@@ -3731,7 +3731,8 @@ \subsubsection{Adding water}
37313731
37323732\begin {note }
37333733{\color {blue}In practice, it is possible to use both \lmpcmd {vashishta} and
3734- \lmpcmd {lj/cut/tip4p/long} pair styles by employing the \lmpcmd {pair\_ style hybrid}
3734+ \lmpcmd {lj/cut/tip4p/long} pair styles at the same time by employing the
3735+ \lmpcmd {pair\_ style hybrid}
37353736command. However, hybridizing force fields should be done with caution, as there
37363737is no guarantee that the resulting force field will produce meaningful results.}
37373738\end {note }
@@ -4157,7 +4158,7 @@ \subsubsection{Method 1: Free sampling}
41574158A \lmpcmd {dump image} command was also added for system visualization.
41584159{\color {blue} The other commands should also be familiar from previous tutorials.}
41594160
4160- Finally, let us perform an equilibration of 50000 steps,
4161+ \noindent Finally, let us perform an equilibration of 50000 steps,
41614162using a timestep of $ 2 \, \text {fs}$ , corresponding to a total duration of $ 100 \, \text {ps}$ :
41624163\ begin{lstlisting}
41634164timestep 2.0
@@ -4193,6 +4194,17 @@ \subsubsection{Method 1: Free sampling}
41934194
41944195\paragraph {Data analysis }
41954196
4197+ \begin {figure }
4198+ \centering
4199+ \includegraphics [width=\linewidth ]{US-system-unbiased}
4200+ \caption {Snapshot of the system simulated during the free sampling
4201+ step of \hyperref [umbrella-sampling-label]{Tutorial 7}.
4202+ The atoms density is the lowest in the central
4203+ part of the box, \lmpcmd {mymes}. Here,
4204+ $ U_0 = 0.36 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\text {\AA {}}$ , and $ x_0 = 10 ~\text {\AA {}}$ .}
4205+ \label {fig:US-system-unbiased }
4206+ \end {figure }
4207+
41964208Once the simulation is complete, the density profile from \flecmd {free-sampling.dat}
41974209shows that the density in the center of the box is
41984210about two orders of magnitude lower than inside the reservoir (Fig.~\ref {fig:US-density }\, a).
@@ -4208,17 +4220,6 @@ \subsubsection{Method 1: Free sampling}
42084220is excellent, despite some noise in the central part, where fewer data points
42094221are available due to the repulsive potential.
42104222
4211- \begin {figure }
4212- \centering
4213- \includegraphics [width=\linewidth ]{US-system-unbiased}
4214- \caption {Snapshot of the system simulated during the free sampling
4215- step of \hyperref [umbrella-sampling-label]{Tutorial 7}.
4216- The atoms density is the lowest in the central
4217- part of the box, \lmpcmd {mymes}. Here,
4218- $ U_0 = 0.36 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\text {\AA {}}$ , and $ x_0 = 10 ~\text {\AA {}}$ .}
4219- \label {fig:US-system-unbiased }
4220- \end {figure }
4221-
42224223\paragraph {The limits of free sampling }
42234224
42244225Increasing the value of $ U_0 $ reduces the average number of atoms in the central
@@ -4381,6 +4382,17 @@ \subsubsection{Method 2: Umbrella sampling}
43814382
43824383\paragraph {WHAM algorithm }
43834384
4385+ \begin {figure }
4386+ \centering
4387+ \includegraphics [width=\linewidth ]{US-free-energy}
4388+ \caption {The potential, $ U$ , as a function of $ x$ , measured using umbrella
4389+ sampling during \hyperref [umbrella-sampling-label]{Tutorial 7} (blue disks),
4390+ is compared to the imposed potential given in Eq.~\eqref {eq:U }
4391+ (dark line). Parameters are $ U_0 = 2.38 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\text {\AA {}}$ ,
4392+ and $ x_0 = 10 ~\text {\AA {}}$ .}
4393+ \label {fig:US-freenergy }
4394+ \end {figure }
4395+
43844396To generate the free energy profile from the particle positions saved in
43854397the \flecmd {umbrella-sampling.i.dat} files, we use the
43864398WHAM~\cite {kumar1992weighted ,kumar1995multidim } algorithm as implemented
@@ -4414,17 +4426,6 @@ \subsubsection{Method 2: Umbrella sampling}
44144426Achieving similar results through free sampling would require performing extremely
44154427long and computationally expensive simulations.
44164428
4417- \begin {figure }
4418- \centering
4419- \includegraphics [width=\linewidth ]{US-free-energy}
4420- \caption {The potential, $ U$ , as a function of $ x$ , measured using umbrella
4421- sampling during \hyperref [umbrella-sampling-label]{Tutorial 7} (blue disks),
4422- is compared to the imposed potential given in Eq.~\eqref {eq:U }
4423- (dark line). Parameters are $ U_0 = 2.38 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\text {\AA {}}$ ,
4424- and $ x_0 = 10 ~\text {\AA {}}$ .}
4425- \label {fig:US-freenergy }
4426- \end {figure }
4427-
44284429\subsection {Tutorial 8: Reactive Molecular Dynamics }
44294430\label {bond-react-label }
44304431
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