# Dielectric constant used in LAMMPS

Dear all. I wonder what is the dielectric constant used to calculate the electrostatic force between atoms in LAMMPS? If vacuum permittivity is used, will lammps calculate the relative permittivity of water molecules by default when there are water molecules in the system? If there are molecules such as oil in the system? Or is it that the vacuum dielectric constant is used by default when calculating the electrostatic force between two atoms in LAMMPS？

When you simulate with explicit water then you must use the dielectric constant for vacuum because vacuum is the medium that your atoms are in. You only need to change this if you have implicit solvent and thus the screening effect of solvent needs to be considered.
See the dielectric command — LAMMPS documentation

I still don’t quite understand. When using the “compute group/group” command to calculate the electrostatic force between two ions in vacuum and aqueous solution respectively, will the results be the same or different?

That is a very bad example. If you use compute group/group you only compute the interaction between the selected atoms, so the solvent does not enter the equation unless it is implicit and cannot be removed.

In the actual aqueous solution system, the electrostatic force between two ions is reduced due to the existence of water molecules, but the electrostatic force between two ions directly calculated in the LAMMPS simulation does not consider the influence of water molecules. If the effect of water molecular medium is to be considered, the force of water molecules on ions should also be calculated.

Do you mean this?

No, the force between the two ions only is not reduced. The total force on the two ions changes due to the presence of the water molecules and thus their trajectories. The total effective net force between those two ions you cannot really compute from a single configuration, but needs to be averaged over some significant time, since the motion and reaction of the water molecules on the motion of other charged particles plays an important role in this.

I have worked on dielectric properties for aqueous solutions from classical MD in my PhD work, so I am speaking with some authority here (even though it was over 20 years ago). Your view on the situation is not quite correct and you need to be spending some significant time reading some not so easy to handle text books and publications, if you really want to get into it. I recall that it took me quite some time to wrap my head around it. Things are not as straightforward as one might naively think with this.
Here are some relevant citations from my PhD thesis (ordered from generic to specific):

``````J. G. KIRKWOOD. J. Chem. Phys., 76, 911, 1939.
H. FRÖHLICH. Theory of Dielectrics. Clarendon Press, 2nd. Auflage, 1958.
C. J. F. BOETTCHER. Theory of Electric Polarization, Elsevier, 1973.
M. NEUMANN. Mol. Phys., 50(4), 841–858, 1983.
M. NEUMANN, O. STEINHAUSER. Mol. Phys., 39(2), 437–454, 1980.
M. NEUMANN, O. S TEINHAUSER. Chem. Phys. Lett., 95(4,5), 417–422, 1983.
S. BORESCH, O. STEINHAUSER. Ber. Bunsenges. Phys. Chem., 101(7), 1019–1029, 1997.
P. HÖCHTEL, S. BORESCH, W. BITOMSKY, O. STEINHAUSER. J. Chem. Phys.,109(12), 4927–4937, 1998.
``````

There likely have been other publications on this topic since and you can find those by looking for papers that cite these publications.

The bottom line is the following. In an all-atom simulation, you must use the vacuum dielectric constant. The dielectric constant of the medium/system is an observable in this case (and can be computed from the fluctuations of the total dipole of your simulation cell under consideration of the dielectric boundary conditions used by the method used to compute coulomb interactions).

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Thank you for your guidance, I will learn relevant knowledge again!

I forgot one important text book. This is not just for dielectric properties: `J. P. HANSEN, I. R. McDONALD . Theory of Simple Liquids. Academic Press, London, 1991.`

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