Slow-growth approach: Difference between revisions
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The resulting work needed to perform a transformation <math>1 \rightarrow 2</math> | The resulting work needed to perform a transformation <math>1 \rightarrow 2</math> | ||
can be computed as: | can be computed as: | ||
<math> | <math> | ||
w^{irrev}_{1 \rightarrow 2}=\int_{{\xi(1)}}^{{\xi(2)}} \left ( \frac{\partial {V(q)}} {\partial \xi} \right ) \cdot \dot{\xi}\, dt. | w^{irrev}_{1 \rightarrow 2}=\int_{{\xi(1)}}^{{\xi(2)}} \left ( \frac{\partial {V(q)}} {\partial \xi} \right ) \cdot \dot{\xi}\, dt. | ||
</math> | </math> | ||
In the limit of infinitesimally small $\dot{\xi}$, the work $w^{irrev}_{1 \rightarrow 2}$ | In the limit of infinitesimally small $\dot{\xi}$, the work $w^{irrev}_{1 \rightarrow 2}$ | ||
corresponds to the free-energy difference between the the final and initial state. | corresponds to the free-energy difference between the the final and initial state. | ||
Revision as of 15:30, 13 March 2019
The free-energy profile along a geometric parameter can be scanned by an approximate slow-growth approach[1]. In this method, the value of is linearly changed from the value characteristic for the initial state (1) to that for the final state (2) with a velocity of transformation . The resulting work needed to perform a transformation can be computed as:
In the limit of infinitesimally small $\dot{\xi}$, the work $w^{irrev}_{1 \rightarrow 2}$ corresponds to the free-energy difference between the the final and initial state. In the general case, $w^{irrev}_{1 \rightarrow 2}$ is the irreversible work related to the free energy via Jarzynski's identity~\cite{Jarzynski:97}: \begin{equation}\label{eq_jarzynski} {\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. \end{equation} Note that calculation of the free-energy via eq.(\ref{eq_jarzynski}) requires averaging of the term ${\rm exp} \left \{-\frac{w^{irrev}_{1 \rightarrow 2}}{k_B\,T} \right \}$ over many realizations of the $1 \rightarrow 2$ transformation. Detailed description of the simulation protocol that employs Jarzynski's identity can be found in Ref.~\cite{Oberhofer:05}.
- For a constrained molecular dynamics run with Andersen thermostat, one has to:
- 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.
For a slow-growth simulation, one has to additionally:
- 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