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doc/html/_sources/fix_ti_spring.txt
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doc/html/_sources/fix_ti_spring.txt
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.. index:: fix ti/spring
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fix ti/spring command
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=====================
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Syntax
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""""""
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.. parsed-literal::
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fix ID group-ID ti/spring K t_switch t_equil keyword value ...
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* ID, group-ID are documented in :doc:`fix <fix>` command
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* ti/spring = style name of this fix command
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* K = spring constant (force/distance units)
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* t_switch/t_equil = number of steps of the switching/equilibration procedure
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* zero or more keyword/value pairs may be appended to args
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* keyword = *function*
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.. parsed-literal::
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*function* value = function-ID
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function-ID = ID of the switching function (1 or 2)
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**Example:**
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.. parsed-literal::
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fix ref all ti/spring 50.0 2000 1000 function 2
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Description
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"""""""""""
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This fix allows you to compute the free energy of solids by performing
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a thermodynamic integration between the solid of interest and an
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Einstein crystal :ref:`(Frenkel) <Frenkel>`. The thermodynamic integration
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is performed using the nonequilibrium method of Adiabatic Switching
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:ref:`(Watanabe, <Watanabe>` :ref:`de Koning96) <deKoning96>`.
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A spring force is applied independently to each atom in the group to
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tether it to its initial position. The initial position for each atom
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is its location at the time the fix command was issued. More details
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about the springs are available in :doc:`fix spring/self <fix_spring_self>`. The forces on the atoms are
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dynamically scaled during the simulation, the rescaling is done in the
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following manner:
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.. image:: Eqs/fix_ti_spring_force.jpg
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:align: center
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where F_harm is the force due to the springs, F_solid is the total
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force on the atoms due to the interatomic potential and lambda is the
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coupling parameter of the thermodynamic integration.
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The fix acts as follows: during the first *t_equil* steps after the
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fix is defined the value of lambda is zero, this is the period to
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equilibrate the system in the lambda = 0 state. After this the value
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of lambda changes continuously from 0 to 1 according to the function
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defined using the keyword *function* (described below), this is done
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in *t_switch* steps. Then comes the second equilibration period of
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*t_equil* to equilibrate the system in the lambda = 1 state. After
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that the switching back to the lambda = 0 state is made using
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*t_switch* timesteps and following the same switching function. After
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this period the value of lambda is kept equal to zero and the fix has
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no action in the dynamics of the system anymore.
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The description of thermodynamic integration in both directions is
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done in :ref:`de Koning97 <deKoning97>`, the main reason is to try to
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eliminate the dissipated heat due to the nonequilibrium process.
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The *function* keyword allows the use of two different switching
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rates, the option *1* results in a constant rescaling where the lambda
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parameter changes at a constant rate during the switching time
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according to the switching function
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.. image:: Eqs/fix_ti_spring_function_1.jpg
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:align: center
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where tau is the scaled time variable t/t_switch. The option number
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*2* performs the switching at a rate defined by the following
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switching function
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.. image:: Eqs/fix_ti_spring_function_2.jpg
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:align: center
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This function has zero slope as lambda approaches its extreme values
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(0 and 1), according to (:ref:`de Koning96) <deKoning96>` this results in
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smaller fluctuations on the integral to be computed on the
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thermodynamic integration.
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.. note::
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It is importante to keep the center of mass fixed during the
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thermodynamic integration, a non-zero total velocity will result in
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divergencies during the integration due to the fact that the atoms are
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'attatched' to its equilibrium positions by the Einstein
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crystal. Check the option *zero* of `fix langevin <fix_langevin_html>`_
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and :doc:`velocity <velocity>`. The use of the Nose-Hoover thermostat
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(:doc:`fix nvt <fix_nh>`) is NOT recommended due to its well documented
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issues with the canonical sampling of harmonic degrees of freedom
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(notice that the *chain* option will NOT solve this problem). The
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Langevin thermostat (`fix langevin <fix_langevin.html">`_) works fine.
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Restart, fix_modify, output, run start/stop, minimize info
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""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
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This fix writes the original coordinates of tethered atoms to :doc:`binary restart files <restart>`, so that the spring effect will be the
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same in a restarted simulation. See the :doc:`read restart <read_restart>` command for info on how to re-specify a fix
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in an input script that reads a restart file, so that the operation of
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the fix continues in an uninterrupted fashion.
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The :doc:`fix modify <fix_modify>` *energy* option is supported by this
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fix to add the energy stored in the per-atom springs to the system's
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potential energy as part of :doc:`thermodynamic output <thermo_style>`.
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This fix computes a global scalar and a global vector quantities which
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can be accessed by various :ref:`output commands <howto_15>`. The scalar is an energy which
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is the sum of the spring energy for each atom, where the per-atom
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energy is 0.5 * K * r^2. The vector has 2 positions, the first one is
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the coupling parameter lambda and the second one is the time
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derivative of lambda. The scalar and vector values calculated by this
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fix are "extensive".
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No parameter of this fix can be used with the *start/stop* keywords of
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the :doc:`run <run>` command.
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The forces due to this fix are imposed during an energy minimization,
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invoked by the :doc:`minimize <minimize>` command.
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.. note::
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If you want the per-atom spring energy to be included in the
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total potential energy of the system (the quantity being minimized),
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you MUST enable the :doc:`fix modify <fix_modify>` *energy* option for
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this fix.
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An example script using this command is provided in the
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examples/USER/misc/ti directory.
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Related commands
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""""""""""""""""
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:doc:`fix spring <fix_spring>`, :doc:`fix ti/rs <fix_ti_rs>`
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Restrictions
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""""""""""""
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This command is part of the USER-MISC package. It is only enabled if
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LAMMPS was built with those packages. See the :ref:`Making LAMMPS <start_3>` section for more info.
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Default
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"""""""
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The keyword default is function = 1.
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----------
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.. _Frenkel:
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**(Frenkel)** Daan Frenkel and Anthony J. C. Ladd, J. Chem. Phys. 81, 3188
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(1984).
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.. _Watanabe:
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**(Watanabe)** M. Watanabe and W. P. Reinhardt, Phys Rev Lett, 65, 3301 (1990).
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.. _deKoning96:
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**(de Koning 96)** M. de Koning and A. Antonelli, Phys Rev E, 53, 465 (1996).
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.. _deKoning97:
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**(de Koning 97)** M. de Koning and A. Antonelli, Phys Rev B, 55, 735 (1997).
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.. _lws: http://lammps.sandia.gov
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.. _ld: Manual.html
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.. _lc: Section_commands.html#comm
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