# charges in LJ reduced units

Hello list,

I'm trying to run some simulations of LJ dumbbells with attached opposite charges to make them dipolar. But I am having some issues with the charge in reduced units. I've scanned the list archives and found some discussions of this issue. One answer I found is that, the charges should be in e's, just like in real units. But I do not believe this is correct. When I run a NVT simulation at about rho*=0.5 and T*=2.5, and q=+- 1e, the LJ energy (evdwl) is about -5.5 and the Coulombic energy (ecoul) is only around -0.13 after a couple million timesteps. The Coulombic energy should be dominant at this density and temperature I believe, so maybe the charges need some conversion factor > 1.

The other answer I've seen is, "Just use real units and don't worry about it!" Well, fair enough, and I will if I have to. But since part of my goal is to scan these systems from uncharged dumbbells up to +- 1e, it would be nice if I could stay in reduced units. At +- 1e I would expect to see something not too far from RPM dumbbells, which I've studied before with GCMC simulations. But I also need to confirm that the definition of reduced units used by people studying primitive model electrolytes is actually the same as that used by people studying LJ systems.

Thanks for any help,
Chris.

Hello list,

I'm trying to run some simulations of LJ dumbbells with attached opposite charges to make them dipolar. But I am having some issues with the charge in reduced units. I've scanned the list archives and found some discussions of this issue. One answer I found is that, the charges should be in e's, just like in real units. But I do not believe this is correct. When I run a NVT simulation at about rho*=0.5 and T*=2.5, and q=+- 1e, the LJ energy (evdwl) is about -5.5 and the Coulombic energy (ecoul) is only around -0.13 after a couple million timesteps. The Coulombic energy should be dominant at this density and temperature I believe, so maybe the charges need some conversion factor > 1.

The other answer I've seen is, "Just use real units and don't worry about it!" Well, fair enough, and I will if I have to. But since part of my goal is to scan these systems from uncharged dumbbells up to +- 1e, it would be nice if I could stay in reduced units. At +- 1e I would expect to see something not too far from RPM dumbbells, which I've studied before with GCMC simulations. But I also need to confirm that the definition of reduced units used by people studying primitive model electrolytes is actually the same as that used by people studying LJ systems.

well, the situation is quite simple. if you identify the charge unit
and the unit of energy independently. so if you identify the charge
unit with the charge of an electron, you also determine what unit
epsilon has to have or vice versa. but on top of that, you also have
the choice of static dielectric constant, which is effectively a
scaling factor for charges. so if you have specific preferences for
what reference you want to use for both charge and energy, you can
make the connection via adjusting the dielectric constant.

HTH,
axel.

You can also look for papers by Mark Stevens from a 10 years
back on modling poly-electrolytes (charged polymers). He
did all his work in LJ units.

Steve

Thanks for the replies Steve and Axel. Every time I go back to using reduced units I get confused for a bit, but I think I finally get it! The whole idea is to scale the temperatures by some energy factor to get a dimensionless number. But of course the energy scale for LJ units (LJ well depth) is much different than the energy scale for RPM-like electrostatic systems (Coulombic interaction at rij=sigma). So if I insist on using LJ units with charges, I must scale the charges by some factor so that the electrostatic energy has the right value in LJ units. And the correct scaling is in fact given right in the LAMMPS manual in the units section, if I’d actually bothered to compute it in the first place! For my system it comes out to about 35.

The issue of dielectric constant is more about interpreting the results and comparing the model to real systems. I know that if you’re thinking of the RPM as a model for the condensation phase transition in some dilute solutions, you introduce the dielectric constant of the solvent to compare to the real experiment. And I see that the Stevens works introduce a Bjerrum length which in a way has the same effect of scaling the Coulombic interaction. I need to think about whether this is appropriate for the systems I’m modelling.

Thanks again,
Chris.