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:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)

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fix ti/rs command :h3

[Syntax:]

fix ID group-ID ti/rs lambda_initial lambda_final t_switch t_equil keyword value ... :pre

ID, group-ID are documented in "fix"_fix.html command :ulb,l
ti/rs = style name of this fix command :l
lambda_initial/lambda_final = initial/final values of the coupling parameter :l
t_switch/t_equil = number of steps of the switching/equilibration procedure :l
keyword = {function} :l
  {function} value = function-ID
    function-ID = ID of the switching function (1, 2 or 3) :pre
:ule

[Example:]

fix ref all ti/rs 50.0 2000 1000 
fix vf vacancy ti/rs 10.0 70000 50000 function 2 :pre

[Description:]

This fix allows you to compute the free energy temperature dependence
by performing a thermodynamic integration procedure known as
Reversible Scaling "(de Koning99,"_#deKoning99 "de
Koning00a)"_#deKoning00a". The thermodynamic integration is performed
using the nonequilibrium method of Adiabatic Switching
"(Watanabe,"_#Watanabe "de Koning96)"_#deKoning96.

The forces on the atoms are dynamically scaled during the simulation,
the rescaling is done in the following manner:

:c,image(Eqs/fix_ti_rs_force.jpg)

where F_int is the total force on the atoms due to the interatomic
potential and lambda is the coupling parameter of the thermodynamic
integration.

The fix acts as follows: during the first {t_equil} steps after the
fix is defined the value of lambda is {lambda_initial} , this is the
period to equilibrate the system in the lambda = {lambda_initial}
state. After this the value of lambda changes continuously from
{lambda_initial} to {lambda_final} according to the function defined
using the keyword {function} (described below), this is done in
{t_switch} steps. Then comes the second equilibration period of
{t_equil} to equilibrate the system in the lambda = {lambda_final}
state. After that the switching back to the lambda = {lambda_initial}
state is done using {t_switch} timesteps and following the same
switching function. After this period the value of lambda is kept
equal to {lambda_initial} indefinitely or until a "unfix"_unfix.html
erase the fix.

The description of thermodynamic integration in both directions is
done in "de Koning00b"_#deKoning00b, the main reason is to try to
eliminate the dissipated heat due to the nonequilibrium process.

The {function} keyword allows the use of three different switching
rates. The option {1} results in a constant rescaling where the lambda
parameter changes at a constant rate during the switching time
according to the switching function

:c,image(Eqs/fix_ti_rs_function_1.jpg)

where tau is the scaled time variable t/t_switch. This switching
function has the characteristic that the temperature scaling is faster
at temperatures closer to the final temperature of the procedure. The
option number {2} performs the switching at a rate defined by the
following switching function

:c,image(Eqs/fix_ti_rs_function_2.jpg)

This switching function has the characteristic that the temperature
scaling occurs at a constant rate during all the procedure. The option
number {3} performs the switching at a rate defined by the following
switching function

:c,image(Eqs/fix_ti_rs_function_3.jpg)

This switching function has the characteristic that the temperature
scaling is faster at temperatures closer to the initial temperature of
the procedure.

An example script using this command is provided in the
examples/USER/misc/ti directory.

[Restart, fix_modify, output, run start/stop, minimize info:]

No information about this fix is written to "binary restart
files"_restart.html.

This fix computes a global vector quantitie which can be accessed by
various "output commands"_Section_howto.html#howto_15. The vector has
2 positions, the first one is the coupling parameter lambda and the
second one is the time derivative of lambda. The scalar and vector
values calculated by this fix are "extensive".

No parameter of this fix can be used with the {start/stop} keywords of
the "run"_run.html command.

The forces due to this fix are imposed during an energy minimization,
invoked by the "minimize"_minimize.html command.

[Related commands:]

"fix ti/spring"_fix_ti_spring.html

[Restrictions:]

This command is part of the USER-MISC package.  It is only enabled if
LAMMPS was built with those packages.  See the "Making
LAMMPS"_Section_start.html#start_3 section for more info.

[Default:]

The keyword default is function = 1.

:line

:link(deKoning99)
[(de Koning 99)] M. de Koning, A. Antonelli and S. Yip, Phys Rev Lett, 83, 3973 (1999).

:link(Watanabe)
[(Watanabe)] M. Watanabe and W. P. Reinhardt, Phys Rev Lett, 65, 3301 (1990).

:link(deKoning96)
[(de Koning 96)] M. de Koning and A. Antonelli, Phys Rev E, 53, 465 (1996).

:link(deKoning00a)
[(de Koning 00a)] M. de Koning, A. Antonelli and S. Yip, J Chem Phys, 115, 11025 (2000).

:link(deKoning00b)
[(de Koning 00b)] M. de Koning et al., Computing in Science & Engineering, 2, 88 (2000).
