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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_start.html">2. Getting Started</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_commands.html">3. Commands</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_packages.html">4. Packages</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_howto.html">6. How-to discussions</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_example.html">7. Example problems</a></li>
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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_modify.html">10. Modifying & extending LAMMPS</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>minimize command</li>
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<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
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<div class="section" id="minimize-command">
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<span id="index-0"></span><h1>minimize command</h1>
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<div class="section" id="syntax">
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<h2>Syntax</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">minimize</span> <span class="n">etol</span> <span class="n">ftol</span> <span class="n">maxiter</span> <span class="n">maxeval</span>
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</pre></div>
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</div>
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<ul class="simple">
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<li>etol = stopping tolerance for energy (unitless)</li>
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<li>ftol = stopping tolerance for force (force units)</li>
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<li>maxiter = max iterations of minimizer</li>
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<li>maxeval = max number of force/energy evaluations</li>
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</ul>
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</div>
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<div class="section" id="examples">
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<h2>Examples</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">minimize</span> <span class="mf">1.0e-4</span> <span class="mf">1.0e-6</span> <span class="mi">100</span> <span class="mi">1000</span>
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<span class="n">minimize</span> <span class="mf">0.0</span> <span class="mf">1.0e-8</span> <span class="mi">1000</span> <span class="mi">100000</span>
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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</h2>
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<p>Perform an energy minimization of the system, by iteratively adjusting
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atom coordinates. Iterations are terminated when one of the stopping
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criteria is satisfied. At that point the configuration will hopefully
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be in local potential energy minimum. More precisely, the
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configuration should approximate a critical point for the objective
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function (see below), which may or may not be a local minimum.</p>
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<p>The minimization algorithm used is set by the
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<a class="reference internal" href="min_style.html"><span class="doc">min_style</span></a> command. Other options are set by the
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<a class="reference internal" href="min_modify.html"><span class="doc">min_modify</span></a> command. Minimize commands can be
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interspersed with <a class="reference internal" href="run.html"><span class="doc">run</span></a> commands to alternate between
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relaxation and dynamics. The minimizers bound the distance atoms move
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in one iteration, so that you can relax systems with highly overlapped
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atoms (large energies and forces) by pushing the atoms off of each
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other.</p>
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<p>Alternate means of relaxing a system are to run dynamics with a small
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or <a class="reference internal" href="fix_nve_limit.html"><span class="doc">limited timestep</span></a>. Or dynamics can be run
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using <a class="reference internal" href="fix_viscous.html"><span class="doc">fix viscous</span></a> to impose a damping force that
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slowly drains all kinetic energy from the system. The <a class="reference internal" href="pair_soft.html"><span class="doc">pair_style soft</span></a> potential can be used to un-overlap atoms while
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running dynamics.</p>
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<p>Note that you can minimize some atoms in the system while holding the
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coordiates of other atoms fixed by applying <a class="reference internal" href="fix_setforce.html"><span class="doc">fix setforce</span></a> to the other atoms. See a fuller
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discussion of using fixes while minimizing below.</p>
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<p>The <a class="reference internal" href="min_style.html"><span class="doc">minimization styles</span></a> <em>cg</em>, <em>sd</em>, and <em>hftn</em>
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involves an outer iteration loop which sets the search direction along
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which atom coordinates are changed. An inner iteration is then
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performed using a line search algorithm. The line search typically
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evaluates forces and energies several times to set new coordinates.
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Currently, a backtracking algorithm is used which may not be optimal
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in terms of the number of force evaulations performed, but appears to
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be more robust than previous line searches we’ve tried. The
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backtracking method is described in Nocedal and Wright’s Numerical
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Optimization (Procedure 3.1 on p 41).</p>
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<p>The <a class="reference internal" href="min_style.html"><span class="doc">minimization styles</span></a> <em>quickmin</em> and <em>fire</em> perform
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damped dynamics using an Euler integration step. Thus they require a
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<a class="reference internal" href="timestep.html"><span class="doc">timestep</span></a> be defined.</p>
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">The damped dynamic minimizers use whatever timestep you have
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defined via the <a class="reference internal" href="timestep.html"><span class="doc">timestep</span></a> command. Often they will
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converge more quickly if you use a timestep about 10x larger than you
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would normally use for dynamics simulations.</p>
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</div>
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<hr class="docutils" />
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<p>In all cases, the objective function being minimized is the total
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potential energy of the system as a function of the N atom
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coordinates:</p>
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<img alt="_images/min_energy.jpg" class="align-center" src="_images/min_energy.jpg" />
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<p>where the first term is the sum of all non-bonded <a class="reference internal" href="pair_style.html"><span class="doc">pairwise interactions</span></a> including <a class="reference internal" href="kspace_style.html"><span class="doc">long-range Coulombic interactions</span></a>, the 2nd thru 5th terms are
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<a class="reference internal" href="bond_style.html"><span class="doc">bond</span></a>, <a class="reference internal" href="angle_style.html"><span class="doc">angle</span></a>,
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<a class="reference internal" href="dihedral_style.html"><span class="doc">dihedral</span></a>, and <a class="reference internal" href="improper_style.html"><span class="doc">improper</span></a>
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interactions respectively, and the last term is energy due to
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<a class="reference internal" href="fix.html"><span class="doc">fixes</span></a> which can act as constraints or apply force to atoms,
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such as thru interaction with a wall. See the discussion below about
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how fix commands affect minimization.</p>
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<p>The starting point for the minimization is the current configuration
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of the atoms.</p>
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<hr class="docutils" />
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<p>The minimization procedure stops if any of several criteria are met:</p>
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<ul class="simple">
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<li>the change in energy between outer iterations is less than <em>etol</em></li>
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<li>the 2-norm (length) of the global force vector is less than the <em>ftol</em></li>
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<li>the line search fails because the step distance backtracks to 0.0</li>
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<li>the number of outer iterations or timesteps exceeds <em>maxiter</em></li>
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<li>the number of total force evaluations exceeds <em>maxeval</em></li>
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</ul>
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<p>For the first criterion, the specified energy tolerance <em>etol</em> is
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unitless; it is met when the energy change between successive
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iterations divided by the energy magnitude is less than or equal to
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the tolerance. For example, a setting of 1.0e-4 for <em>etol</em> means an
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energy tolerance of one part in 10^4. For the damped dynamics
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minimizers this check is not performed for a few steps after
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velocities are reset to 0, otherwise the minimizer would prematurely
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converge.</p>
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<p>For the second criterion, the specified force tolerance <em>ftol</em> is in
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force units, since it is the length of the global force vector for all
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atoms, e.g. a vector of size 3N for N atoms. Since many of the
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components will be near zero after minimization, you can think of
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<em>ftol</em> as an upper bound on the final force on any component of any
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atom. For example, a setting of 1.0e-4 for <em>ftol</em> means no x, y, or z
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component of force on any atom will be larger than 1.0e-4 (in force
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units) after minimization.</p>
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<p>Either or both of the <em>etol</em> and <em>ftol</em> values can be set to 0.0, in
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which case some other criterion will terminate the minimization.</p>
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<p>During a minimization, the outer iteration count is treated as a
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timestep. Output is triggered by this timestep, e.g. thermodynamic
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output or dump and restart files.</p>
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<p>Using the <a class="reference internal" href="thermo_style.html"><span class="doc">thermo_style custom</span></a> command with the
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<em>fmax</em> or <em>fnorm</em> keywords can be useful for monitoring the progress
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of the minimization. Note that these outputs will be calculated only
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from forces on the atoms, and will not include any extra degrees of
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freedom, such as from the <a class="reference internal" href="fix_box_relax.html"><span class="doc">fix box/relax</span></a> command.</p>
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<p>Following minimization, a statistical summary is printed that lists
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which convergence criterion caused the minimizer to stop, as well as
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information about the energy, force, final line search, and
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iteration counts. An example is as follows:</p>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">Minimization</span> <span class="n">stats</span><span class="p">:</span>
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<span class="n">Stopping</span> <span class="n">criterion</span> <span class="o">=</span> <span class="nb">max</span> <span class="n">iterations</span>
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<span class="n">Energy</span> <span class="n">initial</span><span class="p">,</span> <span class="nb">next</span><span class="o">-</span><span class="n">to</span><span class="o">-</span><span class="n">last</span><span class="p">,</span> <span class="n">final</span> <span class="o">=</span>
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<span class="o">-</span><span class="mf">0.626828169302</span> <span class="o">-</span><span class="mf">2.82642039062</span> <span class="o">-</span><span class="mf">2.82643549739</span>
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<span class="n">Force</span> <span class="n">two</span><span class="o">-</span><span class="n">norm</span> <span class="n">initial</span><span class="p">,</span> <span class="n">final</span> <span class="o">=</span> <span class="mf">2052.1</span> <span class="mf">91.9642</span>
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<span class="n">Force</span> <span class="nb">max</span> <span class="n">component</span> <span class="n">initial</span><span class="p">,</span> <span class="n">final</span> <span class="o">=</span> <span class="mf">346.048</span> <span class="mf">9.78056</span>
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<span class="n">Final</span> <span class="n">line</span> <span class="n">search</span> <span class="n">alpha</span><span class="p">,</span> <span class="nb">max</span> <span class="n">atom</span> <span class="n">move</span> <span class="o">=</span> <span class="mf">2.23899e-06</span> <span class="mf">2.18986e-05</span>
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<span class="n">Iterations</span><span class="p">,</span> <span class="n">force</span> <span class="n">evaluations</span> <span class="o">=</span> <span class="mi">2000</span> <span class="mi">12724</span>
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</pre></div>
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</div>
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<p>The 3 energy values are for before and after the minimization and on
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the next-to-last iteration. This is what the <em>etol</em> parameter checks.</p>
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<p>The two-norm force values are the length of the global force vector
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before and after minimization. This is what the <em>ftol</em> parameter
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checks.</p>
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<p>The max-component force values are the absolute value of the largest
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component (x,y,z) in the global force vector, i.e. the infinity-norm
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of the force vector.</p>
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<p>The alpha parameter for the line-search, when multiplied by the max
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force component (on the last iteration), gives the max distance any
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atom moved during the last iteration. Alpha will be 0.0 if the line
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search could not reduce the energy. Even if alpha is non-zero, if the
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“max atom move” distance is tiny compared to typical atom coordinates,
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then it is possible the last iteration effectively caused no atom
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movement and thus the evaluated energy did not change and the
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minimizer terminated. Said another way, even with non-zero forces,
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it’s possible the effect of those forces is to move atoms a distance
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less than machine precision, so that the energy cannot be further
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reduced.</p>
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<p>The iterations and force evaluation values are what is checked by the
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<em>maxiter</em> and <em>maxeval</em> parameters.</p>
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<hr class="docutils" />
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">There are several force fields in LAMMPS which have
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discontinuities or other approximations which may prevent you from
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performing an energy minimization to high tolerances. For example,
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you should use a <a class="reference internal" href="pair_style.html"><span class="doc">pair style</span></a> that goes to 0.0 at the
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cutoff distance when performing minimization (even if you later change
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it when running dynamics). If you do not do this, the total energy of
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the system will have discontinuities when the relative distance
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between any pair of atoms changes from cutoff+epsilon to
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cutoff-epsilon and the minimizer may behave poorly. Some of the
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manybody potentials use splines and other internal cutoffs that
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inherently have this problem. The <a class="reference internal" href="kspace_style.html"><span class="doc">long-range Coulombic styles</span></a> (PPPM, Ewald) are approximate to within the
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user-specified tolerance, which means their energy and forces may not
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agree to a higher precision than the Kspace-specified tolerance. In
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all these cases, the minimizer may give up and stop before finding a
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minimum to the specified energy or force tolerance.</p>
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</div>
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<p>Note that a cutoff Lennard-Jones potential (and others) can be shifted
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so that its energy is 0.0 at the cutoff via the
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<a class="reference internal" href="pair_modify.html"><span class="doc">pair_modify</span></a> command. See the doc pages for
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inidividual <a class="reference internal" href="pair_style.html"><span class="doc">pair styles</span></a> for details. Note that
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Coulombic potentials always have a cutoff, unless versions with a
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long-range component are used (e.g. <a class="reference internal" href="pair_lj.html"><span class="doc">pair_style lj/cut/coul/long</span></a>). The CHARMM potentials go to 0.0 at
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the cutoff (e.g. <a class="reference internal" href="pair_charmm.html"><span class="doc">pair_style lj/charmm/coul/charmm</span></a>),
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as do the GROMACS potentials (e.g. <a class="reference internal" href="pair_gromacs.html"><span class="doc">pair_style lj/gromacs</span></a>).</p>
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<p>If a soft potential (<a class="reference internal" href="pair_soft.html"><span class="doc">pair_style soft</span></a>) is used the
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Astop value is used for the prefactor (no time dependence).</p>
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<p>The <a class="reference internal" href="fix_box_relax.html"><span class="doc">fix box/relax</span></a> command can be used to apply an
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external pressure to the simulation box and allow it to shrink/expand
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during the minimization.</p>
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<p>Only a few other fixes (typically those that apply force constraints)
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are invoked during minimization. See the doc pages for individual
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<a class="reference internal" href="fix.html"><span class="doc">fix</span></a> commands to see which ones are relevant. Current
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examples of fixes that can be used include:</p>
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<ul class="simple">
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<li><a class="reference internal" href="fix_addforce.html"><span class="doc">fix addforce</span></a></li>
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<li><a class="reference internal" href="fix_addtorque.html"><span class="doc">fix addtorque</span></a></li>
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<li><a class="reference internal" href="fix_efield.html"><span class="doc">fix efield</span></a></li>
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<li><a class="reference internal" href="fix_enforce2d.html"><span class="doc">fix enforce2d</span></a></li>
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<li><a class="reference internal" href="fix_indent.html"><span class="doc">fix indent</span></a></li>
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<li><a class="reference internal" href="fix_lineforce.html"><span class="doc">fix lineforce</span></a></li>
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<li><a class="reference internal" href="fix_planeforce.html"><span class="doc">fix planeforce</span></a></li>
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<li><a class="reference internal" href="fix_setforce.html"><span class="doc">fix setforce</span></a></li>
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<li><a class="reference internal" href="fix_spring.html"><span class="doc">fix spring</span></a></li>
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<li><a class="reference internal" href="fix_spring_self.html"><span class="doc">fix spring/self</span></a></li>
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<li><a class="reference internal" href="fix_viscous.html"><span class="doc">fix viscous</span></a></li>
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<li><a class="reference internal" href="fix_wall.html"><span class="doc">fix wall</span></a></li>
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<li><a class="reference internal" href="fix_wall_region.html"><span class="doc">fix wall/region</span></a></li>
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</ul>
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">Some fixes which are invoked during minimization have an
|
|
associated potential energy. For that energy to be included in the
|
|
total potential energy of the system (the quantity being minimized),
|
|
you MUST enable the <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> <em>energy</em> option for
|
|
that fix. The doc pages for individual <a class="reference internal" href="fix.html"><span class="doc">fix</span></a> commands
|
|
specify if this should be done.</p>
|
|
</div>
|
|
</div>
|
|
<hr class="docutils" />
|
|
<div class="section" id="restrictions">
|
|
<h2>Restrictions</h2>
|
|
<p>Features that are not yet implemented are listed here, in case someone
|
|
knows how they could be coded:</p>
|
|
<p>It is an error to use <a class="reference internal" href="fix_shake.html"><span class="doc">fix shake</span></a> with minimization
|
|
because it turns off bonds that should be included in the potential
|
|
energy of the system. The effect of a fix shake can be approximated
|
|
during a minimization by using stiff spring constants for the bonds
|
|
and/or angles that would normally be constrained by the SHAKE
|
|
algorithm.</p>
|
|
<p><a class="reference internal" href="fix_rigid.html"><span class="doc">Fix rigid</span></a> is also not supported by minimization. It
|
|
is not an error to have it defined, but the energy minimization will
|
|
not keep the defined body(s) rigid during the minimization. Note that
|
|
if bonds, angles, etc internal to a rigid body have been turned off
|
|
(e.g. via <a class="reference internal" href="neigh_modify.html"><span class="doc">neigh_modify exclude</span></a>), they will not
|
|
contribute to the potential energy which is probably not what is
|
|
desired.</p>
|
|
<p>Pair potentials that produce torque on a particle (e.g. <a class="reference internal" href="pair_gran.html"><span class="doc">granular potentials</span></a> or the <a class="reference internal" href="pair_gayberne.html"><span class="doc">GayBerne potential</span></a> for ellipsoidal particles) are not
|
|
relaxed by a minimization. More specifically, radial relaxations are
|
|
induced, but no rotations are induced by a minimization, so such a
|
|
system will not fully relax.</p>
|
|
</div>
|
|
<div class="section" id="related-commands">
|
|
<h2>Related commands</h2>
|
|
<p><a class="reference internal" href="min_modify.html"><span class="doc">min_modify</span></a>, <a class="reference internal" href="min_style.html"><span class="doc">min_style</span></a>,
|
|
<a class="reference internal" href="run_style.html"><span class="doc">run_style</span></a></p>
|
|
<p><strong>Default:</strong> none</p>
|
|
</div>
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