Numerical distortion and effects of thermostat in molecular dynamics simulations of single-walled carbon nanotubes

In this paper, single-walled carbon nanotubes (SWCNTs) are studied through molecular dynamics (MD) simulation. The simulations are performed at temperatures of 1 and 300\,K separately, with atomic interactions characterized by the second Reactive Empirical Bond Order (REBO) potential, and temperature controlled by a certain thermostat, i.e. by separately using the velocity scaling, the Berendsen scheme, the Nose--Hoover scheme, and the generalized Langevin scheme. Results for a (5,5) SWCNT with a length of 24.5\,nm show apparent distortions in nanotube configuration, which can further enter into periodic vibrations, except in simulations using the generalized Langevin thermostat, which is ascribed to periodic boundary conditions used in simulation. The periodic boundary conditions may implicitly be applied in the form of an inconsistent constraint along the axis of the nanotube. The combination of the inconsistent constraint with the cumulative errors in calculation causes the distortions of nanotubes. When the generalized Langevin thermostat is applied, inconsistently distributed errors are dispersed by the random forces, and so the distortions and vibrations disappear. This speculation is confirmed by simulation in the case without periodic boundary conditions, where no apparent distortion and vibration occur. It is also revealed that numerically induced distortions and vibrations occur only in simulation of nanotubes with a small diameter and a large length-to-diameter ratio. When MD simulation is applied to a system with a particular geometry, attention should be paid to avoiding the numerical distortion and the result infidelity.