Slow-growth approach: Difference between revisions
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can be found in reference <ref name="oberhofer2005"/>. | can be found in reference <ref name="oberhofer2005"/>. | ||
* For a | * For a slow-growth simulation, one has to perform a calcualtion very similar to {{TAG|Constrained molecular dynamics}} but additionally the transformation velocity-related {{TAG|INCREM}}-tag for each geometric parameter with <tt>STATUS=0</tt> has to be specified: | ||
#Set the standard MD-related tags: {{TAG|IBRION}}=0, {{TAG|TEBEG}}, {{TAG|POTIM}}, and {{TAG|NSW}} | #Set the standard MD-related tags: {{TAG|IBRION}}=0, {{TAG|TEBEG}}, {{TAG|POTIM}}, and {{TAG|NSW}} | ||
#Set {{TAG|MDALGO}}=1, and choose an appropriate setting for {{TAG|ANDERSEN_PROB}} | #Set {{TAG|MDALGO}}=1, and choose an appropriate setting for {{TAG|ANDERSEN_PROB}} | ||
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<ol start="5"> | <ol start="5"> | ||
<li> | <li>Specify the transformation velocity-related {{TAG|INCREM}}-tag for each geometric parameter with <tt>STATUS=0</tt>.</li> | ||
</ol> | </ol> | ||
Revision as of 15:42, 13 March 2019
The free-energy profile along a geometric parameter [math]\displaystyle{ \xi }[/math] can be scanned by an approximate slow-growth approach[1]. In this method, the value of [math]\displaystyle{ \xi }[/math] is linearly changed from the value characteristic for the initial state (1) to that for the final state (2) with a velocity of transformation [math]\displaystyle{ \dot{\xi} }[/math]. The resulting work needed to perform a transformation [math]\displaystyle{ 1 \rightarrow 2 }[/math] can be computed as:
[math]\displaystyle{ w^{irrev}_{1 \rightarrow 2}=\int_{{\xi(1)}}^{{\xi(2)}} \left ( \frac{\partial {V(q)}} {\partial \xi} \right ) \cdot \dot{\xi}\, dt. }[/math]
In the limit of infinitesimally small [math]\displaystyle{ \dot{\xi} }[/math], the work [math]\displaystyle{ w^{irrev}_{1 \rightarrow 2} }[/math] corresponds to the free-energy difference between the the final and initial state. In the general case, [math]\displaystyle{ w^{irrev}_{1 \rightarrow 2}$ }[/math]is the irreversible work related to the free energy via Jarzynski's identity[2]:
[math]\displaystyle{ {\rm exp}\left\{-\frac{\Delta A_{1 \rightarrow 2}}{k_B\,T} \right \}= \bigg \langle {\rm exp} \left \{-\frac{w^{irrev}_{1 \rightarrow 2}}{k_B\,T} \right \} \bigg\rangle. }[/math]
Note that calculation of the free-energy via this equation requires averaging of the term [math]\displaystyle{ {\rm exp} \left \{-\frac{w^{irrev}_{1 \rightarrow 2}}{k_B\,T} \right \} }[/math] over many realizations of the [math]\displaystyle{ 1 \rightarrow 2 }[/math] transformation. Detailed description of the simulation protocol that employs Jarzynski's identity can be found in reference [3].
- For a slow-growth simulation, one has to perform a calcualtion very similar to Constrained molecular dynamics but additionally the transformation velocity-related INCREM-tag for each geometric parameter with STATUS=0 has to be specified:
- Set the standard MD-related tags: IBRION=0, TEBEG, POTIM, and NSW
- Set MDALGO=1, and choose an appropriate setting for ANDERSEN_PROB
- Define geometric constraints in the ICONST-file, and set the STATUS parameter for the constrained coordinates to 0
- When the free-energy gradient is to be computed, set LBLUEOUT=.TRUE.
- Specify the transformation velocity-related INCREM-tag for each geometric parameter with STATUS=0.
VASP can handle multiple (even redundant) constraints. Note, however, that a too large number of constraints can cause problems with the stability of the SHAKE algorithm. In problematic cases, it is recommended to use a looser convergence criterion (see SHAKETOL) and to allow a larger number of iterations (see SHAKEMAXITER) in the SHAKE algorithm. Hard constraints may also be used in metadynamics simulations (see MDALGO=11 | 21). Information about the constraints is written onto the REPORT-file: check the lines following the string: Const_coord