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

René Pool r.pool at vu.nl
Tue Feb 1 16:03:38 CET 2011

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
--
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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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