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6.20 <A HREF = "#howto_20">Calculating thermal conductivity</A><BR>
6.21 <A HREF = "#howto_21">Calculating viscosity</A><BR>
6.22 <A HREF = "#howto_22">Calculating a diffusion coefficient</A><BR>
6.23 <A HREF = "#howto_23">Using chunks to calculate system properties</A> <BR>
6.23 <A HREF = "#howto_23">Using chunks to calculate system properties</A><BR>
6.24 <A HREF = "#howto_24">Setting parameters for the pppm/disp</A> <BR>
<P>The example input scripts included in the LAMMPS distribution and
highlighted in <A HREF = "Section_example.html">Section_example</A> also show how to
@ -2315,6 +2316,106 @@ fix 1 all ave/histo 100 1 100 0 20 20 c_size mode vector ave running beyond igno
</PRE>
<HR>
<A NAME = "howto_24"></A><H4>6.24 Setting parameters for pppm/disp
</H4>
<P>The PPPM method computes interactions by splitting the pair potential
into two parts, one of which is computed in a normal pairwise fashion,
the so-called real-space part, and one of which is computed using the
Fourier transform, the so called reciprocal-space or kspace part.
For both parts, the potential is not computed exactly but is approximated.
Thus, there is an error in both parts of the computation, the real-space
and the kspace error. The just mentioned facts are true both for the
PPPM for Coulomb as well as dispersion interactions. The deciding
difference - and also the reason why the parameters for pppm/disp
have to be selected with more care - is the impact of the errors on
the results: The kspace error of the PPPM for Coulomb and dispersion
interaction and the real-space error of the PPPM for Coulomb interaction
have the character of noise. In contrast, the real-space error of the
PPPM for dispersion has a clear physical interpretation: the underprediction
of cohesion. As a consequence, the real-space error has a much stronger
effect than the kspace error on simulation results for pppm/disp.
Parameters must thus be chosen in a way that this error is much smaller
than the kspace error.
</P>
<P>When using pppm/disp and not making any specifications on the
PPPM parameters via the kspace modify command, parameters will be
tuned such that the real-space error and the kspace error are equal.
This will result in simulations that are either inaccurate or slow,
both of which is not desirable. For selecting parameters for the
pppm/disp that provide fast and accurate simulations, there are two
approaches, which both have their up- and downsides.
</P>
<P>The first approach is to set desired real-space an kspace accuracies
via the <I>kspace_modify force/disp/real</I> and
<I>kspace_modify force/disp/kspace</I> commands. Note that the accuracies
have to be specified in force units and are thus dependend on the chosen
unit settings. For real units, 0.0001 and 0.002 seem to provide reasonable
accurate and efficient computations for the real-space and kspace accuracies.
0.002 and 0.05 work well for most systems using lj units. PPPM parameters will
be generated based on the desired accuracies. The upside of
this approach is that it usually provides
a good set of parameters and will work for both the <I>kspace_modify diff ad</I>
and <I>kspace_modify diff ik</I> options.
The downside of the method is that setting
the PPPM parameters will take some time during the initialization of
the simulation.
</P>
<P>The second approach is to set the parameters for the pppm/disp explicitly
using the <I>kspace_modify mesh/disp</I>, <I>kspace_modify order/disp</I>,
and <I>kspace_modify gewald/disp</I> commands. This approach requires a
more experienced user who understands well the impact of the choice of parameters
on the simulation accuracy and performance. This approach provides a
fast initialization of the simulation. However, it is sensitive to errors:
A combination of parameters that will perform well for one system might result
in far-from-optimal conditions for other simulations. For example, parametes
that provide accurate and fast computations for all-atomistic force fields
can provide insufficient accuracy or united-atomistic force fields (which is
related to that the latter typically have larger dispersion coefficients).
</P>
<P>To avoid inaccurate or inefficient simulations, the pppm/disp stops
simulations with an error message if no action is taken to control the
PPPM parameters. If the automatic parameter generation is desired and
real-space and kspace accuracies are desired to be equal, this error
message can be suppressed using the <I>kspace_modify disp/auto yes</I>
command.
</P>
<P>A reasonable approach that combines the upsides of both methods
is to make the first run using the <I>kspace_modify force/disp/real</I>
and <I>kspace_modify force/disp/kspace</I> commands, write down the PPPM parameters
from the outut, and specify these parameters using the second approach
in subsequent runs (which have the same composition, force field, and
approximately the same volume).
</P>
<P>Concerning the performance of the pppm/disp there are two more
things to consider. The first is that when using the pppm/disp, the
cutoff parameter does no longer affect the accuracy of the simulation
(subject to that gewald/disp is adjusted when changing the cutoff).
The performance can thus be increased by examining different values
for the cutoff parameter. A lower bound for the cutoff is only set
by the truncation error of the repulsive term of pair potentials.
</P>
<P>The second is that the mixing rule of the pair style has an impact on
the computation time when using the pppm/disp. Fastest computations are
achieved when using the geometric mixing rule. Using the arithmetic
mixing rule substantially increases the computational cost.
The computational overhead can be reduced using the
<I>kspace_modify mix/disp geom</I> and <I>kspace_modify splittol</I>
commands. The first command simply enforces geometric mixing of the
dispersion coeffiecients in kspace computations.
This introduces some error in the computations but will also significantly
speed-up the simulations. The second keyword sets the accuracy with
which the dispersion coefficients are approximated using a matrix factorization approach.
This may result in better accuracy then using the first command, but will
usually also not provide an equally good increase of efficiency.
</P>
<P>Finally, pppm/disp can also be used when no mixing rules apply.
This can be achieved using the <I>kspace_modify mix/disp none</I> command.
Note that the code does not check automatically whether any mixing
rule is fulfilled. If mixing rules do not apply, the user will have
to specify this command explicitly.
</P>
<HR>
<HR>
<A NAME = "Berendsen"></A>