# Scaling of Units in LAMMPs LJ units

I am using LAMMPs for non equilibrium molecular dynamics of binary liquid mixtures. I was wondering what LAMMPs uses to scale thermodynamic quantities like temperature, pressure, energy etc when using LJ units for binary or ternary mixtures. Specifically, if the quantities are scaled with the Mass, Epsilon and sigma of Argon or the Mass, Epsilon and sigma obtained by the mixing rule defined in the script.

There have been many discussions in the past about LJ units with lots of explanations. I suggest you search through the forum archive for in-depth information.

Of course the can only be one reference \sigma, \epsilon, mass and so on. How this is chosen, is up to you. For that reference material, the corresponding input parameters will be 1.0. For others not, but the corresponding factor, e.g. \sigma = 1.2 if the effective diameter is 1.2 times that of the atoms with \sigma = 1.0.

I recommend warming up by working through conversions between CGS and SI units. If the CGS energy unit (1 erg) is 1e-7 of a joule and the CGS length (1 cm) is 1e-2 of a meter, then you should be able to work out that the CGS force unit (1 dyne) is 1e-5 of a newton. If in addition the CGS mass (1 gram) is 1e-3 of a kilogram, then you should also be able to work out quickly that the CGS time unit is, in fact, just one second.

Then it’s the exact same process for LJ units. If \sigma = 3 angstrom, \epsilon = 0.42 kcal/mol, and m = 12 amu, then … (You just need to also know that k_B = 1, always, to get the temperature unit.)

It shouldn’t be too difficult after this, but if it is, you can always just use units real.

And once you’ve worked out the base unit conversions, you should follow the common convention of stating LJ-style quantities as unitless, such as “the molecule has length 5” rather than "the molecule has length 5 \sigma ".

This is the easiest way to talk sensibly about force field coefficients, such as:

To model polydispersity, we set \sigma_1 = 0.9, \sigma_2 = 1.4, and \sigma_3 = 1.6, and use an energy scale of \epsilon = 1 for like interactions and \epsilon = 0.5 for unlike interactions.