2010-10-23 05:24:19 +08:00
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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<HR>
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<H3>compute ti command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>compute ID group ti keyword args ...
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</PRE>
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<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
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<LI>ti = style name of this compute command
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<LI>one or more attribute/arg pairs may be appended
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<LI>keyword = pair style (lj/cut, gauss, born, etc) or <I>tail</I> or <I>kspace</I>
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<PRE> pair style args = v_name1 v_name2
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v_name1 = variable with name1 that is energy scale factor and function of lambda
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v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
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<I>tail</I> args = v_name1 v_name2
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v_name1 = variable with name1 that is energy tail correction scale factor and function of lambda
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v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
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<I>kspace</I> args = v_name1 v_name2
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v_name1 = variable with name1 that is K-Space scale factor and function of lambda
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v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
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</PRE>
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</UL>
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<P><B>Examples:</B>
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</P>
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<PRE>compute 1 all ti lj/cut v_lj v_dlj coul/long v_c v_dc kspace v_ks v_dks
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>Define a computation that calculates the derivative of the interaction
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potential with respect to <I>lambda</I>, the coupling parameter used in a
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thermodynamic integration. This derivative can be used to infer a
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free energy difference resulting from an alchemical simulation, as
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described in <A HREF = "#Eike">Eike</A>.
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</P>
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<P>Typically this compute will be used in conjunction with the <A HREF = "fix_adapt.html">fix
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adapt</A> command which can perform alchemical
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transformations by adusting the strength of an interaction potential
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as a simulation runs, as defined by one or more
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<A HREF = "pair_style.html">pair_style</A> or <A HREF = "kspace_style.html">kspace_style</A>
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commands. This scaling is done via a prefactor on the energy, forces,
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virial calculated by the pair or K-Space style. The prefactor is
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often a function of a <I>lambda</I> parameter which may be adjusted from 0
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to 1 (or vice versa) over the course of a <A HREF = "run.html">run</A>. The
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time-dependent adjustment is what the <A HREF = "fix_adapt.html">fix adapt</A>
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command does.
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</P>
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<P>Assume that the unscaled energy of a pair_style or kspace_style is
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given by U. Then the scaled energy is
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</P>
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<PRE>Us = f(lambda) U
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</PRE>
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<P>where f() is some function of lambda. What this compute calculates is
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</P>
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<PRE>dUs / d(lambda) = U df(lambda)/dlambda = Us / f(lambda) df(lambda)/dlambda
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</PRE>
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<P>which is the derivative of the system's scaled potential energy Us
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with respect to <I>lambda</I>.
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</P>
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<P>To do this calculation, you provide two functions, as <A HREF = "variable.html">equal-style
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variables</A>. The first is specified as <I>v_name1</I>, where
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<I>name1</I> is the name of the variable, and is f(lambda) in the notation
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above. The second is specified as <I>v_name2</I>, where <I>name2</I> is the
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name of the variable, and is df(lambda) / dlambda in the notation
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above. I.e. it is the analytic derivative of f() with respect to
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lambda. Note that the <I>name1</I> variable is also typically given as an
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argument to the <A HREF = "fix_adapt.html">fix adapt</A> command.
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</P>
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<P>An alchemical simulation may use several pair potentials together,
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invoked via the <A HREF = "pair_hybrid.html">pair_style hybrid or hybrid/overlay</A>
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command. The total dUs/dlambda for the overall system is calculated
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as the sum of each contributing term as listed by the keywords in the
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compute ti command. Individual pair potentials can be listed, which
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will be sub-styles in the hybrid case. You can also include a K-space
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term via the <I>kspace</I> keyword. You can also include a pairwise
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long-range tail correction to the energy via the <I>tail</I> keyword.
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</P>
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<P>For each term you can specify a different (or the same) scale factor
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by the two variables that you list. Again, these will typically
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correspond toe the scale factors applied to these various potentials
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and the K-Space contribution via the <A HREF = "fix_adapt.html">fix_adapt</A>
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command.
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</P>
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<P>More details about the exact functional forms for the computation of
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du/dl can be found in the paper by <A HREF = "#Eike">Eike</A>.
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</P>
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<P><B>Output info:</B>
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</P>
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<P>This compute calculates a global scalar, namely dUs/dlambda. This
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value can be used by any command that uses a global scalar value from
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2011-08-26 01:01:01 +08:00
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a compute as input. See <A HREF = "Section_howto.html#howto_15">this section</A>
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for an overview of LAMMPS output options.
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2010-10-23 05:24:19 +08:00
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</P>
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<P>The scalar value calculated by this compute is "extensive".
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</P>
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<P>The scalar value will be in energy <A HREF = "units.html">units</A>.
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</P>
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<P><B>Restrictions:</B> none
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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "fix_adapt.html">fix adapt</A>
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</P>
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<P><B>Default:</B> none
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</P>
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<A NAME = "Eike"></A>
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<P><B>(Eike)</B> Eike and Maginn, Journal of Chemical Physics, 124, 164503 (2006).
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</P>
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</HTML>
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