Dear Zahra,

this is indeed a somewhat delicate question. Nevertheless I would like to give some hints from my experiences corresponding to this question. From the mathematical point of view every chemical structure is fully determined by a graph tree, i.e., there are no circular connections between. Every circular connection has to be included (in my experience) by a restriction or by a constraint, because the circular connection is an overdetermination of the structure.  A circular connection is from the mathematical point of view not a real bond.

 I hope I could help you,

Sincerely, Peter Friedel

thanks for your answer.I simulate circular DNA in spherical cell.

Dear Zahra! It seems that your system "explodes" or "freezes" due to numerical instability of integrator. Maybe the problem is in your force-field. I recommend carefully read LAMMPS tutorials about pair_style, pair_coeff, and pair_modify commands. In your case probably necessary to type dots explicitly (in FORTRAN it plays a role, maybe for LAMMPS too) like

pair_coeff 1 1 1.00 1.00 1.22

Also please check, whether the cut-off is really 1.22. In purely repulsive LJ the value should be 1.12, so maybe you have a misprint. And if you want to have not only cutted, but shifted potential, which attains zero at cut-off distance, you also need the line

pair_modify shift yes

This shift (together with cut-off 1.12) provide more smooth behavior of potential around cut-off, and as the result, computations should be more stable. This could solve your problem. You can also try to use shorter time steps (1/10 or 1/100 of desired values) within 1000 or 100000 initial time steps to relax some particle overlaps, producing to high forces and velocities.