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<div class="section" id="fix-ti-rs-command">
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<span id="index-0"></span><h1>fix ti/rs command<a class="headerlink" href="#fix-ti-rs-command" title="Permalink to this headline">¶</a></h1>
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<div class="section" id="syntax">
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<h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
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<div class="highlight-python"><div class="highlight"><pre>fix ID group-ID ti/rs lambda_initial lambda_final t_switch t_equil keyword value ...
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</pre></div>
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</div>
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<ul class="simple">
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<li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
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<li>ti/rs = style name of this fix command</li>
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<li>lambda_initial/lambda_final = initial/final values of the coupling parameter</li>
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<li>t_switch/t_equil = number of steps of the switching/equilibration procedure</li>
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<li>keyword = <em>function</em></li>
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</ul>
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<pre class="literal-block">
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<em>function</em> value = function-ID
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function-ID = ID of the switching function (1, 2 or 3)
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</pre>
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<p><strong>Example:</strong></p>
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<div class="highlight-python"><div class="highlight"><pre>fix ref all ti/rs 50.0 2000 1000
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fix vf vacancy ti/rs 10.0 70000 50000 function 2
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</pre></div>
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</div>
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</div>
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<div class="section" id="description">
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<h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
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<p>This fix allows you to compute the free energy temperature dependence
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by performing a thermodynamic integration procedure known as
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Reversible Scaling <a class="reference internal" href="#dekoning99"><span>(de Koning99,</span></a> <span class="xref std std-ref">de Koning00a)</span>. The thermodynamic integration is performed
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using the nonequilibrium method of Adiabatic Switching
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<a class="reference internal" href="fix_ti_spring.html#watanabe"><span>(Watanabe,</span></a> <a class="reference internal" href="fix_ti_spring.html#dekoning96"><span>de Koning96)</span></a>.</p>
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<p>The forces on the atoms are dynamically scaled during the simulation,
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the rescaling is done in the following manner:</p>
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<img alt="_images/fix_ti_rs_force.jpg" class="align-center" src="_images/fix_ti_rs_force.jpg" />
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<p>where F_int is the total force on the atoms due to the interatomic
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potential and lambda is the coupling parameter of the thermodynamic
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integration.</p>
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<p>The fix acts as follows: during the first <em>t_equil</em> steps after the
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fix is defined the value of lambda is <em>lambda_initial</em> , this is the
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period to equilibrate the system in the lambda = <em>lambda_initial</em>
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state. After this the value of lambda changes continuously from
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<em>lambda_initial</em> to <em>lambda_final</em> according to the function defined
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using the keyword <em>function</em> (described below), this is done in
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<em>t_switch</em> steps. Then comes the second equilibration period of
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<em>t_equil</em> to equilibrate the system in the lambda = <em>lambda_final</em>
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state. After that the switching back to the lambda = <em>lambda_initial</em>
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state is done using <em>t_switch</em> timesteps and following the same
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switching function. After this period the value of lambda is kept
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equal to <em>lambda_initial</em> indefinitely or until a <a class="reference internal" href="unfix.html"><em>unfix</em></a>
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erase the fix.</p>
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<p>The description of thermodynamic integration in both directions is
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done in <a class="reference internal" href="#dekoning00b"><span>de Koning00b</span></a>, the main reason is to try to
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eliminate the dissipated heat due to the nonequilibrium process.</p>
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<p>The <em>function</em> keyword allows the use of three different switching
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rates. The option <em>1</em> results in a constant rescaling where the lambda
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parameter changes at a constant rate during the switching time
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according to the switching function</p>
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<img alt="_images/fix_ti_rs_function_1.jpg" class="align-center" src="_images/fix_ti_rs_function_1.jpg" />
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<p>where tau is the scaled time variable t/t_switch. This switching
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function has the characteristic that the temperature scaling is faster
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at temperatures closer to the final temperature of the procedure. The
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option number <em>2</em> performs the switching at a rate defined by the
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following switching function</p>
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<img alt="_images/fix_ti_rs_function_2.jpg" class="align-center" src="_images/fix_ti_rs_function_2.jpg" />
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<p>This switching function has the characteristic that the temperature
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scaling occurs at a constant rate during all the procedure. The option
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number <em>3</em> performs the switching at a rate defined by the following
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switching function</p>
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<img alt="_images/fix_ti_rs_function_3.jpg" class="align-center" src="_images/fix_ti_rs_function_3.jpg" />
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<p>This switching function has the characteristic that the temperature
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scaling is faster at temperatures closer to the initial temperature of
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the procedure.</p>
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<p>An example script using this command is provided in the
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examples/USER/misc/ti directory.</p>
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</div>
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<div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
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<h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
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<p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
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<p>This fix computes a global vector quantitie which can be accessed by
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various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>. The vector has
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2 positions, the first one is the coupling parameter lambda and the
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second one is the time derivative of lambda. The scalar and vector
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values calculated by this fix are “extensive”.</p>
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<p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
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the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
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<p>The forces due to this fix are imposed during an energy minimization,
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invoked by the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command.</p>
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</div>
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<div class="section" id="related-commands">
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<h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
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<p><a class="reference internal" href="fix_ti_spring.html"><em>fix ti/spring</em></a></p>
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</div>
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<div class="section" id="restrictions">
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<h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
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<p>This command is part of the USER-MISC package. It is only enabled if
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LAMMPS was built with those packages. See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
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</div>
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<div class="section" id="default">
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<h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
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<p>The keyword default is function = 1.</p>
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<hr class="docutils" />
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<p id="dekoning99"><strong>(de Koning 99)</strong> M. de Koning, A. Antonelli and S. Yip, Phys Rev Lett, 83, 3973 (1999).</p>
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<p id="watanabe"><strong>(Watanabe)</strong> M. Watanabe and W. P. Reinhardt, Phys Rev Lett, 65, 3301 (1990).</p>
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<p id="dekoning96"><strong>(de Koning 96)</strong> M. de Koning and A. Antonelli, Phys Rev E, 53, 465 (1996).</p>
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<p id="dekoning00a"><strong>(de Koning 00a)</strong> M. de Koning, A. Antonelli and S. Yip, J Chem Phys, 115, 11025 (2000).</p>
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<p id="dekoning00b"><strong>(de Koning 00b)</strong> M. de Koning et al., Computing in Science & Engineering, 2, 88 (2000).</p>
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