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<p><span class="math notranslate nohighlight">\(\renewcommand{\AA}{\text{Å}}\)</span></p>
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<section id="long-range-dispersion-settings">
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<h1><span class="section-number">8.2.8. </span>Long-range dispersion settings<a class="headerlink" href="#long-range-dispersion-settings" title="Link to this heading"></a></h1>
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<p>The PPPM method computes interactions by splitting the pair potential
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into two parts, one of which is computed in a normal pairwise fashion,
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the so-called real-space part, and one of which is computed using the
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Fourier transform, the so called reciprocal-space or kspace part. For
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both parts, the potential is not computed exactly but is approximated.
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Thus, there is an error in both parts of the computation, the
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real-space and the kspace error. The just mentioned facts are true
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both for the PPPM for Coulomb as well as dispersion interactions. The
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deciding difference - and also the reason why the parameters for
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pppm/disp have to be selected with more care - is the impact of the
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errors on the results: The kspace error of the PPPM for Coulomb and
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dispersion interaction and the real-space error of the PPPM for
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Coulomb interaction have the character of noise. In contrast, the
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real-space error of the PPPM for dispersion has a clear physical
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interpretation: the underprediction of cohesion. As a consequence, the
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real-space error has a much stronger effect than the kspace error on
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simulation results for pppm/disp. Parameters must thus be chosen in a
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way that this error is much smaller than the kspace error.</p>
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<p>When using pppm/disp and not making any specifications on the PPPM
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parameters via the kspace modify command, parameters will be tuned
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such that the real-space error and the kspace error are equal. This
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will result in simulations that are either inaccurate or slow, both of
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which is not desirable. For selecting parameters for the pppm/disp
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that provide fast and accurate simulations, there are two approaches,
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which both have their up- and downsides.</p>
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<p>The first approach is to set desired real-space an kspace accuracies
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via the <em>kspace_modify force/disp/real</em> and <em>kspace_modify
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force/disp/kspace</em> commands. Note that the accuracies have to be
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specified in force units and are thus dependent on the chosen unit
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settings. For real units, 0.0001 and 0.002 seem to provide reasonable
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accurate and efficient computations for the real-space and kspace
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accuracies. 0.002 and 0.05 work well for most systems using lj
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units. PPPM parameters will be generated based on the desired
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accuracies. The upside of this approach is that it usually provides a
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good set of parameters and will work for both the <em>kspace_modify diff
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ad</em> and <em>kspace_modify diff ik</em> options. The downside of the method
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is that setting the PPPM parameters will take some time during the
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initialization of the simulation.</p>
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<p>The second approach is to set the parameters for the pppm/disp
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explicitly using the <em>kspace_modify mesh/disp</em>, <em>kspace_modify
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order/disp</em>, and <em>kspace_modify gewald/disp</em> commands. This approach
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requires a more experienced user who understands well the impact of
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the choice of parameters on the simulation accuracy and
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performance. This approach provides a fast initialization of the
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simulation. However, it is sensitive to errors: A combination of
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parameters that will perform well for one system might result in
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far-from-optimal conditions for other simulations. For example,
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parameters that provide accurate and fast computations for
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all-atomistic force fields can provide insufficient accuracy or
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united-atomistic force fields (which is related to that the latter
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typically have larger dispersion coefficients).</p>
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<p>To avoid inaccurate or inefficient simulations, the pppm/disp stops
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simulations with an error message if no action is taken to control the
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PPPM parameters. If the automatic parameter generation is desired and
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real-space and kspace accuracies are desired to be equal, this error
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message can be suppressed using the <em>kspace_modify disp/auto yes</em>
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command.</p>
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<p>A reasonable approach that combines the upsides of both methods is to
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make the first run using the <em>kspace_modify force/disp/real</em> and
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<em>kspace_modify force/disp/kspace</em> commands, write down the PPPM
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parameters from the output, and specify these parameters using the
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second approach in subsequent runs (which have the same composition,
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force field, and approximately the same volume).</p>
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<p>Concerning the performance of the pppm/disp there are two more things
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to consider. The first is that when using the pppm/disp, the cutoff
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parameter does no longer affect the accuracy of the simulation
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(subject to that gewald/disp is adjusted when changing the cutoff).
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The performance can thus be increased by examining different values
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for the cutoff parameter. A lower bound for the cutoff is only set by
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the truncation error of the repulsive term of pair potentials.</p>
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<p>The second is that the mixing rule of the pair style has an impact on
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the computation time when using the pppm/disp. Fastest computations
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are achieved when using the geometric mixing rule. Using the
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arithmetic mixing rule substantially increases the computational cost.
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The computational overhead can be reduced using the <em>kspace_modify
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mix/disp geom</em> and <em>kspace_modify splittol</em> commands. The first
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command simply enforces geometric mixing of the dispersion
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coefficients in kspace computations. This introduces some error in
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the computations but will also significantly speed-up the
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simulations. The second keyword sets the accuracy with which the
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dispersion coefficients are approximated using a matrix factorization
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approach. This may result in better accuracy then using the first
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command, but will usually also not provide an equally good increase of
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efficiency.</p>
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<p>Finally, pppm/disp can also be used when no mixing rules apply.
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This can be achieved using the <em>kspace_modify mix/disp none</em> command.
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Note that the code does not check automatically whether any mixing
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rule is fulfilled. If mixing rules do not apply, the user will have
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to specify this command explicitly.</p>
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