Understanding negative group/group electrostatic energy for like-charged graphene sheet

[SAMIR_ARUN_KHEWALE]

Hello,

I am a beginner to LAMMPS and trying to understand a result from compute group/group. I am a bit confused about the sign of the energy.

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System details

• Two graphene sheets (parallel plates)

• Each sheet has 416 carbon atoms

• Partial charge per carbon atom: ±0.002403846 e

  • So each sheet carries approximately ±1e total charge

• Simulation box dimensions:

  • ( x = 32.08 , Å )

  • ( y = 34.19 , Å )

  • ( z = 35.5 , Å )

• Units: real

• Long-range electrostatics: kspace_style pppm

• kspace slab 3.0

• What I did

  I defined groups:

  • solute1 → lower graphene sheet

  • solute2 → upper graphene sheet

  Then computed:

  compute A1A1 solute1 group/group solute1 kspace yes
  

  This gives the electrostatic interaction energy of the graphene sheet with itself.

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  Observation

  The value I obtain is:

  A11 ≈ −3.27 kcal/mol
  

My expectation

Since all atoms in a graphene sheet have the same sign of charge, I expected:

Coulomb interaction between atoms → repulsive

Therefore:[U > 0]My current understanding (please confirm/correct)

From my analysis, LAMMPS (via PPPM/Ewald) computes:

[U = U_real + U_kspace + U_self + U_background

U_real: pairwise Coulomb (positive for like charges)

U_kspace: long-range contribution

U_self: self-energy correction (negative)

U_background: neutralizing background (negative if net charge ≠ 0)

Since the graphene sheet has net charge ≈ +1e, a uniform neutralizing background is introduced, which contributes a negative energy.

QUE

• 1. Is the negative value mainly coming from the background and self-energy terms?
  2. More generally, how should I interpret the sign of this group/group electrostatic energy? Does a negative value here really indicate net attraction, or is the sign dominated by Ewald/PPPM corrections rather than simple pairwise interactions?
  3. Does compute group/group include these contributions even when looking at a single group?
  4. Is it correct to say that this A1A1 value is not just “repulsion between atoms,” but includes Ewald-related corrections?
  5. If I want the physically intuitive repulsive interaction within the sheet, is there a better way to compute it?

[akohlmey]

There are two major problems with your reasoning here:

1. There is no meaning to the absolute value of the energy in classical MD potentials. It can be shifted arbitrarily without any impact on the simulation. Thus you cannot infer anything from it. If you want to know if something is attractive or repulsive, you have to look at the gradient, i.e. the force or at energy differences.
2. There is no “background” charge applied. Rather, if you have a system that is not neutral, you would have a diverging term in the lattice sum at the gamma point. Or put differently, the energy of the periodically replicated system would be infinite. That term is simply discarded which in turn means that it has the same effect on the potential as if the system was uniformly shifted to be neutral, but there is no explicitly term added for that (and if it would it would be infinitely large).