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

David van der Spoel spoel at xray.bmc.uu.se
Mon Sep 6 10:22:42 CEST 2004

> 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)
> and
> 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 
> gromacs numerator where an N (number of atoms) is in A&T's expression.  
> The nmol (# of molecules) term in the gromacs equation.
> How can I reconcile these differences?  Did I make an incorrect 
> or error in my derivation?  Any assistance or insight into this would be 
> much appreciated.

I think the A&T book is almost completely written with Lennard-Jones
gases in mind, where indeed 1 atom is 1 molecule. To be honest, I don't
recall where we changed from atoms to molecules but my gut feeling is,
that it is correct to use # molecules. It would be nice to have another
reference to back it up though. One should be able to derive the
equation as well from:
Cv = dH/dT|v

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

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