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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

Date: Tue, 15 May 2007 09:03:52 -0700

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

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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