A new approach to the integration of rotational motion in systems with interacting rigid bodies

Abstract

A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration, whereas orientational positions are expressed in terms of either principal axes or quaternions. As a result, the rigidness of molecules appears to be an integral of motion, despite the atom trajectories are evaluated approximately. The algorithm derived is free of any iterative procedures and it allows to perform both energy- and temperature-conserving simulations. The corresponding integrators are time reversible but the symplectic behaviour is only achieved in mean. Symplectic versions are also described. The provide the conservation of volume in phase space precisely at each time step and, moreover, lead to exact solutions for angular velocities in the inertial-motion regime. It is shown that the algorithm exhibits excellent stability properties and conserves the energy even somewhat better than the atomic-constraint technique.