# Long-range dispersion settings

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.

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.

The first approach is to set desired real-space an kspace accuracies via
the *kspace_modify force/disp/real* and *kspace_modify
force/disp/kspace* commands. Note that the accuracies have to be
specified in force units and are thus dependent 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 *kspace_modify diff ad* and
*kspace_modify diff ik* options. The downside of the method is that
setting the PPPM parameters will take some time during the
initialization of the simulation.

The second approach is to set the parameters for the pppm/disp
explicitly using the *kspace_modify mesh/disp*, *kspace_modify
order/disp*, and *kspace_modify gewald/disp* 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, parameters 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).

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 *kspace_modify disp/auto yes*
command.

A reasonable approach that combines the upsides of both methods is to
make the first run using the *kspace_modify force/disp/real* and
*kspace_modify force/disp/kspace* commands, write down the PPPM
parameters from the output, and specify these parameters using the
second approach in subsequent runs (which have the same composition,
force field, and approximately the same volume).

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.

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 *kspace_modify mix/disp
geom* and *kspace_modify splittol* commands. The first command simply
enforces geometric mixing of the dispersion coefficients 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.

Finally, pppm/disp can also be used when no mixing rules apply. This can
be achieved using the *kspace_modify mix/disp none* 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.