[gmx-developers] details about Heat capacity caculation
David van der Spoel
spoel at xray.bmc.uu.se
Tue Nov 1 21:02:34 CET 2011
On 2011-11-01 21:00, Haiqing Zhao wrote:
>
> Hi,
>
> Energy Average Err.Est. RMSD Tot-Drift
> -------------------------------------------------------------------------------
> Potential -44.6187 0.007 0.293318 0.0281861 (kJ/mol)
> Kinetic En. 7.59226 0.0032 0.19886 0.0201858 (kJ/mol)
> Total Energy -37.0264 0.0091 0.359776 0.0483719 (kJ/mol)
> pV 0.438734 9.5e-05 0.00136276 -0.000679764 (kJ/mol)
> Enthalpy -17216.8 4.2 167.296 22.4922 (kJ/mol)
>
> Yes, I did not doubt Cp=Var(Enthalpy)/k T^2.
> Actually my question is only about Enthalpy. As we see in the example, the total energy= -37.0264KJ/mol, pv = 0.4387 Kj/mol, How can enthalpy= -17216.8 KJ/mol?
>
> sorry for the time.
You did not say how many molecules. Enthalpy is not normalized in the
g_energy output.
>
>
> On Nov 1, 2011, at 2:35 PM, David van der Spoel wrote:
>
>> On 2011-11-01 20:15, Haiqing Zhao wrote:
>>>
>>> Hi, David,
>>>
>>> thanks for reply.
>>>
>>> I checked it. Version 4.5.5 really makes a difference from 4.5.3 which I used.
>>> In 4.5.5, Cv works exactly well by nmol*(RMSD(E))^2/RT^2. (Even though I dont know here why need to multiply the # of molecular.)
>>>
>> This is supposed to work for liquids, hence you need to normalize.
>> How many molecules do you have, 465?
>> Heat capacity of 80 resembles water. I'm pretty sure it works correctly, since we just submitted a paper about it and I have looked into this in detail. We used:
>>
>> kB T^2 c_P = Var (Enthalpy)
>>
>> which comes straight from Allen and Tildesley.
>>
>>> But still I'm sure the Cp is not from simple Enthalpy Fluctuation, as you see from the example below--167296 J/mol, and there is several orders mistake.
>>>
>>> Please help me check it.
>>> Thanks.
>>>
>>> e.g.
>>>
>>> Enthalpy -17216.8 4.2 167.296 22.4922 (kJ/mol)
>>>
>>> You may want to use the -driftcorr flag in order to correct
>>> for spurious drift in the graphs. Note that this is not
>>> a substitute for proper equilibration and sampling!
>>>
>>> Temperature dependent fluctuation properties at T = 300.076.
>>>
>>> Heat capacities obtained from fluctuations do *not* include
>>> quantum corrections. If you want to get a more accurate estimate
>>> please use the g_dos program.
>>>
>>> WARNING: Please verify that your simulations are converged and perform
>>> a block-averaging error analysis (not implemented in g_energy yet)
>>> Volume = 1.8548e-05 m^3/mol
>>> Enthalpy = -37.0255 kJ/mol
>>> Coefficient of Thermal Expansion Alpha_P = 0.0129106 (1/K)
>>> Isothermal Compressibility Kappa = 3.00555e-10 (J/m^3)
>>> Adiabatic bulk modulus = 3.32718e+09 (m^3/J)
>>> Heat capacity at constant pressure Cp = 80.3937 J/mol K
>>>
>>>
>>>
>>> On Nov 1, 2011, at 2:05 PM, David van der Spoel wrote:
>>>
>>>> On 2011-11-01 16:54, Haiqing Zhao wrote:
>>>>>
>>>>> Dear Gmxers,
>>>>>
>>>>> I have one question about how Gromacs calculate the heat capacity. I dont think it is only Enthalpy fluctuation÷(kT^2) in NPT ensemble. And also I checked it in NVT, it is not simply Total energy(/internal energy) fluctuation÷(kT^2).
>>>>>
>>>> Which gmx version? It's more or less correct in 4.5.4 but you really need qm correctiions. Check g_dos for that
>>>>
>>>>
>>>>
>>>>
>>>>> One data for NPT is: ( -nmol 465 -nconstr 3 )
>>>>>
>>>>> Energy Average Err.Est. RMSD Tot-Drift
>>>>> -------------------------------------------------------------------------------
>>>>> Potential -44.6187 0.007 0.293318 0.0281861 (kJ/mol)
>>>>> Kinetic En. 7.59226 0.0032 0.19886 0.0201858 (kJ/mol)
>>>>> Total Energy -37.0264 0.0091 0.359776 0.0483719 (kJ/mol)
>>>>> Temperature 300.076 0.13 7.85971 0.797822 (K)
>>>>> Pressure 0.663728 0.16 447.392 -0.388627 (bar)
>>>>> Volume 14.3219 0.0093 0.133543 -0.0667073 (nm^3)
>>>>> pV 0.438734 9.5e-05 0.00136276 -0.000679764 (kJ/mol)
>>>>> Enthalpy -17216.8 4.2 167.296 22.4922 (kJ/mol)
>>>>>
>>>>> Temperature dependent fluctuation properties at T = 300.076. #constr/mol = 3
>>>>> Isothermal Compressibility: 3.00555e-05 /bar
>>>>> Adiabatic bulk modulus: 33271.8 bar
>>>>> Heat capacity at constant pressure Cp: 67.9219 J/mol K
>>>>> Thermal expansion coefficient alphaP: 9.66233e-05 1/K
>>>>>
>>>>> And data for NVT, ( -nmol 7631 -nconstr 3 )
>>>>>
>>>>> Energy Average Err.Est. RMSD Tot-Drift
>>>>> -------------------------------------------------------------------------------
>>>>> Total Energy -33.2264 0.0003 0.0900307 -0.000219237 (kJ/mol)
>>>>> Temperature 300.008 0.0063 1.95324 -0.0148441 (K)
>>>>>
>>>>> Temperature dependent fluctuation properties at T = 300.008. #constr/mol = 3
>>>>> Heat capacity at constant volume Cv: 70.1813 J/mol K
>>>>>
>>>>> (BTW, I found that (1)if you choose Enthalpy as output, g_energy will always give Cp, no matter what ensemble it is. (2)And only you choose tot energy and temp as output, no other terms, g_energy will give you Cv. If not, you cannot get Cv by g_energy.)
>>>>>
>>>>> I appreciate if anybody could help me to check it.
>>>>> Thanks!!
>>>>>
>>>>> ---------------------------------------------
>>>>> Haiqing Zhao
>>>>> PH.D. candidate
>>>>> in Computational Biophysics
>>>>> Michigan Technological University
>>>>> http://www.phy.mtu.edu/~haizhao
>>>>>
>>>>
>>>>
>>>> --
>>>> David van der Spoel, Ph.D., Professor of Biology
>>>> Dept. of Cell& Molec. Biol., Uppsala University.
>>>> Box 596, 75124 Uppsala, Sweden. Phone: +46184714205.
>>>> spoel at xray.bmc.uu.se http://folding.bmc.uu.se
>>>> --
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>>>
>>
>>
>> --
>> David van der Spoel, Ph.D., Professor of Biology
>> Dept. of Cell& Molec. Biol., Uppsala University.
>> Box 596, 75124 Uppsala, Sweden. Phone: +46184714205.
>> spoel at xray.bmc.uu.se http://folding.bmc.uu.se
>> --
>> gmx-developers mailing list
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>> http://lists.gromacs.org/mailman/listinfo/gmx-developers
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>
--
David van der Spoel, Ph.D., Professor of Biology
Dept. of Cell & Molec. Biol., Uppsala University.
Box 596, 75124 Uppsala, Sweden. Phone: +46184714205.
spoel at xray.bmc.uu.se http://folding.bmc.uu.se
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