name="Iannuzzi03">[http://dx.doi.org/10.1103/PhysRevLett.90.238302 M. Iannuzzi, A. Laio, and M. Parrinello, Phys. Rev. Lett. 90, 238302 (2003).]</ref>
<ref name="Ensing05">[http://dx.doi.org/10.1021/jp045571i B. Ensing, A. Laio, M. Parrinello, and M. L. Klein, J. Phys. Chem. B 109, 6676 (2005).]</ref>
<ref name="Laio05">[http://dx.doi.org/10.1021/jp045424k A. Laio, A. Rodriguez-Fortea, F. L. Gervasio, M. Ceccarelli, and M. Parrinello, J. Phys. Chem. B 109, 6714 (2005).]</ref>
</references>
----
 
[[Category:Molecular Dynamics]][[Category:Metadynamics]][[Category:Theory]][[Category:Howto]]

Revision as of 10:08, 6 April 2022