# [gmx-users] Problems with calculating Cv and Cp

Lum Nforbi lumngwegia at gmail.com
Wed Jan 6 05:27:35 CET 2010

```>
> Hi Andrew Paluch,
>

You had asked me to supply the formulas that I attempted using to
calculate Cv. The formula from J. M. Haile is labelled isometric heat
capacity and given by Cv = Nk/(N-NT*(3(N/2)-1)<Ek*^-1>) and the one in Allen
and Tildesley is quite complicated to write out (has some special characters
in it).
I also found in one of the volumes of gmx-users where someone had
used the formula
Cv = 1/(k_B*T*T)*Var(E) and instead of having the expected 75 J/Kmol, he got
86 J/Kmol. He also mentioned that Var(E) can be obtained from RMSD numbers.
I know that RMSD numbers are displayed from g_energy, but how do you get
Var(E) from these numbers?

Thanks,
Lum

>
> Date: Wed, 9 Dec 2009 20:45:57 -0500
> From: Andrew Paluch <apaluch at nd.edu>
> Subject: Re: [gmx-users] Problems with calculating Cv and Cp
> To: Discussion list for GROMACS users <gmx-users at gromacs.org>
> Message-ID: <8BE66D7C-EA0F-4B04-8DDE-374529EC211F at nd.edu>
> Content-Type: text/plain; charset="us-ascii"
>
> Lum,
>
> You'll have better luck if you perform a few simulations at different
> temperatures at the same pressure and mole number, and then
> numerically differentiate the resulting enthalpy.  I believe that the
> default heat capacity that Gromacs will print out is only valid for
> NVE simulations, and I am not sure of the formulas that you are
> referring to from Allen and Tildesley & J.M. Haile.  Also, don't
> expect your calculated heat capacity with TIP3P to agree the
> experimental value. You should under-predict the experimental value.
>
> Lastly, depending on what you are interested in, you may have better
> luck with a water model other than TIP3P.
>
> Hope this helps,
>
> Andrew
> _______________________________________________
> _______________________________________________
> Andrew Paluch
> Department of Chemical and Biomolecular Engineering
> University of Notre Dame du Lac
> apaluch at nd.edu
> _______________________________________________
> _______________________________________________
>
> On Dec 9, 2009, at 8:18 PM, Lum Nforbi wrote:
>
> > Dear all,
> >
> >       I have run an 8 ns NPT simulation of 2000 molecules of  TIP3P
> > water and I have a very low Cv value of 12.4748 J/mol K (factor =
> > 0.000164481). The result is below. I ignored this value and have
> > tried using formulas for Cv that I found in the two books: Allen
> > and Tildesley & J. M. Haile but I can't come out with the right
> >      Has anyone ever calculated Cv or Cp for water manually from
> > scratch and gotten the right answer? If so, please, could you give
> > me the details of what you did?
> >
> > Statistics over 4000001 steps [ 0.0000 thru 8000.0005 ps ], 10 data
> > sets
> > All averages are exact over 4000001 steps
> >
> > Energy                      Average       RMSD     Fluct.
> > Drift  Tot-Drift
> > ------------------------------
> > -------------------------------------------------
> > Potential                  -79498.8    285.331    285.331
> > 0.000110205   0.881641
> > Kinetic En.                 14960.5    191.868    191.854
> > -0.0010135   -8.10799
> > Total Energy               -64538.3    353.238    353.232
> > -0.000903288   -7.22631
> > Temperature                 299.962    3.84702    3.84673
> > -2.0321e-05  -0.162568
> > Pressure (bar)             0.945534    194.613    194.613
> > 0.000164281    1.31425
> > Box-X                       3.94528 0.00514348 0.00514348
> > 0          0
> > Box-Y                       3.94528 0.00514348 0.00514348
> > 0          0
> > Box-Z                       3.94528 0.00514348 0.00514348
> > 0          0
> > Volume                      61.4097   0.240325    0.24032
> > 6.42593e-07 0.00514075
> > Density (SI)                  974.3    3.80629    3.80622
> > -1.04747e-05 -0.0837974
> > Heat Capacity Cv:      12.4748 J/mol K (factor = 0.000164481)
> > Isothermal Compressibility: 2.27095e-05 /bar
> > Adiabatic bulk modulus:        44034.4  bar
> >
> >
> > Thank you,
> >
> > Lum
> >
> > --
>
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