What is the epsilon value for softcore LJ when C6 or C12 is zero?

GROMACS version: 2023
GROMACS modification: Yes/No

Hi,

I know that we can set the sc_sigma variable for specifying the sigma value in the softcore LJ potential if the atom does not have LJ parameters (epsilon=sigma=0, or C6=C12=0). But I was wondering what is the epsilon value used in that case? Don’t we also need the epsilon value to derive the actual LJ softcore potential being used?

Thank you,
Xiaowei

The are no LJ interactions. When C6=C12=0, the sigma parameter is only used for evaluating the soft-core function for the Coulomb interactions.

Thank you for the reply. In the Gromacs documentation 2023 (p.420) there is this paragraph, so it seems to me the sc-sigma is for LJ interaction? Also I think there is no sigma variable in the Coulomb softcore expression?

It explicitly says there “of hydrogens WITHOUT LJ”.

Note that sc_sigma is used when C6=0 or C12=0, so it is also used when only C6 or C12 is set. But your question was about interactions without LJ.

I’m still a little confused. I would like to ask about the softcore LJ function used between, e.g. a hydrogen WITHOUT LJ parameters and another atom (with LJ parameters). As I understand, sc-sigma would be assigned to the H atom (if its original sigma and epsilon are 0). Then for evaluating the softcore LJ interaction between the 2 atoms, the following functional form is used (this is from the original Beutler paper and gromacs uses a variation of this), which requires epsilon_ij and sigma_ij, and those two should be computed through some sort of combination rule between the sigma/epsilon parameters of the two atoms. Now we know what sigma value to use for the H atom, but what epsilon value is used for that H atom?

Did I misunderstand anything?

Thanks!

You should see the free-energy non-bonded interactions only in terms of pair interactions. sc_sigma applies to pair interactions only, not to atoms. So any atom pair involving an H atom with epsilon=0 with have no LJ interactions.

What combination rule is used depends on the force field, but an H with epsilon=0 with never have LJ interactions with any atom.

Yes I am asking about pair interactions (between a H atom previously without LJ parameters and another atom with LJ parameters). So what exactly is sc_sigma assigned to, sigma_ij in my equation? In that case then if H had epsilon=0, then this interaction will still be 0. Then what’s the point of assigning sc-sigma in the first place?

Yes, it is for assigning sigma_ij.
You only show the LJ potential, but sigma_ij is also needed for computing the soft-core r for the Coulomb interaction.

Where is sigma_ij needed for Coulomb softcore?

image

That formula is not from the GROMACS manual.

GROMACS uses the same soft-core r for LJ and Coulomb:
https://manual.gromacs.org/current/reference-manual/functions/free-energy-interactions.html#equation-eqnfepsoftcore

Ah! Ok, that makes sense. Thank you!