|
|
| (4 intermediate revisions by 2 users not shown) |
| Line 1: |
Line 1: |
| == Theory ==
| | #REDIRECT [[Metadynamics]] |
| In metadynamics,{{cite|laio:pnas:02}}{{cite|iannuzzi:prl:03}} the bias potential
| |
| that acts on a selected number of geometric parameters (collective variables) ξ={ξ<sub>1</sub>, ξ<sub>2</sub>, ...,ξ<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.{{cite|ensing:jpc:05}} and {{cite|laio:jpc:05}}.
| |
| | |
| The error estimation in free-energy calculations with metadynamics is discussed in Ref.{{cite|laio:jpc:05}}.
| |
| | |
| == How to ==
| |
| | |
| === 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/>
| |
| | |
| <noinclude>
| |
| ----
| |
| [[The_VASP_Manual|Contents]] | |
| | |
| [[Category:VASP|Metadynamics]][[Category:Molecular Dynamics]]
| |
