# long range Coulomb interaction

Hi LAMMPS users,

I just want to make sure I have an exact/correct understanding of the calculation of long range Coulomb interaction in lammps.

About “coul/long”, the doc page says: “The Coulombic cutoff specified for this style means that pairwise interactions within this distance are computed directly; interactions outside that distance are computed in reciprocal space.”
While the textbook’s way (like A.Leach’s Molecular Modeling) handles it by adding Gaussian charge distribution to point charges, so the screened charges and screening charges both converge in real and k space, thus both terms can be cut. And finally the total Coulomb energy is the sum of those two terms plus a self term.

It seems to me the lammps’s way and textbook’s way are slightly different by replacing the real space term + self term with a direct computation within a cutoff, am I right ?
If I am wrong and the two ways are actually equivalent, could someone enlighten me how? as I don’t see it.
If I am right, then why would lammps choose such a way? what’s the trade-off?

Thanks a lot.

Liu

Hi LAMMPS users,

I just want to make sure I have an exact/correct understanding of the
calculation of long range Coulomb interaction in lammps.

About "coul/long", the doc page says: "The Coulombic cutoff specified for
this style means that pairwise interactions within this distance are
computed directly; interactions outside that distance are computed in
reciprocal space."
While the textbook's way (like A.Leach's Molecular Modeling) handles it by
adding Gaussian charge distribution to point charges, so the screened
charges and screening charges both converge in real and k space, thus both
terms can be cut. And finally the total Coulomb energy is the sum of those
two terms plus a self term.

It seems to me the lammps's way and textbook's way are slightly different by
replacing the real space term + self term with a direct computation within a
cutoff, am I right ?

no.

If I am wrong and the two ways are actually equivalent, could someone
enlighten me how? as I don't see it.

they are the same. any "coul/long" style does add the screening
and thus has to be used in combination with a kspace style
to provide the corresponding reciprocal space contributions.

axel.

Thank, so the real-space term cutoff is set by user, but where is the k-space cutoff set?

And, how is the Gaussian distribution width chosen? does lammps use a fixed universal value throughout? or variable?

Thank, so the real-space term cutoff is set by user, but where is the
k-space cutoff set?

And, how is the Gaussian distribution width chosen? does lammps use a fixed
universal value throughout? or variable?

axel.

I see the kspace_style documentation says the accuracy setting determines the # of k-space vectors for ewald.
But I don’t find anywhere say about the width of the screening charge distribution, could you please give more hint or perhaps there’s another doc page that I don’t know related ? Thank you.

I see the kspace_style documentation says the accuracy setting determines
the # of k-space vectors for ewald.
But I don't find anywhere say about the width of the screening charge
distribution, could you please give more hint or perhaps there's another doc
page that I don't know related ? Thank you.

more details are in the referenced papers and the sources.

axel.