How to add temperature at some rate

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Even though Berendsen thermostat is not good enough,why did so many papers
choose it??

i can only speculate that too many people don't spend the
time thinking about about how the thermostat works and
*why* it is so bad for their specific purpose.

a berendsen thermostat is trivial to implement (especially
compared to nose-hoover chains) and for well equilibrated
homogeneous bulk liquids, for which it was originally conceived,
its bad side effects don't show, if the system is large enough.

the second thing about berendsen is that it is easy to control,
i.e. you can easily enforce the total temperature that you want
to see. however, that does not mean, that your system is in
the state that you want it to be in. in most cases, it actually
does the opposite of what would be desirable, especially when
trying to heat up or cool down a system. the only thing that is
worse is temperature rescaling (which on top of having the
same problems as berendsen, also gives your system also
a "kick" every time the temperature is rescaled).

what you want when doing these kind of operations, is to
reach representative sampling of relevant statistical mechanical
states and that has as a prerequisite that you have equipartitioning
of the kinetic energy. fix langevin helps with the latter, through its
dissipative term, but it also applies a temperature dependent
bias that would need to be adjusted for. using fix nvt (with a long
enough chain) on the other hand will help with the sampling,
but its mechanism is not made to quickly exchange energy.
fix berendsen only provides a quick exchange of the energy,
but in the process worsens the distribution of states, so that
your sampling is going down the drain. whenever you do
velocity scaling across the board, you make atoms that are
already fast, faster and atoms that are slow, relatively seen
slower.

as you can hopefully see from these simplified back of the
envelope type considerations, there is a bit of a statistical
mechanical background required to fully comprehend what
the implications of the choices of integrator and thermostat
are, and - to come back to your original question - many
folks seem to "just want to get the simulation done" and
you can blame referees for letting them get away with it.
but then again, if the publication is not placed in a physical
chemistry or chemical physics focused journal, the reviewers
may not have that deep a background knowledge, too.

bottom line: sometimes people get away with doing a bad
thing and sometimes it doesn't matter so much. but at
the very least you should take a second look and see
if you can make sense of the advice been given to you.

axel.