Exactly Time-Reversible Molecular Dynamics Algorithm for Rigid-Body Systems

A simple, time-reversible simulation algorithm for rigid molecules is proposed. No time-reversible simulation algorithm for rigid molecules as simple as the velocity-Verlet algorithm for point atoms has been devised owing to the complex mutual dependence of the angular position and the angular velocity. In the present algorithm, the time reversibility of the rotational motion of a rigid molecule is enforced at every time step by determining numerically the angular velocity required to satisfy its non linear equation. The numerical complexity and the stability of the present algorithm are compared with those of the former algorithms, including the symplectic one, through demonstrative simulation of a nanometer-sized water droplet. Despite the simplicity of the present algorithm, the total energy in the present algorithm is conserved well, as in the symplectic algorithm. The principal idea behind the present algorithm, to enforce the time reversibility numerically, is generally applicable to the numerical simulation of various time-evolution equations.