[gmx-users] Re: Heat capacity for infinite systems
obrien at CLEMSON.EDU
Mon Sep 6 01:57:24 CEST 2004
>Date: Thu, 26 Aug 2004 00:36:04 +0200
>From: David <spoel at xray.bmc.uu.se>
>Subject: Re: [gmx-users] Heat capacity for infinite systems
>To: Discussion list for GROMACS users <gmx-users at gromacs.org>
>Message-ID: <1093473364.5091.2.camel at h107n2fls34o1123.telia.com>
>On Thu, 2004-08-26 at 00:02, Chris O'Brien wrote:
> > Dear gmx-users,
> > I am simulating a system of 32 infinite (pbc=full) crystalline polymer
> > chains, and I am wondering what basis g_energy uses for its calculation of
> > the heat capacity. I obtain a value of 12.5 J/mol/K, and I would like to
> > compare it to a literature value with units of J/kg/K but I am not sure
> > to make the conversion. What role (if any) does the option -nmol play in
> > the calculation of Cv?
>This is crucial, however for polymers the definition of a molecule maybe
>not so clear (but that's your problem). For small molecules you need to
>The equations for Cv come from Allen and TIldesley and are based on the
>fluctuation of the temperature. If you have Berendsen coupling your
>fluctuations are damped and you will get a too low Cv. If you have
>Nose-Hoover coupling you have other artefacts. Best is to measure
>without T coupling.
> > Also, what does the (factor = xxxxx) indicate after the value of the heat
> > capacity?
>IIRC that's an intermediate result. Forget it. Of course you can check
>the source code.
> > Thank you,
> > Chris O'Brien
> > Department of Chemical Engineering
> > Clemson University
> > Clemson, SC 29634-0909
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>David van der Spoel, PhD, Assoc. Prof., Molecular Biophysics group,
>Dept. of Cell and Molecular Biology, Uppsala University.
>Husargatan 3, Box 596, 75124 Uppsala, Sweden
>phone: 46 18 471 4205 fax: 46 18 511 755
>spoel at xray.bmc.uu.se spoel at gromacs.org http://xray.bmc.uu.se/~spoel
Thank you for answering David.
After looking at the source code for the heat capacity calculations and
comparing that expression to equation 2.82 in A&T's text, I have further
questions. First, based upon my derivations, I can't get the gromacs
expression for Cv to match that of A&T.
Gromacs: cv = 3*Na*kT^2/(2T^2 - 3N*nmol*varT)
A&T for microcanonical ensemble: Cv = 3NkT^2/(2T^2 - 3NvarT)
The differences that I notice are 1) gromacs solves for molar heat
capacity, while A&T does not. 2) An Na (Avagadro's number) appears in the
gromacs numerator where an N (number of atoms) is in A&T's expression. 3)
The nmol (# of molecules) term in the gromacs equation.
How can I reconcile these differences? Did I make an incorrect assumption
or error in my derivation? Any assistance or insight into this would be
Department of Chemical Engineering
Clemson, SC 29634-0909
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