# Re: AMBER: Energy Spread using GB & Langevin Dynamics (NAB)

From: David A. Case <case.scripps.edu>
Date: Tue, 15 May 2007 09:03:52 -0700

On Tue, May 15, 2007, Andreas Svrcek-Seiler wrote:

> >Hi, I've run some MD simulations (simulated annealing from 500 --> 400
> >--> 300 with 100,000 steps per temperature), and realised that in my
> >MD run, the energy and temperature fluctuations are rather large. (Total
> >energy as
> >given in the "MD:" row). Energy fluctuations are ~80kcal/mol, while
> >temperature fluctuations are ~50K.

> ...When using Langevin Dynamics, you're simulating a canonical ensemble.
> For this, some algebra gives a total Energy variance:
> Var(E) = k T^2 C_v.
> (k...Boltzmann constant, T temperature, C_v heat capacity at constant
> volume)
> Combining that with the equipartition theorem (which gives a heat capacity
> of k/2 per degree of freedom under conditions not exactly fulfilled in
> MD), this gives
> Var(E) ~= k^2 T^2 * (1/2) * 3N (for N atoms).
>
> So you'd expect temperature fuluctuations of about
> <E> +- kT * sqrt((3/2)*N).

This not quite correct. The mean square fluctuation in temperature is:

<(deltaT)^2> = kT^2/C_v

Setting C_v = 3Nk/2 gives:

<(deltaT)^2> = 2T^2/3N or <(deltaT)^2>^1/2 = T sqrt(2/3N)

Note that the temperature fluctuations go *down* as the system size increases,
not the other way around.

The original poster had a system where 255 atoms were moving, running at a
temperature of 500K. For those conditions, one would exptect rms temperature
fluctuations of 25 K or so.

Using the formulas here (http://amber.ch.ic.ac.uk/archive/200608/0329.html),
and assuming a moving mass of about 175 amu, gives a rms temperature
fluctuation of about 30 K. (This uses a different estimate of the heat
capacity.)

So, the reports in the original post are not far from what one would expect.
For a small protein in explicit water (say 25,000) atoms, the expected rms
temperature fluctuation is more like 1.5 K (at T = 300).

...hope this helps....dac

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Received on Wed May 16 2007 - 06:07:33 PDT
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