[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

> 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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