[gmx-users] REMD: average potential energy as a function of temperatue

[Robert Johnson]

Hello Pascal,
I'm not sure I can really comment on (1), but the reason why your
energy gap decreases in (2) is because the energy fluctuations in your
system increase as you raise the temperature. For example, at low
temperatures your potential energy distributions will be sharply
peaked about the average value. However, as you increase the
temperature, the peak will broaden because of the increased thermal
fluctuations. As a result, you will have more overlap between your
potential energy distributions at higher temperature.

If you would like a constant acceptance ratio for your replicas, a
linear temperature distribution is not going to work (for the reason I
just described). For a constant acceptance ratio, the temperatures
should be exponentially distributed. In fact, the way I choose my
temperatures is to fit them to the following functional form: T(n) = A
+ B exp(n/C) where n is the nth replica. What you can do is vary the
temperature of a few of your low temperature replicas until you get
the correct acceptance ratio and then do the same thing at higher
temperature. Then you can fit the curve to that. It's kinda a quick
and dirty method, however I have found that it works pretty well. It
enabled me to get pretty much constant acceptance ratios (within a 1-3
percent) across the entire temperature range of a 64 replica REMD
simulation.
Bob


On Tue, May 6, 2008 at 9:50 AM,  <pascal.baillod at epfl.ch> wrote:
> Dear community,
>
>  I am performing some REMD tests with the trp-cage peptide. In order to figure
>  out the optimal temperature distribution ensuring similar exchange probabilities
>  at every temperature, I have performed short MD runs at increasing temperatures,
>  with a run every 5K from 300K to 500K. If I plot the average potential energy as
>  a function of temperature, I obtain the following trend:
>
>  1) For NPT, the gap between average potential energies progressively increases
>  with equal increments of temperature.
>
>  2) For NVT, the gap between average potential energies progressively decreases
>  with equal increments temperature.
>
>  I also read a very interesting paper on this issue:
>  Alexandra Patriksson and David van der Spoel, A temperature predictor for
>  parallel tempering simulations Phys. Chem. Chem. Phys., 10 pp. 2073-2077 (2008)
>
>  The temperature predictor works with a set of parameters obtained from a number
>  of simulations of different proteins at different temperatures. Among the test
>  proteins, the Trp-cage peptide is also used, but the authors describe a linear
>  function for average potential energy as a function of temperature. However,
>  this result was obtained in the 284 to the 330K range, and my results also
>  appear linear in this domain.
>
>  As far as I understand, potential energy should scale with the number of degrees
>  of freedom f and temperature T:
>
>  Epot_{avg} ~= f k_B T    (k_B is Boltzmann's constant)
>
>  Could anybody explain to me why the relation I obtain in 1) and 2) here above
>  are not linear? Is the linearity broken from a higher threshhold temperature,
>  for which force field parameters are not designed, onwards?
>
>  Thanks a lot in advance!!
>
>  Pascal
>
>
>
>  *******************************************************************************
>  Pascal Baillod (PhD student)
>  *******************************************************************************
>  Swiss Federal Institute of Technology EPFL              Tel: +41-(0)21-693-0322
>  Institute of Chemical Sciences and Engineering ,        Fax: +41-(0)21-693-0320
>  Laboratory of Computational Chemistry and Biochemistry  pascal.baillod at epfl.ch
>  Room BCH 4121, Avenue Forel,                            http://lcbcpc21.epfl.ch
>  CH-1015 Lausanne
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