forked from lijiext/lammps
195 lines
8.3 KiB
HTML
195 lines
8.3 KiB
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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<HR>
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<H3>fix qtb command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>fix ID group-ID qtb keyword value ...
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</PRE>
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<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
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<LI>qtb = style name of this fix
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<LI>zero or more keyword/value pairs may be appended
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<LI>keyword = <I>temp</I> or <I>damp</I> or <I>seed</I> or <I>f_max</I> or <I>N_f</I>
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<PRE> <I>temp</I> value = target quantum temperature (temperature units)
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<I>damp</I> value = damping parameter (time units) inverse of friction <i>&gamma</i>;
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<I>seed</I> value = random number seed (positive integer)
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<I>f_max</I> value = upper cutoff frequency of the vibration spectrum (1/time units)
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<I>N_f</I> value = number of frequency bins (positive integer)
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</PRE>
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</UL>
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<P><B>Examples:</B>
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</P>
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<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>
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<P><B>Description:</B>
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</P>
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<P>This command performs the quantum thermal bath scheme proposed by
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<A HREF = "#Dammak">(Dammak)</A> to include self-consistent quantum nuclear effects,
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when used in conjunction with the <A HREF = "fix_nve.html">fix nve</A> or <A HREF = "fix_nh.html">fix
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nph</A> commands.
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</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.
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</P>
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<P>The equation of motion implemented by this command follows a Langevin
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form:
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</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>
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<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>γ</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>ω</i> will have a
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temperature-sensitive energy <i>θ</i>(<i>ω,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:
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</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>
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<P>To efficiently generate the random forces, we employ the method
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of <A HREF = "#Barrat">(Barrat)</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.
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</P>
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<P>The <I>temp</I> 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.
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</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>
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<P>The <I>damp</I> parameter is specified in time units, and it equals the
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inverse of the frictional coefficient <i>γ</i>. <i>γ</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>γ</i> is too large, it gives an energy spectrum that
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differs from the desired Bose-Einstein spectrum. When <i>γ</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>γ</i> between 5 THz and 1 THz
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could be appropriate depending on the system.
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</P>
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<P>The random number <I>seed</I> 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.
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</P>
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<P>The <I>f_max</I> parameter truncate the noise frequency domain so that
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vibrational modes with frequencies higher than <I>f_max</I> will not be
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modulated. If we denote Δ<i>t</i> as the time interval for the
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MD integration, <I>f_max</I> is always reset by the code to make
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<i>α</i> = (int)(2<I>f_max</I>Δ<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 <I>f_max</I> 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.
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</P>
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<P>The <I>N_f</I> parameter is the frequency grid size, the number of points
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from 0 to <I>f_max</I> in the frequency domain that will be
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sampled. <i>3×2</i> <I>N_f</I> 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 <I>N_f</I> provides a more accurate sampling of the
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spectrum while consumes more memory. With fixed <I>f_max</I> and
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<i>γ</i>, <I>N_f</I> 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.
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</P>
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<P>IMPORTANT NOTE: Unlike the <A HREF = "fix_nh.html">fix nvt</A> command which
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performs Nose/Hoover thermostatting AND time integration, this fix
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does NOT perform time integration. It only modifies forces to a
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colored thermostat. Thus you must use a separate time integration fix,
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like <A HREF = "fix_nve.html">fix nve</A> or <A HREF = "fix_nh.html">fix nph</A> to actually
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update the 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 HREF = "fix_nh.html">fix
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nvt</A> and <A HREF = "fix_temp_rescale.html">fix temp/rescale</A>.
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</P>
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<HR>
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<P><B>Restart, fix_modify, output, run start/stop, minimizie info:</B>
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</P>
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<P>No information about this fix is written to <A HREF = "restart.html">binary restart
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files</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.
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</P>
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<P>This fix is not invoked during <A HREF = "minimize.html">energy minimization</A>.
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</P>
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<HR>
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<P><B>Restrictions:</B>
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</P>
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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 HREF = "Section_start.html#start_3">Making
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LAMMPS</A> section for more info.
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</P>
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<HR>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "fix_nve.html">fix nve</A>, <A HREF = "fix_nh.html">fix nph</A>, <A HREF = "fix_langevin.html">fix
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langevin</A>, <A HREF = "fix_qbmsst.html">fix qbmsst</A>
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</P>
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<HR>
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<P><B>Default:</B>
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</P>
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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.
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</P>
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<HR>
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<A NAME = "Dammak"></A>
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<P><B>(Dammak)</B> Dammak, Chalopin, Laroche, Hayoun, and Greffet, Phys Rev
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Lett, 103, 190601 (2009).
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</P>
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<A NAME = "Barrat"></A>
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<P><B>(Barrat)</B> Barrat and Rodney, J. Stat. Phys, 144, 679 (2011).
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</P>
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</HTML>
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