@@ -3901,15 +3901,17 @@ \subsubsection{Method 1: Free sampling}
39013901
39023902\subsubsection {Method 2: Umbrella sampling }
39033903
3904- Umbrella sampling is a biased molecular dynamics method in which additional forces
3905- are added to a chosen atom to force it to explore the more unfavorable areas of
3906- the system~\cite {kastner2011umbrella , allen2017computer , frenkel2023understanding }.
3907- Here, to encourage one of the atoms to explore the central region of the box,
3908- we apply a potential $ V$ and force it to move along the $ x$ -axis. The chosen path
3909- is called the axis of reaction. Several simulations (called windows) will be
3910- conducted with varying positions for the center of the applied biasing. The results
3911- will be analyzed using the weighted histogram analysis method (WHAM)~\cite {kumar1992weighted ,kumar1995multidim },
3912- which allows for the removal of the biasing effect and ultimately deduces the
3904+ Umbrella sampling is a biased molecular dynamics method in which
3905+ additional forces are added to a chosen atom to force it to explore the
3906+ more unfavorable areas of the system~\cite {kastner2011umbrella ,
3907+ allen2017computer , frenkel2023understanding }. Here, to encourage one
3908+ of the atoms to explore the central region of the box, we apply a
3909+ potential $ V$ and force it to move along the $ x$ -axis. The chosen path
3910+ is called the axis of reaction. Several simulations (called windows)
3911+ will be conducted with varying positions for the center of the applied
3912+ biasing. The results will be analyzed using the weighted histogram
3913+ analysis method (WHAM)~\cite {kumar1992weighted ,kumar1995multidim }, which
3914+ allows for the removal of the biasing effect and ultimately deduces the
39133915unbiased free energy profile.
39143916
39153917\paragraph {LAMMPS input script }
@@ -4038,18 +4040,21 @@ \subsubsection{Method 2: Umbrella sampling}
40384040WHAM~\cite {kumar1992weighted ,kumar1995multidim } algorithm as implemented
40394041by Marc Grossfield~\cite {grossfieldimplementation }. You can download it
40404042from \href {http://membrane.urmc.rochester.edu/?page_id=126}{Alan
4041- Grossfield}'s website. The executable called \flecmd {wham} generated
4042- by following the instructions from the website must be placed next to
4043+ Grossfield}'s website. Make sure you download the WHAM code version
4044+ 2.1.0 or later which introduces the \lmpcmd {units} command-line option
4045+ used below. The executable called \flecmd {wham} generated by following
4046+ the instructions from the website must be placed next to
40434047\flecmd {umbrella-sampling.lmp}. To apply the WHAM algorithm to our
40444048simulation, we need a metadata file containing:
40454049\begin {itemize }
40464050\item the paths to all the data files,
40474051\item the values of $ x_\text {des}$ ,
40484052\item the values of $ k$ .
40494053\end {itemize }
4050- Download the \href {\filepath tutorial7/umbrella-sampling.meta}{\dwlcmd {umbrella-sampling.meta}} file
4051- and save it next to \flecmd {umbrella-sampling.lmp}. Then, run the WHAM algorithm
4052- by typing the following command in the terminal:
4054+ Download the \href {\filepath
4055+ tutorial7/umbrella-sampling.meta }{\dwlcmd {umbrella-sampling.meta}}
4056+ file and save it next to \flecmd {umbrella-sampling.lmp}. Then, run the
4057+ WHAM algorithm by typing the following command in the terminal:
40534058\ begin{lstlisting}
40544059./wham units real -30 30 50 1e-8 119.8 0 \
40554060 umbrella-sampling.meta umbrella-sampling.dat
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