[gmx-users] Question about Berendsen thermostat and Nose-Hoover temp coupling

David Osguthorpe david.osguthorpe at gmail.com
Tue Jul 22 22:46:36 CEST 2008

On Mon, Jul 21, 2008 at 11:46:00PM -0400, Justin A. Lemkul wrote:
> I too rely heavily on the Berendsen methods for T- and P-coupling, and have 
> always found them satisfactory.  I have not seen much beyond the casual 
> references to the fact that N-H T-coupling and Parrinello-Rahman P-coupling 
> are superior in terms of membrane simulations.  I have tried both, and have 
> found both setups to be equally reasonable in their results.  It seems, 
> overall, that Nose-Hoover schemes are often applied using NAMD and CHARMM 
> software.  I don't know if this choice is motivated by the software, or the 
> force fields used.
> There are a few casual references to Berendsen being less than optimal in 
> the literature and in archived presentation materials (which I can probably 
> unearth if I can recall my Googling :).

In an attempt to correct some mis-information that seems to exist here.

The question is whether you want to do science or to play.

There are extensive references from the 80s as to why the Berendsen thermostat is invalid
(unfortunately probably in the "lost" literature ie. that literature only available
in paper form in those weird institutions called libraries)

Hoover and others e.g. Andersen (J.Chem.Phys. 72, 2384, 1980) developed thermostats and barostats
that they mathematically proved lead to NVT or NPT averages over long timescales
(i.e. not by running simulations)
no such proof exists for the Berendsen thermostat - nor even which ensemble long time averages belong to
- it is  a simple extension of the early arbitrary velocity scaling that was used in dynamics
programs - hence it is scientifically strictly "invalid" and lead to the "less than optimal" references.
- this is probably why CHARMM and NAMD use Nose-Hoover - it certainly has nothing to do with force fields

You should also try and get a copy of the book Computer Simulation of Liquids by Allen and Tildesley 1987
on page 232 it discusses the difference between the Berendsen and Hoover thermostats
- essentially in the  Berendsen thermostat the velocity scale factor directly depends on the current
temperature difference whereas for the Hoover its the rate of change with time (ie. time derivative)
of the velocity scale factor that depends on the current temperature difference

by the way it is also true that if you use a thermostat or barostat then although long time averages
are equivalent to averages in the NVT or NPT ensemble strictly the dynamics is no longer valid as
a Newtonian trajectory so you should not derive dynamic properties from such trajectories.

This is from actually reading a lot of this literature at the time when the first comments were
made about the Berendsen thermostat.


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