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<li class="toctree-l1"><a class="reference internal" href="Section_intro.html">1. Introduction</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_accelerate.html">5. Accelerating LAMMPS performance</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_python.html">11. Python interface to LAMMPS</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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<li>compute ti command</li>
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<div class="section" id="compute-ti-command">
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<span id="index-0"></span><h1>compute ti command<a class="headerlink" href="#compute-ti-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 ti keyword args ...
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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="compute.html"><em>compute</em></a> command</li>
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<li>ti = style name of this compute command</li>
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<li>one or more attribute/arg pairs may be appended</li>
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<li>keyword = pair style (lj/cut, gauss, born, etc) or <em>tail</em> or <em>kspace</em></li>
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</ul>
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<pre class="literal-block">
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pair style args = atype v_name1 v_name2
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atype = atom type (see asterisk form below)
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v_name1 = variable with name1 that is energy scale factor and function of lambda
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v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
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<em>tail</em> args = atype v_name1 v_name2
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atype = atom type (see asterisk form below)
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v_name1 = variable with name1 that is energy tail correction scale factor and function of lambda
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v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
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<em>kspace</em> args = atype v_name1 v_name2
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atype = atom type (see asterisk form below)
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v_name1 = variable with name1 that is K-Space scale factor and function of lambda
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v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
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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 ti lj/cut 1 v_lj v_dlj coul/long 2 v_c v_dc kspace 1 v_ks v_dks
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compute 1 all ti lj/cut 1*3 v_lj v_dlj coul/long * v_c v_dc kspace * v_ks v_dks
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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>Define a computation that calculates the derivative of the interaction
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potential with respect to <em>lambda</em>, the coupling parameter used in a
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thermodynamic integration. This derivative can be used to infer a
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free energy difference resulting from an alchemical simulation, as
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described in <a class="reference internal" href="#eike"><span>Eike</span></a>.</p>
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<p>Typically this compute will be used in conjunction with the <a class="reference internal" href="fix_adapt.html"><em>fix adapt</em></a> command which can perform alchemical
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transformations by adusting the strength of an interaction potential
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as a simulation runs, as defined by one or more
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<a class="reference internal" href="pair_style.html"><em>pair_style</em></a> or <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a>
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commands. This scaling is done via a prefactor on the energy, forces,
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virial calculated by the pair or K-Space style. The prefactor is
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often a function of a <em>lambda</em> parameter which may be adjusted from 0
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to 1 (or vice versa) over the course of a <a class="reference internal" href="run.html"><em>run</em></a>. The
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time-dependent adjustment is what the <a class="reference internal" href="fix_adapt.html"><em>fix adapt</em></a>
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command does.</p>
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<p>Assume that the unscaled energy of a pair_style or kspace_style is
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given by U. Then the scaled energy is</p>
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<div class="highlight-python"><div class="highlight"><pre>Us = f(lambda) U
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</pre></div>
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</div>
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<p>where f() is some function of lambda. What this compute calculates is</p>
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<div class="highlight-python"><div class="highlight"><pre>dUs / d(lambda) = U df(lambda)/dlambda = Us / f(lambda) df(lambda)/dlambda
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</pre></div>
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</div>
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<p>which is the derivative of the system’s scaled potential energy Us
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with respect to <em>lambda</em>.</p>
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<p>To perform this calculation, you provide one or more atom types as
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<em>atype</em>. <em>Atype</em> can be specified in one of two ways. An explicit
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numeric values can be used, as in the 1st example above. Or a
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wildcard asterisk can be used in place of or in conjunction with the
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<em>atype</em> argument to select multiple atom types. This takes the form
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“*” or “<em>n” or “n</em>” or “m*n”. If N = the number of atom types, then
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an asterisk with no numeric values means all types from 1 to N. A
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leading asterisk means all types from 1 to n (inclusive). A trailing
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asterisk means all types from n to N (inclusive). A middle asterisk
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means all types from m to n (inclusive).</p>
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<p>You also specify two functions, as <a class="reference internal" href="variable.html"><em>equal-style variables</em></a>. The first is specified as <em>v_name1</em>, where
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<em>name1</em> is the name of the variable, and is f(lambda) in the notation
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above. The second is specified as <em>v_name2</em>, where <em>name2</em> is the
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name of the variable, and is df(lambda) / dlambda in the notation
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above. I.e. it is the analytic derivative of f() with respect to
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lambda. Note that the <em>name1</em> variable is also typically given as an
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argument to the <a class="reference internal" href="fix_adapt.html"><em>fix adapt</em></a> command.</p>
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<p>An alchemical simulation may use several pair potentials together,
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invoked via the <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid or hybrid/overlay</em></a>
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command. The total dUs/dlambda for the overall system is calculated
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as the sum of each contributing term as listed by the keywords in the
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compute ti command. Individual pair potentials can be listed, which
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will be sub-styles in the hybrid case. You can also include a K-space
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term via the <em>kspace</em> keyword. You can also include a pairwise
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long-range tail correction to the energy via the <em>tail</em> keyword.</p>
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<p>For each term you can specify a different (or the same) scale factor
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by the two variables that you list. Again, these will typically
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correspond toe the scale factors applied to these various potentials
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and the K-Space contribution via the <a class="reference internal" href="fix_adapt.html"><em>fix_adapt</em></a>
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command.</p>
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<p>More details about the exact functional forms for the computation of
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du/dl can be found in the paper by <a class="reference internal" href="#eike"><span>Eike</span></a>.</p>
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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 scalar, namely dUs/dlambda. This
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value can be used by any command that uses a global scalar value from
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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.</p>
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<p>The scalar value calculated by this compute is “extensive”.</p>
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<p>The scalar value will be in energy <a class="reference internal" href="units.html"><em>units</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 compute is part of the MISC package. It is only enabled if
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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.html"><em>fix adapt</em></a></p>
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<p><strong>Default:</strong> none</p>
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<hr class="docutils" />
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<p id="eike"><strong>(Eike)</strong> Eike and Maginn, Journal of Chemical Physics, 124, 164503 (2006).</p>
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