<div class="gmail_quote"><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">Hi Andrew Paluch,<br></blockquote><div><br> 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).<br>
I also found in one of the volumes of gmx-users where someone had used the formula<br>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?<br>
<br>Thanks,<br>Lum<br> <br></div><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
<br>
Date: Wed, 9 Dec 2009 20:45:57 -0500<br>
From: Andrew Paluch <<a href="mailto:apaluch@nd.edu">apaluch@nd.edu</a>><br>
Subject: Re: [gmx-users] Problems with calculating Cv and Cp<br>
To: Discussion list for GROMACS users <<a href="mailto:gmx-users@gromacs.org">gmx-users@gromacs.org</a>><br>
Message-ID: <<a href="mailto:8BE66D7C-EA0F-4B04-8DDE-374529EC211F@nd.edu">8BE66D7C-EA0F-4B04-8DDE-374529EC211F@nd.edu</a>><br>
Content-Type: text/plain; charset="us-ascii"<br>
<br>
Lum,<br>
<br>
You'll have better luck if you perform a few simulations at different<br>
temperatures at the same pressure and mole number, and then<br>
numerically differentiate the resulting enthalpy. I believe that the<br>
default heat capacity that Gromacs will print out is only valid for<br>
NVE simulations, and I am not sure of the formulas that you are<br>
referring to from Allen and Tildesley & J.M. Haile. Also, don't<br>
expect your calculated heat capacity with TIP3P to agree the<br>
experimental value. You should under-predict the experimental value.<br>
<br>
Lastly, depending on what you are interested in, you may have better<br>
luck with a water model other than TIP3P.<br>
<br>
Hope this helps,<br>
<br>
Andrew<br>
_______________________________________________<br>
_______________________________________________<br>
Andrew Paluch<br>
Department of Chemical and Biomolecular Engineering<br>
University of Notre Dame du Lac<br>
<a href="mailto:apaluch@nd.edu">apaluch@nd.edu</a><br>
_______________________________________________<br>
_______________________________________________<br>
<br>
On Dec 9, 2009, at 8:18 PM, Lum Nforbi wrote:<br>
<br>
> Dear all,<br>
><br>
> I have run an 8 ns NPT simulation of 2000 molecules of TIP3P<br>
> water and I have a very low Cv value of 12.4748 J/mol K (factor =<br>
> 0.000164481). The result is below. I ignored this value and have<br>
> tried using formulas for Cv that I found in the two books: Allen<br>
> and Tildesley & J. M. Haile but I can't come out with the right<br>
> answer.<br>
> Has anyone ever calculated Cv or Cp for water manually from<br>
> scratch and gotten the right answer? If so, please, could you give<br>
> me the details of what you did?<br>
><br>
> Statistics over 4000001 steps [ 0.0000 thru 8000.0005 ps ], 10 data<br>
> sets<br>
> All averages are exact over 4000001 steps<br>
><br>
> Energy Average RMSD Fluct.<br>
> Drift Tot-Drift<br>
> ------------------------------<br>
> -------------------------------------------------<br>
> Potential -79498.8 285.331 285.331<br>
> 0.000110205 0.881641<br>
> Kinetic En. 14960.5 191.868 191.854<br>
> -0.0010135 -8.10799<br>
> Total Energy -64538.3 353.238 353.232<br>
> -0.000903288 -7.22631<br>
> Temperature 299.962 3.84702 3.84673<br>
> -2.0321e-05 -0.162568<br>
> Pressure (bar) 0.945534 194.613 194.613<br>
> 0.000164281 1.31425<br>
> Box-X 3.94528 0.00514348 0.00514348<br>
> 0 0<br>
> Box-Y 3.94528 0.00514348 0.00514348<br>
> 0 0<br>
> Box-Z 3.94528 0.00514348 0.00514348<br>
> 0 0<br>
> Volume 61.4097 0.240325 0.24032<br>
> 6.42593e-07 0.00514075<br>
> Density (SI) 974.3 3.80629 3.80622<br>
> -1.04747e-05 -0.0837974<br>
> Heat Capacity Cv: 12.4748 J/mol K (factor = 0.000164481)<br>
> Isothermal Compressibility: 2.27095e-05 /bar<br>
> Adiabatic bulk modulus: 44034.4 bar<br>
><br>
><br>
> Thank you,<br>
><br>
> Lum<br>
><br>
> --<br>
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