<li><pclass="first">zero or more keyword/value pairs may be appended</p>
</li>
<li><pclass="first">keyword = <em>q</em> or <em>mu</em> or <em>p0</em> or <em>v0</em> or <em>e0</em> or <em>tscale</em> or <em>damp</em> or <em>seed</em>or <em>f_max</em> or <em>N_f</em> or <em>eta</em> or <em>beta</em> or <em>T_init</em></p>
<preclass="literal-block">
<em>q</em> value = cell mass-like parameter (mass^2/distance^4 units)
<em>mu</em> value = artificial viscosity (mass/distance/time units)
<em>p0</em> value = initial pressure in the shock equations (pressure units)
<em>v0</em> value = initial simulation cell volume in the shock equations (distance^3 units)
<em>e0</em> value = initial total energy (energy units)
<em>tscale</em> value = reduction in initial temperature (unitless fraction between 0.0 and 1.0)
<em>damp</em> value = damping parameter (time units) inverse of friction <i>&gamma;</i>
<em>seed</em> value = random number seed (positive integer)
<em>f_max</em> value = upper cutoff frequency of the vibration spectrum (1/time units)
<em>N_f</em> value = number of frequency bins (positive integer)
<em>eta</em> value = coupling constant between the shock system and the quantum thermal bath (positive unitless)
<em>beta</em> value = the quantum temperature is updated every beta time steps (positive integer)
<em>T_init</em> value = quantum temperature for the initial state (temperature units)
</pre>
</li>
</ul>
</div>
<divclass="section"id="examples">
<h2>Examples</h2>
<preclass="literal-block">
fix 1 all qbmsst z 0.122 q 25 mu 0.9 tscale 0.01 damp 200 seed 35082 f_max 0.3 N_f 100 eta 1 beta 400 T_init 110 (liquid methane modeled with the REAX force field, real units)
fix 2 all qbmsst z 72 q 40 tscale 0.05 damp 1 seed 47508 f_max 120.0 N_f 100 eta 1.0 beta 500 T_init 300 (quartz modeled with the BKS force field, metal units)
</pre>
<p>Two example input scripts are given, including shocked alpha quartz
and shocked liquid methane. The input script first equilibrate an
initial state with the quantum thermal bath at the target temperature
and then apply the qbmsst to simulate shock compression with quantum
nuclear correction. The following two figures plot related quantities
<p>The fix qbmsst command couples the shock system to a quantum thermal
bath with a rate that is proportional to the change of the total
energy of the shock system, <i>etot</i> - <i>etot</i><sub>0</sub>.
Here <i>etot</i> consists of both the system energy and a thermal
term, see <aclass="reference internal"href="#qi"><spanclass="std std-ref">(Qi)</span></a>, and <i>etot</i><sub>0</sub> = <em>e0</em> is the
initial total energy.</p>
<p>The <em>eta</em> (<i>&eta;</i>) parameter is a unitless coupling constant
between the shock system and the quantum thermal bath. A small <em>eta</em>
value cannot adjust the quantum temperature fast enough during the
temperature ramping period of shock compression while large <em>eta</em>
leads to big temperature oscillation. A value of <em>eta</em> between 0.3 and
1 is usually appropriate for simulating most systems under shock
compression. We observe that different values of <em>eta</em> lead to almost
the same final thermodynamic state behind the shock, as expected.</p>
<p>The quantum temperature is updated every <em>beta</em> (<i>&beta;</i>) steps
with an integration time interval <em>beta</em> times longer than the
simulation time step. In that case, <i>etot</i> is taken as its
average over the past <em>beta</em> steps. The temperature of the quantum
thermal bath <i>T</i><sup>qm</sup> changes dynamically according to
the following equation where &Delta;<i>t</i> is the MD time step and
<i>&gamma;</i> is the friction constant which is equal to the inverse
<li><em>dhugoniot</em> is the departure from the Hugoniot (temperature units).</li>
<li><em>drayleigh</em> is the departure from the Rayleigh line (pressure units).</li>
<li><em>lagrangian_speed</em> is the laboratory-frame Lagrangian speed (particle velocity) of the computational cell (velocity units).</li>
<li><em>lagrangian_position</em> is the computational cell position in the reference frame moving at the shock speed. This is the distance of the computational cell behind the shock front.</li>
<li><em>quantum_temperature</em> is the temperature of the quantum thermal bath <i>T</i><sup>qm</sup>.</li>
</ol>
<p>To print these quantities to the log file with descriptive column
headers, the following LAMMPS commands are suggested. Here the
<aclass="reference internal"href="fix_modify.html"><spanclass="doc">fix_modify</span></a> energy command is also enabled to allow
the thermo keyword <em>etotal</em> to print the quantity <i>etot</i>. See
also the <aclass="reference internal"href="thermo_style.html"><spanclass="doc">thermo_style</span></a> command.</p>
<preclass="literal-block">
fix fix_id all msst z
fix_modify fix_id energy yes
variable dhug equal f_fix_id[1]
variable dray equal f_fix_id[2]
variable lgr_vel equal f_fix_id[3]
variable lgr_pos equal f_fix_id[4]
variable T_qm equal f_fix_id[5]
thermo_style custom step temp ke pe lz pzz etotal v_dhug v_dray v_lgr_vel v_lgr_pos v_T_qm f_fix_id
</pre>
<p>The global scalar under the entry f_fix_id is the quantity of thermo
energy as an extra part of <i>etot</i>. This global scalar and the
vector of 5 quantities can be accessed by various <aclass="reference internal"href="Section_howto.html#howto-15"><spanclass="std std-ref">output commands</span></a>. It is worth noting that the
temp keyword under the <aclass="reference internal"href="thermo_style.html"><spanclass="doc">thermo_style</span></a> command print
the instantaneous classical temperature <i>T</i><sup>cl</sup> as
described in the command <aclass="reference internal"href="fix_qtb.html"><spanclass="doc">fix qtb</span></a>.</p>
</div>
<hrclass="docutils"/>
<divclass="section"id="restrictions">
<h2>Restrictions</h2>
<p>This fix style is part of the USER-QTB package. It is only enabled if
LAMMPS was built with that package. See the <aclass="reference internal"href="Section_start.html#start-3"><spanclass="std std-ref">Making LAMMPS</span></a> section for more info.</p>
<p>All cell dimensions must be periodic. This fix can not be used with a
triclinic cell. The QBMSST fix has been tested only for the group-ID
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