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<div class="section" id="fix-qtb-command">
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<span id="index-0"></span><h1>fix qtb command<a class="headerlink" href="#fix-qtb-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>fix ID group-ID qtb 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 <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
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<li>qtb = style name of this fix</li>
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<li>zero or more keyword/value pairs may be appended</li>
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<li>keyword = <em>temp</em> or <em>damp</em> or <em>seed</em> or <em>f_max</em> or <em>N_f</em></li>
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</ul>
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<pre class="literal-block">
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<em>temp</em> value = target quantum temperature (temperature units)
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<em>damp</em> value = damping parameter (time units) inverse of friction <i>&gamma</i>;
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<em>seed</em> value = random number seed (positive integer)
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<em>f_max</em> value = upper cutoff frequency of the vibration spectrum (1/time units)
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<em>N_f</em> value = number of frequency bins (positive integer)
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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>fix 1 all nve
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fix 1 all qtb temp 110 damp 200 seed 35082 f_max 0.3 N_f 100 (liquid methane modeled with the REAX force field, real units)
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fix 2 all nph iso 1.01325 1.01325 1
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fix 2 all qtb temp 300 damp 1 seed 47508 f_max 120.0 N_f 100 (quartz modeled with the BKS force field, metal units)
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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>This command performs the quantum thermal bath scheme proposed by
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<a class="reference internal" href="#dammak"><span>(Dammak)</span></a> to include self-consistent quantum nuclear effects,
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when used in conjunction with the <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a> or <a class="reference internal" href="fix_nh.html"><em>fix nph</em></a> commands.</p>
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<p>Classical molecular dynamics simulation does not include any quantum
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nuclear effect. Quantum treatment of the vibrational modes will
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introduce zero point energy into the system, alter the energy power
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spectrum and bias the heat capacity from the classical limit. Missing
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all the quantum nuclear effects, classical MD cannot model systems at
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temperatures lower than their classical limits. This effect is
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especially important for materials with a large population of hydrogen
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atoms and thus higher classical limits.</p>
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<p>The equation of motion implemented by this command follows a Langevin
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form:</p>
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<center><font size="4"><i> m<sub>i</sub>a<sub>i</sub> = f<sub>i</sub>
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+ R<sub>i</sub> -
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m<sub>i</sub>γv<sub>i</sub>. </i></font></center><p>Here <i>m<sub>i</sub></i>, <i>a<sub>i</sub></i>, <i>f<sub>i</sub>
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</i>, <i>R<sub>i</sub></i>, <i>&gamma;</i> and <i>v<sub>i</sub> </i>
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represent mass, acceleration, force exerted by all other atoms, random
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force, frictional coefficient (the inverse of damping parameter damp),
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and velocity. The random force <i>R<sub>i</sub></i> is “colored” so
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that any vibrational mode with frequency <i>&omega;</i> will have a
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temperature-sensitive energy <i>&theta;</i>(<i>&omega;,T</i>) which
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resembles the energy expectation for a quantum harmonic oscillator
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with the same natural frequency:</p>
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<center><font size="4"> <i>θ</i>(<i>ω,T</i>) =
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ℏω/2 +
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ℏω[</i>exp(<i>ℏω/k</i><sub>B</sub><i>T</i>)<i>-1</i>]<i><sup>-1</sup></i>
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</font></center><p>To efficiently generate the random forces, we employ the method
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of <a class="reference internal" href="#barrat"><span>(Barrat)</span></a>, that circumvents the need to generate all
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random forces for all times before the simulation. The memory
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requirement of this approach is less demanding and independent
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of the simulation duration. Since the total random force <i>R</i><sub>tot</sub>
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does not necessarily vanish for a finite number of atoms,
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<i>R<sub>i</sub></i> is replaced by <i>R<sub>i</sub></i> - <i>R</i><sub>tot</sub>/<i>N</i><sub>tot</sub>
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to avoid collective motion of the system.</p>
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<p>The <em>temp</em> parameter sets the target quantum temperature. LAMMPS will
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still have an output temperature in its thermo style. That is the
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instantaneous classical temperature <i>T</i><sup>cl</sup> derived from
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the atom velocities at thermal equilibrium. A non-zero
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<i>T</i><sup>cl</sup> will be present even when the quantum
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temperature approaches zero. This is associated with zero-point energy
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at low temperatures.</p>
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<center><font size="4"> <i>T</i><sup>cl</sup> = ∑
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<i>m<sub>i</sub>v<sub>i</sub><sup>2</sup>/3Nk</i><sub>B</sub>
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</font></center><p>The <em>damp</em> parameter is specified in time units, and it equals the
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inverse of the frictional coefficient <i>&gamma;</i>. <i>&gamma;</i>
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should be as small as possible but slightly larger than the timescale
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of anharmonic coupling in the system which is about 10 ps to 100
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ps. When <i>&gamma;</i> is too large, it gives an energy spectrum that
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differs from the desired Bose-Einstein spectrum. When <i>&gamma;</i>
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is too small, the quantum thermal bath coupling to the system will be
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less significant than anharmonic effects, reducing to a classical
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limit. We find that setting <i>&gamma;</i> between 5 THz and 1 THz
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could be appropriate depending on the system.</p>
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<p>The random number <em>seed</em> is a positive integer used to initiate a
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Marsaglia random number generator. Each processor uses the input seed
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to generate its own unique seed and its own stream of random
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numbers. Thus the dynamics of the system will not be identical on two
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runs on different numbers of processors.</p>
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<p>The <em>f_max</em> parameter truncate the noise frequency domain so that
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vibrational modes with frequencies higher than <em>f_max</em> will not be
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modulated. If we denote &Delta;<i>t</i> as the time interval for the
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MD integration, <em>f_max</em> is always reset by the code to make
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<i>&alpha;</i> = (int)(2*f_max*&Delta;<i>t</i>)<sup><i>-1</i></sup> a
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positive integer and print out relative information. An appropriate
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value for the cutoff frequency <em>f_max</em> would be around 2~3
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<i>f</i><sub>D</sub>, where <i>f</i><sub>D</sub> is the Debye
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frequency.</p>
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<p>The <em>N_f</em> parameter is the frequency grid size, the number of points
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from 0 to <em>f_max</em> in the frequency domain that will be
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sampled. <i>3&times;2</i> <em>N_f</em> per-atom random numbers are required
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in the random force generation and there could be as many atoms as in
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the whole simulation that can migrate into every individual
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processor. A larger <em>N_f</em> provides a more accurate sampling of the
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spectrum while consumes more memory. With fixed <em>f_max</em> and
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<i>&gamma;</i>, <em>N_f</em> should be big enough to converge the classical
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temperature <i>T</i><sup>cl</sup> as a function of target quantum bath
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temperature. Memory usage per processor could be from 10 to 100
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Mbytes.</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">Unlike the <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a> command which performs
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Nose/Hoover thermostatting AND time integration, this fix does NOT
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perform time integration. It only modifies forces to a colored
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thermostat. Thus you must use a separate time integration fix, like
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<a class="reference internal" href="fix_nve.html"><em>fix nve</em></a> or <a class="reference internal" href="fix_nh.html"><em>fix nph</em></a> to actually update the
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velocities and positions of atoms (as shown in the
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examples). Likewise, this fix should not normally be used with other
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fixes or commands that also specify system temperatures , e.g. <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a> and <a class="reference internal" href="fix_temp_rescale.html"><em>fix temp/rescale</em></a>.</p>
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</div>
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<hr class="docutils" />
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<p><strong>Restart, fix_modify, output, run start/stop, minimizie info:</strong></p>
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<p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>. Because the state of the random number generator
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is not saved in restart files, this means you cannot do “exact”
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restarts with this fix. However, in a statistical sense, a restarted
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simulation should produce similar behaviors of the system.</p>
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<p>This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
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</div>
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<hr class="docutils" />
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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 fix style is part of the USER-QTB 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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<hr class="docutils" />
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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_nve.html"><em>fix nve</em></a>, <a class="reference internal" href="fix_nh.html"><em>fix nph</em></a>, <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a>, <a class="reference internal" href="fix_qbmsst.html"><em>fix qbmsst</em></a></p>
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</div>
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<hr class="docutils" />
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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 keyword defaults are temp = 300, damp = 1, seed = 880302,
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f_max=200.0 and N_f = 100.</p>
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<hr class="docutils" />
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<p id="dammak"><strong>(Dammak)</strong> Dammak, Chalopin, Laroche, Hayoun, and Greffet, Phys Rev
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Lett, 103, 190601 (2009).</p>
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<p id="barrat"><strong>(Barrat)</strong> Barrat and Rodney, J. Stat. Phys, 144, 679 (2011).</p>
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