# Re: problem in fitting Maxwell-Boltzmann distribution

From: JC Gumbart (gumbart_at_ks.uiuc.edu)
Date: Wed Jan 14 2009 - 19:00:12 CST

Actually the tutorial is not wrong. In step 20 on page 40 of the
current Unix/Mac version of the NAMD tutorial, there is an a0^3,
where a0 = kbT. However, this a0^3 is under the square root along
with Pi, making it 3/2 overall. Will changing this correct your fit?

Also, did you normalize your distribution? This is an option in the
Histogram window of xmgrace. Not having done that may explain why
you get values greater than 1.

On Jan 14, 2009, at 5:08 PM, CHINDEA Vlad wrote:

> Hi everybody
>
> I am doing an MD of a protein in a water box with NPT conditions
> (310 K temperature). In order to check the sanity of the simulation
> I have done a temperature estimation by fitting Maxwell-Boltzmann
> distribution to the equilibrated velocity data as explained in the
> tutorial, but although the temperature reported in the log file
> looked quite OK (305-313 K) the result obtained by fitting was just
> 254 K ! What is more strange is that the peak of the kinetic energy
> distribution is higher then 1 (about 1,2-1,3) which is
> statistically (and physically) impossible. Since the initial run
> was just 24 ps I though that maybe I did not equilibrated the
> system enaugh so I restarted the simulation for another 30 ps, but
> the result was about the same both in fitted temperature (251 K)
> and distribution peak. As suggested inhttp://www.ks.uiuc.edu/
> Research/namd/mailing_list/namd-l/1354.html I have corrected also
> the mathematical expresion of the distribution from (kT)^3 (as
> shown in the tutorial) to (kT)^3/2.
>
> The step size was 2 fs and RigidBonds was on. Is it possible that
> this might have such a deleteriouse effect on the fit due to the
> missing degrees of freedom ?
>
> I understand that I will never get the expected temperature due to
> the finite size of the system but the difference from 250 to 310 K
> seems quite large to me. Please let me know if you need anything
> else in order to see what might be wrong.
>
> Many thanks and kind regards