# Long-range Coulomb changes with cutoff?

I have performed calculations on a simple charged system using LAMMPS and used the PPPM method to calculate long-range forces. However, I have noticed a significant dependence of particle forces and system energy on the cutoff radius I set. In my understanding, the size of the Coulomb force cutoff radius only affects the contributions of real space and k-space and calculation speed, and should not affect the magnitude of forces and energy. Where did I go wrong? I have attached my code below.

boundary p p p

units real
atom_style full

region box block 0 30 0 30 0 30
create_box 2 box
mass 1 16
mass 2 16

create_atoms 1 single 10 10 10
create_atoms 2 single 10 10 11

set type 1 charge 1
set type 2 charge -1

pair_style coul/long 10
pair_coeff * *
kspace_style pppm 0.0001

compute ekspace all pe kspace

timestep 2
thermo 1
thermo_style custom step atoms pe c_ekspace
dump 1 all custom 1 test.dump id type x y z fx fy fz
run 10

When I replaced ‘pair_style coul/long 10’ with ‘pair_style coul/long 5’, the running results showed a significant change in both force and energy.
Thanks a lot for any help.

Jianghui

With the default settings the coulomb potential is approximated by a table. That can result in changes for just a single pair of atoms. For many atoms, the errors from tabulation usually mostly cancel. This can be changed with the pair_modify command. Furthermore, you are using the automated guess for the reciprocal space cutoff and that may be less accurate for a sparse system, e.g. your reciprocal space cutoff may not be fully converged. That can be addressed by setting it manually with kspace_modify.

BTW: you didn’t quantify what you consider to be a “significant change”

PPPM is a Fourier-based method which was designed and benchmarked to be applied mainly to dense, homogeneous systems (which the vast majority of MD simulations are).

If you are familiar with the mathematics of Fourier transforms you should understand that the settings that work for, say, a box of liquid water will be less relatively accurate for two point charges in empty space, since far more of the electrostatic potential in the second case is rapidly varying in space.

Reducing the cutoff forces PPPM to try to handle even more fast-varying potential, further reducing its accuracy (at unchanged parameters). 5 angstrom is too short a cutoff to be used in standard simulations in any case.

What you should be able to observe, minimally, is that:

• the electrostatic energies should change less going from a 10 angstrom cutoff to longer cutoffs;
• the electrostatic energies should change less with cutoff change when the target accuracy (“0.0001” in your script) changes.

Thanks axel

In the above example, the magnitude of the force changes with cutoff by orders of magnitude, so I call it ‘significant change’. I tested the system with 4,000 particles and found that there was no such problem.