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

Michel Cuendet michel.cuendet at isb-sib.ch
Wed Jul 23 15:50:27 CEST 2008

Hi all,

One of the conceptual difference between Berendsen and Nose-Hoover (NH), 
is the following. NH is basically a second order relaxation to the 
target temperature, which implies an oscillatory behavior. Berendsen is 
a first order relaxation (exponential type of behavior). This is 
preferable when the initial temperature is far from the target 
temperature, in which case NH is likely to produce large oscillations 
and, in general, take longer to equilibrate. Hence the practice to use 
Berendsen for the first part of the equilibration, and NH for production.

There are still papers published on the subject in the "alive" 
literature. For example there is an analysis of the Berendsen dynamics in

Morishita, JCP 113 (8) : 2976 (2000)

In short, he finds approximate expressions for the configurational part 
of the state distribution function. It essentially varies between 
canonical for exceedingly small time constants (of the order of the 
timestep) to microcanonical for very large time constants. The 
distribution of momenta remains unknown.

In addition to the average temperature, the temperature fluctuations 
expected for the NVT ensemble must be reproduced in the simulation. 
Nose-Hoover was shown to do this correctly. This could be important when 
studying the stability of a conformation for example.

Now concerning Chris' question:
chris.neale at utoronto.ca wrote:
> Have you seen any information to suggest that this is actually a 
> non-trivial conce"rn? That is, given static point charges, an 
> empirical LJ force, short cutoffs, etc., do you believe that the 
> application of nose-hoover, berendsen, or even the arbitrary velocity 
> rescaling significantly degrades the quality of the obtained dynamics?
There are two aspects here: (a) point charges and LJ force, which 
constitute the physical model, and (b) the cutoffs and such, which are 
simulation artefacts and disrupt the physics of the model (by allowing 
creation of energy, etc...). My opinion is that, given a physical model 
(even approximate), one should simulate the dynamics as accurately as 
possible, in order to produce the thermodynamical ensemble corresponding 
to the underlying physical model. Before plugging in the thermostat, one 
should check that the simulation conserves energy "not too bad"(using 
PME or switch functions, etc...). Now if there is still an energy drift, 
the thermostat will absorb the excess energy, and the system will end up 
in a non-equilibrium steady state, with a heat well (cutoffs, etc) and a 
heat sink (thermostat). The good side is that the NH thermostat was 
shown (by Hoover himself) to produce a stationary canonical distribution 
even in a non-equilibrium case.

Sorry for the long email :)



Michel Cuendet, Ph.D
Molecular Modeling Group
Swiss Institute of Bioinformatics
CH-1015 Lausanne, Switzerland

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