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<title>compute fep command — LAMMPS 15 May 2015 version documentation</title>
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<li class="toctree-l1"><a class="reference internal" href="Section_perf.html">8. Performance & scalability</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_errors.html">12. Errors</a></li>
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<div class="section" id="compute-fep-command">
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<span id="index-0"></span><h1>compute fep command<a class="headerlink" href="#compute-fep-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>compute ID group-ID fep temp attribute args ... 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 the <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
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<li>fep = name of this compute command</li>
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<li>temp = external temperature (as specified for constant-temperature run)</li>
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<li>one or more attributes with args may be appended</li>
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<li>attribute = <em>pair</em> or <em>atom</em></li>
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</ul>
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<pre class="literal-block">
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<em>pair</em> args = pstyle pparam I J v_delta
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pstyle = pair style name, e.g. lj/cut
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pparam = parameter to perturb
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I,J = type pair(s) to set parameter for
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v_delta = variable with perturbation to apply (in the units of the parameter)
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<em>atom</em> args = aparam I v_delta
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aparam = parameter to perturb
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I = type to set parameter for
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v_delta = variable with perturbation to apply (in the units of the parameter)
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</pre>
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<ul class="simple">
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<li>zero or more keyword/value pairs may be appended</li>
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<li>keyword = <em>tail</em> or <em>volume</em></li>
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</ul>
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<pre class="literal-block">
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<em>tail</em> value = <em>no</em> or <em>yes</em>
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<em>no</em> = ignore tail correction to pair energies (usually small in fep)
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<em>yes</em> = include tail correction to pair energies
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<em>volume</em> value = <em>no</em> or <em>yes</em>
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<em>no</em> = ignore volume changes (e.g. in <em>NVE</em> or <em>NVT</em> trajectories)
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<em>yes</em> = include volume changes (e.g. in <em>NpT</em> trajectories)
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</pre>
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</div>
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<div class="section" id="examples">
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<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
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<div class="highlight-python"><div class="highlight"><pre>compute 1 all fep 298 pair lj/cut epsilon 1 * v_delta pair lj/cut sigma 1 * v_delta volume yes
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compute 1 all fep 300 atom charge 2 v_delta
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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>Apply a perturbation to parameters of the interaction potential and
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recalculate the pair potential energy without changing the atomic
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coordinates from those of the reference, unperturbed system. This
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compute can be used to calculate free energy differences using several
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methods, such as free-energy perturbation (FEP), finite-difference
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thermodynamic integration (FDTI) or Bennet’s acceptance ratio method
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(BAR).</p>
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<p>The potential energy of the system is decomposed in three terms: a
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background term corresponding to interaction sites whose parameters
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remain constant, a reference term <a href="#id1"><span class="problematic" id="id2">*</span></a>U*<sub>0</sub> corresponding to the
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initial interactions of the atoms that will undergo perturbation, and
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a term <a href="#id3"><span class="problematic" id="id4">*</span></a>U*<sub>1</sub> corresponding to the final interactions of
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these atoms:</p>
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<img alt="_images/compute_fep_u.jpg" class="align-center" src="_images/compute_fep_u.jpg" />
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<p>A coupling parameter &lambda; varying from 0 to 1 connects the
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reference and perturbed systems:</p>
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<img alt="_images/compute_fep_lambda.jpg" class="align-center" src="_images/compute_fep_lambda.jpg" />
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<p>It is possible but not necessary that the coupling parameter (or a
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function thereof) appears as a multiplication factor of the potential
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energy. Therefore, this compute can apply perturbations to interaction
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parameters that are not directly proportional to the potential energy
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(e.g. &sigma; in Lennard-Jones potentials).</p>
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<p>This command can be combined with <a class="reference internal" href="fix_adapt.html"><em>fix adapt</em></a> to
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perform multistage free-energy perturbation calculations along
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stepwise alchemical transformations during a simulation run:</p>
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<img alt="_images/compute_fep_fep.jpg" class="align-center" src="_images/compute_fep_fep.jpg" />
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<p>This compute is suitable for the finite-difference thermodynamic
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integration (FDTI) method <a class="reference internal" href="#mezei"><span>(Mezei)</span></a>, which is based on an
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evaluation of the numerical derivative of the free energy by a
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perturbation method using a very small &delta;:</p>
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<img alt="_images/compute_fep_fdti.jpg" class="align-center" src="_images/compute_fep_fdti.jpg" />
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<p>where <a href="#id5"><span class="problematic" id="id6">*</span></a>w*<sub>i</sub> are weights of a numerical quadrature. The <a class="reference internal" href="fix_adapt.html"><em>fix adapt</em></a> command can be used to define the stages of
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&lambda; at which the derivative is calculated and averaged.</p>
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<p>The compute fep calculates the exponential Boltzmann term and also the
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potential energy difference <a href="#id7"><span class="problematic" id="id8">*</span></a>U*<sub>1</sub>-<a href="#id9"><span class="problematic" id="id10">*</span></a>U*<sub>0</sub>. By
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choosing a very small perturbation &delta; the thermodynamic
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integration method can be implemented using a numerical evaluation of
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the derivative of the potential energy with respect to &lambda;:</p>
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<img alt="_images/compute_fep_ti.jpg" class="align-center" src="_images/compute_fep_ti.jpg" />
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<p>Another technique to calculate free energy differences is the
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acceptance ratio method <a class="reference internal" href="#bennet"><span>(Bennet)</span></a>, which can be implemented
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by calculating the potential energy differences with &delta; = 1.0 on
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both the forward and reverse routes:</p>
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<img alt="_images/compute_fep_bar.jpg" class="align-center" src="_images/compute_fep_bar.jpg" />
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<p>The value of the free energy difference is determined by numerical
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root finding to establish the equality.</p>
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<p>Concerning the choice of how the atomic parameters are perturbed in
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order to setup an alchemical transformation route, several strategies
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are available, such as single-topology or double-topology strategies
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<a class="reference internal" href="#pearlman"><span>(Pearlman)</span></a>. The latter does not require modification of
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bond lengths, angles or other internal coordinates.</p>
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<p>IMPORTANT NOTES: This compute command does not take kinetic energy
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into account, therefore the masses of the particles should not be
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modified between the reference and perturbed states, or along the
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alchemical transformation route. This compute command does not change
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bond lengths or other internal coordinates <a class="reference internal" href="#boreschkarplus"><span>(Boresch, Karplus)</span></a>.</p>
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<hr class="docutils" />
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<p>The <em>pair</em> attribute enables various parameters of potentials defined
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by the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> and <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a>
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commands to be changed, if the pair style supports it.</p>
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<p>The <em>pstyle</em> argument is the name of the pair style. For example,
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<em>pstyle</em> could be specified as “lj/cut”. The <em>pparam</em> argument is the
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name of the parameter to change. This is a (non-exclusive) list of
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pair styles and parameters that can be used with this compute. See
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the doc pages for individual pair styles and their energy formulas for
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the meaning of these parameters:</p>
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<table border="1" class="docutils">
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<colgroup>
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<col width="59%" />
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<col width="27%" />
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<col width="15%" />
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</colgroup>
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<tbody valign="top">
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<tr class="row-odd"><td><a class="reference internal" href="pair_lj.html"><em>lj/cut</em></a></td>
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<td>epsilon,sigma</td>
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<td>type pairs</td>
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</tr>
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<tr class="row-even"><td><a class="reference internal" href="pair_lj.html"><em>lj/cut/coul/cut</em></a></td>
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<td>epsilon,sigma</td>
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<td>type pairs</td>
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</tr>
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<tr class="row-odd"><td><a class="reference internal" href="pair_lj.html"><em>lj/cut/coul/long</em></a></td>
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<td>epsilon,sigma</td>
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<td>type pairs</td>
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</tr>
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<tr class="row-even"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/soft</em></a></td>
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<td>epsilon,sigma,lambda</td>
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<td>type pairs</td>
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</tr>
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<tr class="row-odd"><td><a class="reference internal" href="pair_lj_soft.html"><em>coul/cut/soft</em></a></td>
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<td>lambda</td>
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<td>type pairs</td>
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</tr>
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<tr class="row-even"><td><a class="reference internal" href="pair_lj_soft.html"><em>coul/long/soft</em></a></td>
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<td>lambda</td>
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<td>type pairs</td>
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</tr>
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<tr class="row-odd"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/coul/cut/soft</em></a></td>
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<td>epsilon,sigma,lambda</td>
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<td>type pairs</td>
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</tr>
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<tr class="row-even"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/coul/long/soft</em></a></td>
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<td>epsilon,sigma,lambda</td>
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<td>type pairs</td>
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</tr>
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<tr class="row-odd"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/tip4p/long/soft</em></a></td>
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<td>epsilon,sigma,lambda</td>
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<td>type pairs</td>
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</tr>
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<tr class="row-even"><td><a class="reference internal" href="pair_lj_soft.html"><em>tip4p/long/soft</em></a></td>
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<td>lambda</td>
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<td>type pairs</td>
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</tr>
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<tr class="row-odd"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/charmm/coul/long/soft</em></a></td>
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<td>epsilon,sigma,lambda</td>
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<td>type pairs</td>
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</tr>
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<tr class="row-even"><td><a class="reference internal" href="pair_born.html"><em>born</em></a></td>
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<td>a,b,c</td>
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<td>type pairs</td>
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</tr>
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<tr class="row-odd"><td><a class="reference internal" href="pair_buck.html"><em>buck</em></a></td>
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<td>a,c</td>
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<td>type pairs</td>
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</tr>
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</tbody>
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</table>
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<p>Note that it is easy to add new potentials and their parameters to
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this list. All it typically takes is adding an extract() method to
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the pair_*.cpp file associated with the potential.</p>
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<p>Similar to the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command, I and J can be
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specified in one of two ways. Explicit numeric values can be used for
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each, as in the 1st example above. I <= J is required. LAMMPS sets
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the coefficients for the symmetric J,I interaction to the same
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values. A wild-card asterisk can be used in place of or in conjunction
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with the I,J arguments to set the coefficients for multiple pairs of
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atom types. This takes the form “*” or “<em>n” or “n</em>” or “m*n”. If N =
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the number of atom types, then an asterisk with no numeric values
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means all types from 1 to N. A leading asterisk means all types from
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1 to n (inclusive). A trailing asterisk means all types from n to N
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(inclusive). A middle asterisk means all types from m to n
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(inclusive). Note that only type pairs with I <= J are considered; if
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asterisks imply type pairs where J < I, they are ignored.</p>
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<p>If <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid or hybrid/overlay</em></a> is being
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used, then the <em>pstyle</em> will be a sub-style name. You must specify
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I,J arguments that correspond to type pair values defined (via the
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<a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command) for that sub-style.</p>
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<p>The <em>v_name</em> argument for keyword <em>pair</em> is the name of an
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<a class="reference internal" href="variable.html"><em>equal-style variable</em></a> which will be evaluated each time
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this compute is invoked. It should be specified as v_name, where name
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is the variable name.</p>
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<hr class="docutils" />
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<p>The <em>atom</em> attribute enables atom properties to be changed. The
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<em>aparam</em> argument is the name of the parameter to change. This is the
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current list of atom parameters that can be used with this compute:</p>
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<ul class="simple">
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<li>charge = charge on particle</li>
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</ul>
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<p>The <em>v_name</em> argument for keyword <em>pair</em> is the name of an
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<a class="reference internal" href="variable.html"><em>equal-style variable</em></a> which will be evaluated each time
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this compute is invoked. It should be specified as v_name, where name
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is the variable name.</p>
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<hr class="docutils" />
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<p>The <em>tail</em> keyword controls the calculation of the tail correction to
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“van der Waals” pair energies beyond the cutoff, if this has been
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activated via the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> command. If the
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perturbation is small, the tail contribution to the energy difference
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between the reference and perturbed systems should be negligible.</p>
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<p>If the keyword <em>volume</em> = <em>yes</em>, then the Boltzmann term is multiplied
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by the volume so that correct ensemble averaging can be performed over
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trajectories during which the volume fluctuates or changes <a class="reference internal" href="#allentildesley"><span>(Allen and Tildesley)</span></a>:</p>
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<img alt="_images/compute_fep_vol.jpg" class="align-center" src="_images/compute_fep_vol.jpg" />
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<hr class="docutils" />
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<p><strong>Output info:</strong></p>
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<p>This compute calculates a global vector of length 3 which contains the
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energy difference (<em>U*<sub>1</sub>-*U*<sub>0</sub>) as c_ID[1], the
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Boltzmann factor exp(-(*U*<sub>1</sub>-*U*<sub>0</sub>)/*kT</em>), or
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<em>V*exp(-(*U*<sub>1</sub>-*U*<sub>0</sub>)/*kT</em>), as c_ID[2] and the
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volume of the simulation box <em>V</em> as c_ID[3]. <a href="#id11"><span class="problematic" id="id12">*</span></a>U*<sub>1</sub> is the
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pair potential energy obtained with the perturbed parameters and
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<a href="#id13"><span class="problematic" id="id14">*</span></a>U*<sub>0</sub> is the pair potential energy obtained with the
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unperturbed parameters. The energies include kspace terms if these
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are used in the simulation.</p>
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<p>These output results can be used by any command that uses a global
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scalar or vector from a compute as input. See <a class="reference internal" href="Section_howto.html#howto-15"><span>Section_howto 15</span></a> for an overview of LAMMPS output
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options. For example, the computed values can be averaged using <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a>.</p>
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<p>The values calculated by this compute are “extensive”.</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 compute is distributed as the USER-FEP package. It is only
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enabled if LAMMPS was built with that package. 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="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_adapt_fep.html"><em>fix adapt/fep</em></a>, <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a>,
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<a class="reference external" href="pair_lj_soft_coul_soft.txt">pair_lj_soft_coul_soft</a></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 option defaults are <em>tail</em> = <em>no</em>, <em>volume</em> = <em>no</em>.</p>
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<hr class="docutils" />
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<p id="pearlman"><strong>(Pearlman)</strong> Pearlman, J Chem Phys, 98, 1487 (1994)</p>
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<p id="mezei"><strong>(Mezei)</strong> Mezei, J Chem Phys, 86, 7084 (1987)</p>
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<p id="bennet"><strong>(Bennet)</strong> Bennet, J Comput Phys, 22, 245 (1976)</p>
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<p id="boreschkarplus"><strong>(BoreschKarplus)</strong> Boresch and Karplus, J Phys Chem A, 103, 103 (1999)</p>
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<p id="allentildesley"><strong>(AllenTildesley)</strong> Allen and Tildesley, Computer Simulation of
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Liquids, Oxford University Press (1987)</p>
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