# [lammps-users] Questions about lennard jones potential paratmeters

Dear lammps users,

I am a little confused about determining the sigma in the Lennard Jones potential. When I read papers and look for simulation parameters, people are using different terminology of sigma value in LJ potential. Some use vdw radius and others use diameter. In lammps, sigma in LJ potential is defined as zero crossing distance of LJ potential. If I follow this definition, the diameter of the particle is defined as 1.12*sigma.

1. Let me say that I found a reference that the diameter of particle A is defined as sigma_A. Then, should I implement sigma in pair_coeff as sigma_A/1.12?

2. If I found vdw radius of the particle a as vdw_A, then which value of the sigma in pair_coeff should I use?

This is a really basic concept, I think. But I am still confused. Can anyone give me an advice?

With my best regards

Hi, Yeung Kyu,

Which system are you dealing with? If one of your references obtain the data from DFT simulations, I'd say to follow them. But trying both values and seeing which one gives better results is always an option.

Álvaro

Dear lammps users,

I am a little confused about determining the sigma in the Lennard Jones potential. When I read papers and look for simulation parameters, people are using different terminology of sigma value in LJ potential. Some use vdw radius and others use diameter. In lammps, sigma in LJ potential is defined as zero crossing distance of LJ potential. If I follow this definition, the diameter of the particle is defined as 1.12*sigma.

1. Let me say that I found a reference that the diameter of particle A is defined as sigma_A. Then, should I implement sigma in pair_coeff as sigma_A/1.12?

2. If I found vdw radius of the particle a as vdw_A, then which value of the sigma in pair_coeff should I use?

This is a really basic concept, I think. But I am still confused. Can anyone give me an advice?

There are multiple issues to keep in mind here:

a) the Lennard-Jones sigma parameter is related to the “effective diameter” of a particle, but that does not mean that if you have an experimental value for that, that this determines what is a good choice for sigma.

b) there are two conventions for what sigma represents in the functional form. it can be to point where the potential energy crosses zero (which is the convention that LAMMPS uses) or the minimum of the potential. the difference is a factor 2^(1/6) or 1.12246204830937298142. you can tell the difference from the functional form of the potential. with sigma being the minimum the attractive term has a factor of 2 in addition.

c) force field parameterization is a mostly empirical process. one can take some initial guess from experimental data but them adjusts the parameters so that the resulting potential can reproduce properties of interest (e.g. density, g(r), diffusivity, solvation free energy) at the conditions of interest. since most potentials are simplifications, not all properties can be represented equally well. it also depends on the material in question. e.g. LJ has been shown to model noble gases well, but is less applicable say for diamond. this is often due to atomic interactions often being directional, which is not included in a pairwise additive model like LJ

d) some force fields (Amber, CHARMM, OPLS, GROMOS, etc) have “rules” for how to derive its parameters or its initial guesses, or use specific fitting algorithms, often with the help for quantum chemical calculations. this is so that new parameters can be added in a consistent fashion. however, that also limits the ability to “optimize” parameters for a specific material, but favors choices that apply to a more generic categorization of atoms based on the concept of functional groups.

to learn more about this, I suggest to revert to some of the available text book material on how MD simulation parameters are derived and study some of the publications for how force fields in particular are derived.

TL;DR. don’t just use any property to set your parameters. only use parameters from publications that have been verified to represent the property of interest well. it may even mean to use a different functional form (i.e. pair style in LAMMPS) or lowered expectations of accuracy. also, never use anything without checking against the reference examples first and thus confirming that you did everything correctly.

axel.