Re: problem in fitting Maxwell-Boltzmann distribution

From: Peter Freddolino (petefred_at_ks.uiuc.edu)
Date: Thu Jan 15 2009 - 08:22:19 CST

Did you use the correct number of degrees of freedom in your analysis?
You mentioned that you use rigidbonds; a rigid water molecule has only 6
degrees of freedom, and every bond involving a hydrogen in your solute
is also constrained (if you're using rigidbonds all) and removes a
degree of freedom. You can find a count of the number of degrees of
Best,
Peter

> You are right about the tutorial (actually I am using the Windows
> version). I took for granted what was written on the list also due to
> the fact that with the ^3/2 factor the fit was emproved a little bit.
> With the correct ^3 factor the fitted temperature is only 199 K ! And
> now also the theoretical M-B distribution peaks at over 1,0 probability
> ! Of course I have normalized the frequency by dividing the counts in
> every bin to the total area under the histogram, as explained in the
> tutorial.
>
> Best regards
>
>
> ------------------------------------------------------------------------
>
> CC: namd-l_at_ks.uiuc.edu
> From: gumbart_at_ks.uiuc.edu
> Subject: Re: namd-l: problem in fitting Maxwell-Boltzmann distribution
> Date: Wed, 14 Jan 2009 19:00:12 -0600
> To: vchindea_at_hotmail.com
>
> 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