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<div class="section" id="compute-fep-command">
<span id="index-0"></span><h1>compute fep command<a class="headerlink" href="#compute-fep-command" title="Permalink to this headline">¶</a></h1>
<div class="section" id="syntax">
<h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
<div class="highlight-python"><div class="highlight"><pre>compute ID group-ID fep temp attribute args ... keyword value ...
</pre></div>
</div>
<ul class="simple">
<li>ID, group-ID are documented in the <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
<li>fep = name of this compute command</li>
<li>temp = external temperature (as specified for constant-temperature run)</li>
<li>one or more attributes with args may be appended</li>
<li>attribute = <em>pair</em> or <em>atom</em></li>
</ul>
<pre class="literal-block">
<em>pair</em> args = pstyle pparam I J v_delta
pstyle = pair style name, e.g. lj/cut
pparam = parameter to perturb
I,J = type pair(s) to set parameter for
v_delta = variable with perturbation to apply (in the units of the parameter)
<em>atom</em> args = aparam I v_delta
aparam = parameter to perturb
I = type to set parameter for
v_delta = variable with perturbation to apply (in the units of the parameter)
</pre>
<ul class="simple">
<li>zero or more keyword/value pairs may be appended</li>
<li>keyword = <em>tail</em> or <em>volume</em></li>
</ul>
<pre class="literal-block">
<em>tail</em> value = <em>no</em> or <em>yes</em>
<em>no</em> = ignore tail correction to pair energies (usually small in fep)
<em>yes</em> = include tail correction to pair energies
<em>volume</em> value = <em>no</em> or <em>yes</em>
<em>no</em> = ignore volume changes (e.g. in <em>NVE</em> or <em>NVT</em> trajectories)
<em>yes</em> = include volume changes (e.g. in <em>NpT</em> trajectories)
</pre>
</div>
<div class="section" id="examples">
<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
<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
compute 1 all fep 300 atom charge 2 v_delta
</pre></div>
</div>
</div>
<div class="section" id="description">
<h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
<p>Apply a perturbation to parameters of the interaction potential and
recalculate the pair potential energy without changing the atomic
coordinates from those of the reference, unperturbed system. This
compute can be used to calculate free energy differences using several
methods, such as free-energy perturbation (FEP), finite-difference
thermodynamic integration (FDTI) or Bennet&#8217;s acceptance ratio method
(BAR).</p>
<p>The potential energy of the system is decomposed in three terms: a
background term corresponding to interaction sites whose parameters
remain constant, a reference term <a href="#id1"><span class="problematic" id="id2">*</span></a>U*&lt;sub&gt;0&lt;/sub&gt; corresponding to the
initial interactions of the atoms that will undergo perturbation, and
a term <a href="#id3"><span class="problematic" id="id4">*</span></a>U*&lt;sub&gt;1&lt;/sub&gt; corresponding to the final interactions of
these atoms:</p>
<img alt="_images/compute_fep_u.jpg" class="align-center" src="_images/compute_fep_u.jpg" />
<p>A coupling parameter &amp;lambda; varying from 0 to 1 connects the
reference and perturbed systems:</p>
<img alt="_images/compute_fep_lambda.jpg" class="align-center" src="_images/compute_fep_lambda.jpg" />
<p>It is possible but not necessary that the coupling parameter (or a
function thereof) appears as a multiplication factor of the potential
energy. Therefore, this compute can apply perturbations to interaction
parameters that are not directly proportional to the potential energy
(e.g. &amp;sigma; in Lennard-Jones potentials).</p>
<p>This command can be combined with <a class="reference internal" href="fix_adapt.html"><em>fix adapt</em></a> to
perform multistage free-energy perturbation calculations along
stepwise alchemical transformations during a simulation run:</p>
<img alt="_images/compute_fep_fep.jpg" class="align-center" src="_images/compute_fep_fep.jpg" />
<p>This compute is suitable for the finite-difference thermodynamic
integration (FDTI) method <a class="reference internal" href="#mezei"><span>(Mezei)</span></a>, which is based on an
evaluation of the numerical derivative of the free energy by a
perturbation method using a very small &amp;delta;:</p>
<img alt="_images/compute_fep_fdti.jpg" class="align-center" src="_images/compute_fep_fdti.jpg" />
<p>where <a href="#id5"><span class="problematic" id="id6">*</span></a>w*&lt;sub&gt;i&lt;/sub&gt; 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
&amp;lambda; at which the derivative is calculated and averaged.</p>
<p>The compute fep calculates the exponential Boltzmann term and also the
potential energy difference <a href="#id7"><span class="problematic" id="id8">*</span></a>U*&lt;sub&gt;1&lt;/sub&gt;-<a href="#id9"><span class="problematic" id="id10">*</span></a>U*&lt;sub&gt;0&lt;/sub&gt;. By
choosing a very small perturbation &amp;delta; the thermodynamic
integration method can be implemented using a numerical evaluation of
the derivative of the potential energy with respect to &amp;lambda;:</p>
<img alt="_images/compute_fep_ti.jpg" class="align-center" src="_images/compute_fep_ti.jpg" />
<p>Another technique to calculate free energy differences is the
acceptance ratio method <a class="reference internal" href="#bennet"><span>(Bennet)</span></a>, which can be implemented
by calculating the potential energy differences with &amp;delta; = 1.0 on
both the forward and reverse routes:</p>
<img alt="_images/compute_fep_bar.jpg" class="align-center" src="_images/compute_fep_bar.jpg" />
<p>The value of the free energy difference is determined by numerical
root finding to establish the equality.</p>
<p>Concerning the choice of how the atomic parameters are perturbed in
order to setup an alchemical transformation route, several strategies
are available, such as single-topology or double-topology strategies
<a class="reference internal" href="#pearlman"><span>(Pearlman)</span></a>. The latter does not require modification of
bond lengths, angles or other internal coordinates.</p>
<p>NOTES: This compute command does not take kinetic energy into account,
therefore the masses of the particles should not be modified between
the reference and perturbed states, or along the alchemical
transformation route. This compute command does not change bond
lengths or other internal coordinates <a class="reference internal" href="#boreschkarplus"><span>(Boresch, Karplus)</span></a>.</p>
<hr class="docutils" />
<p>The <em>pair</em> attribute enables various parameters of potentials defined
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>
commands to be changed, if the pair style supports it.</p>
<p>The <em>pstyle</em> argument is the name of the pair style. For example,
<em>pstyle</em> could be specified as &#8220;lj/cut&#8221;. The <em>pparam</em> argument is the
name of the parameter to change. This is a (non-exclusive) list of
pair styles and parameters that can be used with this compute. See
the doc pages for individual pair styles and their energy formulas for
the meaning of these parameters:</p>
<table border="1" class="docutils">
<colgroup>
<col width="59%" />
<col width="27%" />
<col width="15%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><a class="reference internal" href="pair_lj.html"><em>lj/cut</em></a></td>
<td>epsilon,sigma</td>
<td>type pairs</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="pair_lj.html"><em>lj/cut/coul/cut</em></a></td>
<td>epsilon,sigma</td>
<td>type pairs</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="pair_lj.html"><em>lj/cut/coul/long</em></a></td>
<td>epsilon,sigma</td>
<td>type pairs</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/soft</em></a></td>
<td>epsilon,sigma,lambda</td>
<td>type pairs</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="pair_lj_soft.html"><em>coul/cut/soft</em></a></td>
<td>lambda</td>
<td>type pairs</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="pair_lj_soft.html"><em>coul/long/soft</em></a></td>
<td>lambda</td>
<td>type pairs</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/coul/cut/soft</em></a></td>
<td>epsilon,sigma,lambda</td>
<td>type pairs</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/coul/long/soft</em></a></td>
<td>epsilon,sigma,lambda</td>
<td>type pairs</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/tip4p/long/soft</em></a></td>
<td>epsilon,sigma,lambda</td>
<td>type pairs</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="pair_lj_soft.html"><em>tip4p/long/soft</em></a></td>
<td>lambda</td>
<td>type pairs</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/charmm/coul/long/soft</em></a></td>
<td>epsilon,sigma,lambda</td>
<td>type pairs</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="pair_born.html"><em>born</em></a></td>
<td>a,b,c</td>
<td>type pairs</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="pair_buck.html"><em>buck</em></a></td>
<td>a,c</td>
<td>type pairs</td>
</tr>
</tbody>
</table>
<p>Note that it is easy to add new potentials and their parameters to
this list. All it typically takes is adding an extract() method to
the pair_*.cpp file associated with the potential.</p>
<p>Similar to the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command, I and J can be
specified in one of two ways. Explicit numeric values can be used for
each, as in the 1st example above. I &lt;= J is required. LAMMPS sets
the coefficients for the symmetric J,I interaction to the same
values. A wild-card asterisk can be used in place of or in conjunction
with the I,J arguments to set the coefficients for multiple pairs of
atom types. This takes the form &#8220;*&#8221; or &#8220;<em>n&#8221; or &#8220;n</em>&#8221; or &#8220;m*n&#8221;. If N =
the number of atom types, then an asterisk with no numeric values
means all types from 1 to N. A leading asterisk means all types from
1 to n (inclusive). A trailing asterisk means all types from n to N
(inclusive). A middle asterisk means all types from m to n
(inclusive). Note that only type pairs with I &lt;= J are considered; if
asterisks imply type pairs where J &lt; I, they are ignored.</p>
<p>If <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid or hybrid/overlay</em></a> is being
used, then the <em>pstyle</em> will be a sub-style name. You must specify
I,J arguments that correspond to type pair values defined (via the
<a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command) for that sub-style.</p>
<p>The <em>v_name</em> argument for keyword <em>pair</em> is the name of an
<a class="reference internal" href="variable.html"><em>equal-style variable</em></a> which will be evaluated each time
this compute is invoked. It should be specified as v_name, where name
is the variable name.</p>
<hr class="docutils" />
<p>The <em>atom</em> attribute enables atom properties to be changed. The
<em>aparam</em> argument is the name of the parameter to change. This is the
current list of atom parameters that can be used with this compute:</p>
<ul class="simple">
<li>charge = charge on particle</li>
</ul>
<p>The <em>v_name</em> argument for keyword <em>pair</em> is the name of an
<a class="reference internal" href="variable.html"><em>equal-style variable</em></a> which will be evaluated each time
this compute is invoked. It should be specified as v_name, where name
is the variable name.</p>
<hr class="docutils" />
<p>The <em>tail</em> keyword controls the calculation of the tail correction to
&#8220;van der Waals&#8221; pair energies beyond the cutoff, if this has been
activated via the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> command. If the
perturbation is small, the tail contribution to the energy difference
between the reference and perturbed systems should be negligible.</p>
<p>If the keyword <em>volume</em> = <em>yes</em>, then the Boltzmann term is multiplied
by the volume so that correct ensemble averaging can be performed over
trajectories during which the volume fluctuates or changes <a class="reference internal" href="#allentildesley"><span>(Allen and Tildesley)</span></a>:</p>
<img alt="_images/compute_fep_vol.jpg" class="align-center" src="_images/compute_fep_vol.jpg" />
<hr class="docutils" />
<p><strong>Output info:</strong></p>
<p>This compute calculates a global vector of length 3 which contains the
energy difference (<em>U*&lt;sub&gt;1&lt;/sub&gt;-*U*&lt;sub&gt;0&lt;/sub&gt;) as c_ID[1], the
Boltzmann factor exp(-(*U*&lt;sub&gt;1&lt;/sub&gt;-*U*&lt;sub&gt;0&lt;/sub&gt;)/*kT</em>), or
<em>V*exp(-(*U*&lt;sub&gt;1&lt;/sub&gt;-*U*&lt;sub&gt;0&lt;/sub&gt;)/*kT</em>), as c_ID[2] and the
volume of the simulation box <em>V</em> as c_ID[3]. <a href="#id11"><span class="problematic" id="id12">*</span></a>U*&lt;sub&gt;1&lt;/sub&gt; is the
pair potential energy obtained with the perturbed parameters and
<a href="#id13"><span class="problematic" id="id14">*</span></a>U*&lt;sub&gt;0&lt;/sub&gt; is the pair potential energy obtained with the
unperturbed parameters. The energies include kspace terms if these
are used in the simulation.</p>
<p>These output results can be used by any command that uses a global
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
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>
<p>The values calculated by this compute are &#8220;extensive&#8221;.</p>
</div>
<div class="section" id="restrictions">
<h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
<p>This compute is distributed as the USER-FEP 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>Making LAMMPS</span></a> section for more info.</p>
</div>
<div class="section" id="related-commands">
<h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
<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>,
<a class="reference external" href="pair_lj_soft_coul_soft.txt">pair_lj_soft_coul_soft</a></p>
</div>
<div class="section" id="default">
<h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
<p>The option defaults are <em>tail</em> = <em>no</em>, <em>volume</em> = <em>no</em>.</p>
<hr class="docutils" />
<p id="pearlman"><strong>(Pearlman)</strong> Pearlman, J Chem Phys, 98, 1487 (1994)</p>
<p id="mezei"><strong>(Mezei)</strong> Mezei, J Chem Phys, 86, 7084 (1987)</p>
<p id="bennet"><strong>(Bennet)</strong> Bennet, J Comput Phys, 22, 245 (1976)</p>
<p id="boreschkarplus"><strong>(BoreschKarplus)</strong> Boresch and Karplus, J Phys Chem A, 103, 103 (1999)</p>
<p id="allentildesley"><strong>(AllenTildesley)</strong> Allen and Tildesley, Computer Simulation of
Liquids, Oxford University Press (1987)</p>
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