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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>fix ID group-ID shake tol iter N constraint values ... keyword value ...
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<PRE>fix ID group-ID <I>shake/rattle</I> tol iter N constraint values ... keyword value ...
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</PRE>
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<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
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<LI>shake = style name of this fix command
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<LI>shake or rattle = style name of this fix command
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<LI>tol = accuracy tolerance of SHAKE solution
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@ -51,11 +51,32 @@
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fix 1 sub shake 0.0001 20 10 t 5 6 m 1.0 a 31
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fix 1 sub shake 0.0001 20 10 t 5 6 m 1.0 a 31 mol myMol
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</PRE>
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<PRE>fix 1 sub rattle 0.0001 20 10 t 5 6 m 1.0 a 31
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fix 1 sub rattle 0.0001 20 10 t 5 6 m 1.0 a 31 mol myMol
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>Apply bond and angle constraints to specified bonds and angles in the
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simulation. This typically enables a longer timestep.
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</P>
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<P><B>SHAKE vs. RATTLE:</B>
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</P>
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<P>The SHAKE algorithm was invented for schemes such as Verlet, where only the coordinates
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are integrated and the velocities are approximated as finite differences to the trajectories (<A HREF = "#Ryckaert">Ryckaert et al. (1977)</A>).
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If the velocities are integrated explicitly, for example with velocity Verlet,
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a second set of constraining forces is required in order to eliminate velocity components along the bonds (<A HREF = "#Andersen">Andersen (1983)</A>).
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</P>
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<P>In order to formulate the individual constraints for SHAKE and RATTLE, let us focus on a single molecule whose
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bonds are to be constrained. Let image(Eqs/fix_rattle_ri.jpg) and image(Eqs/fix_rattle_vi.jpg) be the position and velocity of atom <I>i</I> at time <I>n</I>, for <I>i</I>=1,...,<I>N</I>, where <I>N</I> is the number of sites of our reference molecule. The distance vector between sites <I>i</I> and <I>j</I> is given by image(Eqs/fix_rattle_rij.jpg). The constraints can then be formulated as
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</P>
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<CENTER><IMG SRC = "Eqs/fix_rattle_constraints.jpg">
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</CENTER>
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<P>The SHAKE algorithm satisfies the first condition, i.e. the sites at time <I>n+1</I> will have the desired separations image(Eqs/fix_rattle_dij.jpg) immediately after the coordinates are integrated.
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If we also enforce the second condition, the velocity components along the bonds will vanish.
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RATTLE satisfies both conditions and fix rattle is implemented in a way that it uses fix shake for dealing with the coordinate constraints. Therefore all the information about SHAKE below is also relevant for RATTLE.
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</P>
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<P><B>SHAKE:</B>
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</P>
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<P>Each timestep the specified bonds and angles are reset to their
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equilibrium lengths and angular values via the well-known SHAKE
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algorithm. This is done by applying an additional constraint force so
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@ -144,6 +165,24 @@ more instructions on how to use the accelerated styles effectively.
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</P>
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<HR>
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<P><B>RATTLE:</B>
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</P>
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<P>The velocity constraints lead to a linear system of equations which
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can be solved analytically. The implementation of the algorithm in LAMMPS
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closely follows <A HREF = "#Andersen">Andersen (1983)</A>.
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</P>
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<P>IMPORTANT NOTE: This command modifies forces and velocities and
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it has to come after all other integration fixes. If you define other
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fixes that modify velocities or forces after fix rattle operates,
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then this fix will not take them into account and the time integration
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will typically not satisfy the RATTLE constraints. You can check whether
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the constraints work correctly by setting the value of RATTLE_DEBUG in fix_rattle.cpp
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to 1 and recompiling LAMMPS.
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</P>
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<P>IMPORTANT NOTE: RATTLE does not support cuda at the moment.
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</P>
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<HR>
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<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
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</P>
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<P>No information about this fix is written to <A HREF = "restart.html">binary restart
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@ -173,4 +212,16 @@ of SHAKE parameters and monitoring the energy versus time.
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</P>
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<P><B>Default:</B> none
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</P>
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<HR>
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<A NAME = "Ryckaert"></A>
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<P><B>(Ryckaert)</B> J.-P. Ryckaert, G. Ciccotti and H. J. C. Berendsen,
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Journal of Computational Physics, 23, 327–341 (1977).
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</P>
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<A NAME = "Andersen"></A>
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<P><B>(Andersen)</B> H. Andersen,
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Journal of Computational Physics, 52, 24-34 (1983).
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</P>
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</HTML>
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@ -11,10 +11,10 @@ fix shake/cuda command :h3
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[Syntax:]
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fix ID group-ID shake tol iter N constraint values ... keyword value ... :pre
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fix ID group-ID {shake/rattle} tol iter N constraint values ... keyword value ... :pre
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ID, group-ID are documented in "fix"_fix.html command :ulb,l
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shake = style name of this fix command :l
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shake or rattle = style name of this fix command :l
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tol = accuracy tolerance of SHAKE solution :l
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iter = max # of iterations in each SHAKE solution :l
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N = print SHAKE statistics every this many timesteps (0 = never) :l
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@ -35,12 +35,34 @@ keyword = {mol} :l
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fix 1 sub shake 0.0001 20 10 b 4 19 a 3 5 2
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fix 1 sub shake 0.0001 20 10 t 5 6 m 1.0 a 31
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fix 1 sub shake 0.0001 20 10 t 5 6 m 1.0 a 31 mol myMol :pre
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fix 1 sub rattle 0.0001 20 10 t 5 6 m 1.0 a 31
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fix 1 sub rattle 0.0001 20 10 t 5 6 m 1.0 a 31 mol myMol :pre
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[Description:]
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Apply bond and angle constraints to specified bonds and angles in the
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simulation. This typically enables a longer timestep.
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[SHAKE vs. RATTLE:]
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The SHAKE algorithm was invented for schemes such as Verlet, where only the coordinates
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are integrated and the velocities are approximated as finite differences to the trajectories ("Ryckaert et al. (1977)"_#Ryckaert).
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If the velocities are integrated explicitly, for example with velocity Verlet,
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a second set of constraining forces is required in order to eliminate velocity components along the bonds ("Andersen (1983)"_#Andersen).
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In order to formulate the individual constraints for SHAKE and RATTLE, let us focus on a single molecule whose
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bonds are to be constrained. Let image(Eqs/fix_rattle_ri.jpg) and image(Eqs/fix_rattle_vi.jpg) be the position and velocity of atom {i} at time {n}, for {i}=1,...,{N}, where {N} is the number of sites of our reference molecule. The distance vector between sites {i} and {j} is given by image(Eqs/fix_rattle_rij.jpg). The constraints can then be formulated as
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:c,image(Eqs/fix_rattle_constraints.jpg)
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The SHAKE algorithm satisfies the first condition, i.e. the sites at time {n+1} will have the desired separations image(Eqs/fix_rattle_dij.jpg) immediately after the coordinates are integrated.
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If we also enforce the second condition, the velocity components along the bonds will vanish.
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RATTLE satisfies both conditions and fix rattle is implemented in a way that it uses fix shake for dealing with the coordinate constraints. Therefore all the information about SHAKE below is also relevant for RATTLE.
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[SHAKE:]
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Each timestep the specified bonds and angles are reset to their
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equilibrium lengths and angular values via the well-known SHAKE
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algorithm. This is done by applying an additional constraint force so
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@ -92,6 +114,7 @@ satisfy the SHAKE constraints. The solution for this is to make sure
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that fix shake is defined in your input script after any other fixes
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which add or change forces (to atoms that fix shake operates on).
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:line
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The {mol} keyword should be used when other commands, such as "fix
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@ -127,6 +150,27 @@ use the "suffix"_suffix.html command in your input script.
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See "Section_accelerate"_Section_accelerate.html of the manual for
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more instructions on how to use the accelerated styles effectively.
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:line
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[RATTLE:]
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The velocity constraints lead to a linear system of equations which
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can be solved analytically. The implementation of the algorithm in LAMMPS
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closely follows "Andersen (1983)"_#Andersen.
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IMPORTANT NOTE: This command modifies forces and velocities and
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it has to come after all other integration fixes. If you define other
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fixes that modify velocities or forces after fix rattle operates,
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then this fix will not take them into account and the time integration
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will typically not satisfy the RATTLE constraints. You can check whether
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the constraints work correctly by setting the value of RATTLE_DEBUG in fix_rattle.cpp
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to 1 and recompiling LAMMPS.
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IMPORTANT NOTE: RATTLE does not support cuda at the moment.
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:line
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[Restart, fix_modify, output, run start/stop, minimize info:]
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@ -157,3 +201,15 @@ of SHAKE parameters and monitoring the energy versus time.
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[Related commands:] none
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[Default:] none
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:line
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:link(Ryckaert)
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[(Ryckaert)] J.-P. Ryckaert, G. Ciccotti and H. J. C. Berendsen,
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Journal of Computational Physics, 23, 327–341 (1977).
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:link(Andersen)
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[(Andersen)] H. Andersen,
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Journal of Computational Physics, 52, 24-34 (1983).
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