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

Shirts, Michael (mrs5pt) mrs5pt at eservices.virginia.edu
Tue Feb 1 16:47:37 CET 2011

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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