You need to recognize the definition of short-range and long-range interactions. Consider an interaction given by the potential function u(r). If the integral:

U = int (rho * u(r) * 4 pi r^2 dr) between 0 and inf

converges, that interaction is considered short-range. Otherwise, it is a long-range interaction. If you consider u(r) ~ 1/r^n, then for n > 3 we have short-range interactions. So, the Coulomb interaction with n = 1 is obviously long-range, and if you calculate it in a simulation the same as a short-range interaction like Lennard-Jones, you get wrong results. There are special techniques for numerically integrating Coulomb interactions over the infinite periodic images of the simulation box, among which Ewald summation and Particle-Particle Particle-Mesh methods worth mentioning. LAMMPS can enable the use of such methods, if you use the keyword long, and specify the parameters of the long-range handling method. Or, you can accept the error and tell it to cut Coulomb interactions as it would any other interactions with the keyword cut.

Dr Sadeghi

Thanks you much for kind response.

I catch underlying reason of coul/long and coul/cut, however, both keywords need a cut-off value to be specified in LAMMPS. http://lammps.sandia.gov/doc/pair_lj.html

Why coul/long needs such parameter? As you noticed me, this poses an approximation which is incorporated by coul/cut keyword.

Sincere thanks in advance.

Usually, the methods for long-range integration of electrostatic interactions are composed of two parts, which are summation of forces in real space, and summation of the effects of periodic boxes in Fourier space (the k-space in Ewald summation notation). So, you can specify the cut-off for real space interactions in this LAMMPS command. Then you need to specify the parameters of k-space summation separately. Quoting from LAMMPS documentation:

"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."