Time-Reversible, Symplectic, Angular Velocity Based Integrator for Rigid Linear Molecules

Abstract

A very simple explicit integrator for the rotational motion of rigid linear molecules is presented which can preserve the rigidity of the molecules without requiring any constraint force. The integrator is time-reversible and symplectic, thus preserving volume in phase space. It also conserves angular momentum. As expected, having all these virtues, it remains stable for large time-steps. Both the leap-frog and velocity-Verlet versions of the integrator are described. Since it features angular velocities explicitly, the integrator can be conveniently coupled to different thermostats. As a specific example, the Nose-Hoover thermostatting is discussed in detail to aid ready implementation. A simpler and faster adaptation of the main integrator, appropriate for double precision computing, is also offered.