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<div class="section" id="compute-ti-command">
<span id="index-0"></span><h1>compute ti command</h1>
<div class="section" id="syntax">
<h2>Syntax</h2>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">compute</span> <span class="n">ID</span> <span class="n">group</span> <span class="n">ti</span> <span class="n">keyword</span> <span class="n">args</span> <span class="o">...</span>
</pre></div>
</div>
<ul class="simple">
<li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><span class="doc">compute</span></a> command</li>
<li>ti = style name of this compute command</li>
<li>one or more attribute/arg pairs may be appended</li>
<li>keyword = pair style (lj/cut, gauss, born, etc) or <em>tail</em> or <em>kspace</em></li>
</ul>
<pre class="literal-block">
pair style args = atype v_name1 v_name2
atype = atom type (see asterisk form below)
v_name1 = variable with name1 that is energy scale factor and function of lambda
v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
<em>tail</em> args = atype v_name1 v_name2
atype = atom type (see asterisk form below)
v_name1 = variable with name1 that is energy tail correction scale factor and function of lambda
v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
<em>kspace</em> args = atype v_name1 v_name2
atype = atom type (see asterisk form below)
v_name1 = variable with name1 that is K-Space scale factor and function of lambda
v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
</pre>
</div>
<div class="section" id="examples">
<h2>Examples</h2>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">compute</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">ti</span> <span class="n">lj</span><span class="o">/</span><span class="n">cut</span> <span class="mi">1</span> <span class="n">v_lj</span> <span class="n">v_dlj</span> <span class="n">coul</span><span class="o">/</span><span class="n">long</span> <span class="mi">2</span> <span class="n">v_c</span> <span class="n">v_dc</span> <span class="n">kspace</span> <span class="mi">1</span> <span class="n">v_ks</span> <span class="n">v_dks</span>
<span class="n">compute</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">ti</span> <span class="n">lj</span><span class="o">/</span><span class="n">cut</span> <span class="mi">1</span><span class="o">*</span><span class="mi">3</span> <span class="n">v_lj</span> <span class="n">v_dlj</span> <span class="n">coul</span><span class="o">/</span><span class="n">long</span> <span class="o">*</span> <span class="n">v_c</span> <span class="n">v_dc</span> <span class="n">kspace</span> <span class="o">*</span> <span class="n">v_ks</span> <span class="n">v_dks</span>
</pre></div>
</div>
</div>
<div class="section" id="description">
<h2>Description</h2>
<p>Define a computation that calculates the derivative of the interaction
potential with respect to <em>lambda</em>, the coupling parameter used in a
thermodynamic integration. This derivative can be used to infer a
free energy difference resulting from an alchemical simulation, as
described in <a class="reference internal" href="#eike"><span class="std std-ref">Eike</span></a>.</p>
<p>Typically this compute will be used in conjunction with the <a class="reference internal" href="fix_adapt.html"><span class="doc">fix adapt</span></a> command which can perform alchemical
transformations by adusting the strength of an interaction potential
as a simulation runs, as defined by one or more
<a class="reference internal" href="pair_style.html"><span class="doc">pair_style</span></a> or <a class="reference internal" href="kspace_style.html"><span class="doc">kspace_style</span></a>
commands. This scaling is done via a prefactor on the energy, forces,
virial calculated by the pair or K-Space style. The prefactor is
often a function of a <em>lambda</em> parameter which may be adjusted from 0
to 1 (or vice versa) over the course of a <a class="reference internal" href="run.html"><span class="doc">run</span></a>. The
time-dependent adjustment is what the <a class="reference internal" href="fix_adapt.html"><span class="doc">fix adapt</span></a>
command does.</p>
<p>Assume that the unscaled energy of a pair_style or kspace_style is
given by U. Then the scaled energy is</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">Us</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="k">lambda</span><span class="p">)</span> <span class="n">U</span>
</pre></div>
</div>
<p>where f() is some function of lambda. What this compute calculates is</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">dUs</span> <span class="o">/</span> <span class="n">d</span><span class="p">(</span><span class="k">lambda</span><span class="p">)</span> <span class="o">=</span> <span class="n">U</span> <span class="n">df</span><span class="p">(</span><span class="k">lambda</span><span class="p">)</span><span class="o">/</span><span class="n">dlambda</span> <span class="o">=</span> <span class="n">Us</span> <span class="o">/</span> <span class="n">f</span><span class="p">(</span><span class="k">lambda</span><span class="p">)</span> <span class="n">df</span><span class="p">(</span><span class="k">lambda</span><span class="p">)</span><span class="o">/</span><span class="n">dlambda</span>
</pre></div>
</div>
<p>which is the derivative of the system&#8217;s scaled potential energy Us
with respect to <em>lambda</em>.</p>
<p>To perform this calculation, you provide one or more atom types as
<em>atype</em>. <em>Atype</em> can be specified in one of two ways. An explicit
numeric values can be used, as in the 1st example above. Or a
wildcard asterisk can be used in place of or in conjunction with the
<em>atype</em> argument to select multiple 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).</p>
<p>You also specify two functions, as <a class="reference internal" href="variable.html"><span class="doc">equal-style variables</span></a>. The first is specified as <em>v_name1</em>, where
<em>name1</em> is the name of the variable, and is f(lambda) in the notation
above. The second is specified as <em>v_name2</em>, where <em>name2</em> is the
name of the variable, and is df(lambda) / dlambda in the notation
above. I.e. it is the analytic derivative of f() with respect to
lambda. Note that the <em>name1</em> variable is also typically given as an
argument to the <a class="reference internal" href="fix_adapt.html"><span class="doc">fix adapt</span></a> command.</p>
<p>An alchemical simulation may use several pair potentials together,
invoked via the <a class="reference internal" href="pair_hybrid.html"><span class="doc">pair_style hybrid or hybrid/overlay</span></a>
command. The total dUs/dlambda for the overall system is calculated
as the sum of each contributing term as listed by the keywords in the
compute ti command. Individual pair potentials can be listed, which
will be sub-styles in the hybrid case. You can also include a K-space
term via the <em>kspace</em> keyword. You can also include a pairwise
long-range tail correction to the energy via the <em>tail</em> keyword.</p>
<p>For each term you can specify a different (or the same) scale factor
by the two variables that you list. Again, these will typically
correspond toe the scale factors applied to these various potentials
and the K-Space contribution via the <a class="reference internal" href="fix_adapt.html"><span class="doc">fix adapt</span></a>
command.</p>
<p>More details about the exact functional forms for the computation of
du/dl can be found in the paper by <a class="reference internal" href="#eike"><span class="std std-ref">Eike</span></a>.</p>
<hr class="docutils" />
<p><strong>Output info:</strong></p>
<p>This compute calculates a global scalar, namely dUs/dlambda. This
value can be used by any command that uses a global scalar value from
a compute as input. See <a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">Section_howto 15</span></a> for an overview of LAMMPS output
options.</p>
<p>The scalar value calculated by this compute is &#8220;extensive&#8221;.</p>
<p>The scalar value will be in energy <a class="reference internal" href="units.html"><span class="doc">units</span></a>.</p>
</div>
<div class="section" id="restrictions">
<h2>Restrictions</h2>
<p>This compute is part of the MISC 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_adapt.html"><span class="doc">fix adapt</span></a></p>
<p><strong>Default:</strong> none</p>
<hr class="docutils" />
<p id="eike"><strong>(Eike)</strong> Eike and Maginn, Journal of Chemical Physics, 124, 164503 (2006).</p>
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