[gmx-users] Re: Heat capacity for infinite systems

Chris O'Brien obrien at CLEMSON.EDU
Mon Sep 6 01:57:24 CEST 2004

>Message: 7
>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>
>Content-Type: text/plain
>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 
> how
> > 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
>add this.
>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 
much appreciated.

Thank you,
Chris O'Brien

Department of Chemical Engineering
Clemson University
Clemson, SC  29634-0909

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