# [gmx-developers] GCMC, equations of state and dispersion correction

René Pool r.pool at vu.nl
Wed Feb 2 08:01:29 CET 2011

Okay, thanks!
=====================================================
René Pool
IBIVU/Bioinformatics
Vrije Universiteit Amsterdam
De Boelelaan 1081a
1081HV AMSTERDAM, the Netherlands
Room P120
E: r.pool at few.vu.nl
T: +31 20 59 83714
F: +31 20 59 87653
=====================================================

Shirts, Michael (mrs5pt) wrote:
> The dispersion correction gives the pressure you would get if the
> Lennard-Jones cutoff was extended to infinity, with the assumption that
> g(O-O) is 1 outside of the cutoff.  It is a function of the number density
> rho, the chemical composition, and the total number of particles, but not
> otherwise a function of the coordinates of the system.
>
> So, if you want to get answers that are independent of the cutoff, then you
> need to use the dispersion correction; you just have to be careful that when
> you are changing particle number and box volume that the correction is
> calculated correctly.
>
> ~~~~~~~~~~~~
> Michael Shirts
> Assistant Professor
> Department of Chemical Engineering
> University of Virginia
> michael.shirts at virginia.edu
> (434)-243-1821
>
>
>> From: René Pool <r.pool at vu.nl>
>> Reply-To: "r.pool at vu.nl" <r.pool at vu.nl>, Discussion list for GROMACS
>> development <gmx-developers at gromacs.org>
>> Date: Tue, 1 Feb 2011 10:03:38 -0500
>> To: Discussion list for GROMACS development <gmx-developers at gromacs.org>
>> Subject: [gmx-developers] GCMC, equations of state and dispersion correction
>>
>> Hi all,
>>
>> I implemented grand canonical Monte Carlo using the gromacs library. To
>> check if the outcomes of the muVT ensemble compare to those of the NVT
>> ensemble, I perform the following test:
>> At T > T_critical I compute the equation of state of system containing a
>> sinlge molecule type by NVT MD. I do the same for the muVT ensemble.
>> To translate the muVT results to the NVT equation of state, I use the
>> following equation:
>>
>> Rho*(dmu/dRho) = (dP/dRho),         (1)
>>
>> where Rho is the molecular number density, mu the chemical potential and
>> P the pressure. The equation of state is obtained via
>>
>> P(Rho) = Rho*k*T + \int{Rho*(dmu_ex/dRho),dRho},  (2)
>>
>> where k is the Boltzmann constant and mu_ex is the excess part of the
>> chemical potential that is readily available from the muVT simulation
>> results.
>>
>> For a simple LJ fluid, the muVT data agrees perfectly with the NVT data.
>> However for a  system of SPC waters, something goes wrong: the muVT
>> equation of state overestimates the NVT one.
>> In the LJ fluid NVT and muVT simulations, dispersion correction was not
>> taken into account during simulation. For the SPC simulation, dispersion
>> correction was turned on (EnerPress) in both the muVT and NVT simulations.
>> My question therefore is, should I still account for dispersion
>> correction to the pressure? I.e. should I add P_dispersion(Rho) to the
>> right-hand side of Eq. 2 ?
>> If so, the muVT/NVT agreement is much better.
>> If not, could I be overlooking some other aspect? ( Assuming that I did
>> my coding correctly ;-) )
>>
>> Cheers,
>> René
>> --
>> =====================================================
>> René Pool
>> IBIVU/Bioinformatics
>> Vrije Universiteit Amsterdam
>> De Boelelaan 1081a
>> 1081HV AMSTERDAM, the Netherlands
>> Room P120
>> E: r.pool at few.vu.nl
>> T: +31 20 59 83714
>> F: +31 20 59 87653
>> =====================================================
>> --
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>