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<div class="section" id="fix-ehex-command">
<span id="index-0"></span><h1>fix ehex command</h1>
<div class="section" id="syntax">
<h2>Syntax</h2>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="n">ID</span> <span class="n">group</span><span class="o">-</span><span class="n">ID</span> <span class="n">ehex</span> <span class="n">nevery</span> <span class="n">F</span> <span class="n">keyword</span> <span class="n">value</span>
</pre></div>
</div>
<ul class="simple">
<li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><span class="doc">fix</span></a> command</li>
<li>ehex = style name of this fix command</li>
<li>nevery = add/subtract heat every this many timesteps</li>
<li>F = energy flux into the reservoir (energy/time units)</li>
<li>zero or more keyword/value pairs may be appended to args</li>
<li>keyword = <em>region</em> or <em>constrain</em> or <em>com</em> or <em>hex</em></li>
</ul>
<pre class="literal-block">
<em>region</em> value = region-ID
region-ID = ID of region (reservoir) atoms must be in for added thermostatting force
<em>constrain</em> value = none
apply the constraint algorithm (SHAKE or RATTLE) again at the end of the timestep
<em>com</em> value = none
rescale all sites of a constrained cluster of atom if its COM is in the reservoir
<em>hex</em> value = none
omit the coordinate correction to recover the HEX algorithm
</pre>
</div>
<div class="section" id="examples">
<h2>Examples</h2>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="c1"># Lennard-Jones, from examples/in.ehex.lj</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="n">fnve</span> <span class="nb">all</span> <span class="n">nve</span>
<span class="c1"># specify regions rhot and rcold</span>
<span class="o">...</span>
<span class="n">fix</span> <span class="n">fhot</span> <span class="nb">all</span> <span class="n">ehex</span> <span class="mi">1</span> <span class="mf">0.15</span> <span class="n">region</span> <span class="n">rhot</span>
<span class="n">fix</span> <span class="n">fcold</span> <span class="nb">all</span> <span class="n">ehex</span> <span class="mi">1</span> <span class="o">-</span><span class="mf">0.15</span> <span class="n">region</span> <span class="n">rcold</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="c1"># SPC/E water, from examples/in.ehex.spce</span>
<span class="n">fix</span> <span class="n">fnve</span> <span class="nb">all</span> <span class="n">nve</span>
<span class="c1"># specify regions rhot and rcold</span>
<span class="o">...</span>
<span class="n">fix</span> <span class="n">fhot</span> <span class="nb">all</span> <span class="n">ehex</span> <span class="mi">1</span> <span class="mf">0.075</span> <span class="n">region</span> <span class="n">rhot</span> <span class="n">constrain</span> <span class="n">com</span>
<span class="n">fix</span> <span class="n">fcold</span> <span class="nb">all</span> <span class="n">ehex</span> <span class="mi">1</span> <span class="o">-</span><span class="mf">0.075</span> <span class="n">region</span> <span class="n">rcold</span> <span class="n">constrain</span> <span class="n">com</span>
<span class="n">fix</span> <span class="n">frattle</span> <span class="nb">all</span> <span class="n">rattle</span> <span class="mi">1</span><span class="n">e</span><span class="o">-</span><span class="mi">10</span> <span class="mi">400</span> <span class="mi">0</span> <span class="n">b</span> <span class="mi">1</span> <span class="n">a</span> <span class="mi">1</span>
</pre></div>
</div>
</div>
<div class="section" id="description">
<h2>Description</h2>
<p>This fix implements the asymmetric version of the enhanced heat
exchange algorithm <a class="reference internal" href="#wirnsberger"><span class="std std-ref">(Wirnsberger)</span></a>. The eHEX algorithm is
an extension of the heat exchange algorithm <a class="reference internal" href="#ikeshoji"><span class="std std-ref">(Ikeshoji)</span></a> and
adds an additional coordinate integration to account for higher-order
truncation terms in the operator splitting. The original HEX
algorithm (implemented as <a class="reference internal" href="fix_heat.html"><span class="doc">fix heat</span></a>) is known to
exhibit a slight energy drift limiting the accessible simulation times
to a few nanoseconds. This issue is greatly improved by the new
algorithm decreasing the energy drift by at least a factor of a
hundred (LJ and SPC/E water) with little computational overhead.</p>
<p>In both algorithms (non-translational) kinetic energy is constantly
swapped between regions (reservoirs) to impose a heat flux onto the
system. The equations of motion are therefore modified if a particle
<span class="math">\(i\)</span> is located inside a reservoir <span class="math">\(\Gamma_k\)</span> where <span class="math">\(k&gt;0\)</span>. We
use <span class="math">\(\Gamma_0\)</span> to label those parts of the simulation box which
are not thermostatted.) The input parameter <em>region-ID</em> of this fix
corresponds to <span class="math">\(k\)</span>. The energy swap is modelled by introducing an
additional thermostatting force to the equations of motion, such that
the time evolution of coordinates and momenta of particle <span class="math">\(i\)</span>
becomes <a class="reference internal" href="#wirnsberger"><span class="std std-ref">(Wirnsberger)</span></a></p>
<img alt="_images/fix_ehex_eom.jpg" class="align-center" src="_images/fix_ehex_eom.jpg" />
<p>The thermostatting force is given by</p>
<img alt="_images/fix_ehex_f.jpg" class="align-center" src="_images/fix_ehex_f.jpg" />
<p>where <span class="math">\(m_i\)</span> is the mass and <span class="math">\(k(\mathbf r_i)\)</span> maps the particle
position to the respective reservoir. The quantity
<span class="math">\(F_{\Gamma_{k(\mathbf r_i)}}\)</span> corresponds to the input parameter
<em>F</em>, which is the energy flux into the reservoir. Furthermore,
<span class="math">\(K_{\Gamma_{k(\mathbf r_i)}}\)</span> and <span class="math">\(v_{\Gamma_{k(\mathbf r_i)}}\)</span>
denote the non-translational kinetic energy and the centre of mass
velocity of that reservoir. The thermostatting force does not affect
the centre of mass velocities of the individual reservoirs and the
entire simulation box. A derivation of the equations and details on
the numerical implementation with velocity Verlet in LAMMPS can be
found in reference &#8220;(Wirnsberger)&#8221;#_Wirnsberger.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">This fix only integrates the thermostatting force and must be
combined with another integrator, such as <a class="reference internal" href="fix_nve.html"><span class="doc">fix nve</span></a>, to
solve the full equations of motion.</p>
</div>
<p>This fix is different from a thermostat such as <a class="reference internal" href="fix_nh.html"><span class="doc">fix nvt</span></a>
or <a class="reference internal" href="fix_temp_rescale.html"><span class="doc">fix temp/rescale</span></a> in that energy is
added/subtracted continually. Thus if there isn&#8217;t another mechanism
in place to counterbalance this effect, the entire system will heat or
cool continuously.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">If heat is subtracted from the system too aggressively so that
the group&#8217;s kinetic energy would go to zero, then LAMMPS will halt
with an error message. Increasing the value of <em>nevery</em> means that
heat is added/subtracted less frequently but in larger portions. The
resulting temperature profile will therefore be the same.</p>
</div>
<p>This fix will default to <a class="reference internal" href="fix_heat.html"><span class="doc">fix_heat</span></a> (HEX algorithm) if
the keyword <em>hex</em> is specified.</p>
<hr class="docutils" />
<p><strong>Compatibility with SHAKE and RATTLE (rigid molecules)</strong>:</p>
<p>This fix is compatible with <a class="reference internal" href="fix_shake.html"><span class="doc">fix shake</span></a> and <a class="reference internal" href="fix_shake.html"><span class="doc">fix rattle</span></a>. If either of these constraining algorithms is
specified in the input script and the keyword <em>constrain</em> is set, the
bond distances will be corrected a second time at the end of the
integration step. It is recommended to specify the keyword <em>com</em> in
addition to the keyword <em>constrain</em>. With this option all sites of a
constrained cluster are rescaled, if its centre of mass is located
inside the region. Rescaling all sites of a cluster by the same factor
does not introduce any velocity components along fixed bonds. No
rescaling takes place if the centre of mass lies outside the region.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">You can only use the keyword <em>com</em> along with <em>constrain</em>.</p>
</div>
<p>To achieve the highest accuracy it is recommended to use <a class="reference internal" href="fix_shake.html"><span class="doc">fix rattle</span></a> with the keywords <em>constrain</em> and <em>com</em> as
shown in the second example. Only if RATTLE is employed, the velocity
constraints will be satisfied.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">Even if RATTLE is used and the keywords <em>com</em> and <em>constrain</em>
are both set, the coordinate constraints will not necessarily be
satisfied up to the target precision. The velocity constraints are
satisfied as long as all sites of a cluster are rescaled (keyword
<em>com</em>) and the cluster does not span adjacent reservoirs. The current
implementation of the eHEX algorithm introduces a small error in the
bond distances, which goes to zero with order three in the
timestep. For example, in a simulation of SPC/E water with a timestep
of 2 fs the maximum relative error in the bond distances was found to
be on the order of <span class="math">\(10^{-7}\)</span> for relatively large
temperature gradients. A higher precision can be achieved by
decreasing the timestep.</p>
</div>
</div>
<hr class="docutils" />
<div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
<h2>Restart, fix_modify, output, run start/stop, minimize info</h2>
<p>No information about this fix is written to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>. None of the <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> options
are relevant to this fix.</p>
<p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
the <a class="reference internal" href="run.html"><span class="doc">run</span></a> command. This fix is not invoked during <a class="reference internal" href="minimize.html"><span class="doc">energy minimization</span></a>.</p>
</div>
<div class="section" id="restrictions">
<h2>Restrictions</h2>
<p>This fix is part of the RIGID package. It is only enabled if LAMMPS
was built with that package. See the <a class="reference internal" href="Section_start.html#start-3"><span class="std std-ref">Making LAMMPS</span></a> section for more info.</p>
</div>
<div class="section" id="related-commands">
<h2>Related commands</h2>
<p><a class="reference internal" href="fix_heat.html"><span class="doc">fix heat</span></a>, <a class="reference internal" href="fix_thermal_conductivity.html"><span class="doc">fix thermal/conductivity</span></a>, <a class="reference internal" href="compute_temp.html"><span class="doc">compute temp</span></a>, <a class="reference internal" href="compute_temp_region.html"><span class="doc">compute temp/region</span></a></p>
<p><strong>Default:</strong> none</p>
<hr class="docutils" />
<p id="ikeshoji"><strong>(Ikeshoji)</strong> Ikeshoji and Hafskjold, Molecular Physics, 81, 251-261 (1994).</p>
<p id="wirnsberger"><strong>(Wirnsberger)</strong> Wirnsberger, Frenkel, and Dellago, J Chem Phys, 143,
124104 (2015).</p>
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