Symplectic Splitting Methods for Rigid Body Molecular Dynamics

Andreas Dullweber, Benedict Leimkuhler and Robert McLachlan

Abstract

Rigid body molecular models possess symplectic structure and time-reversal symmetry. Standard numerical integration methods destroy both properties, introducing nonphysical dynamical behavior such as numerically-induced dissipative states and drift in the energy during long term simulations. This article describes the construction, implementation and practical application of fast explicit symplectic-reversible integrators for multiple rigid body molecular simulations. These methods use a reduction to Euler equations for the free rigid body, together with a symplectic splitting technique. In every timestep, the orientational dynamics of each rigid body are integrated by a sequence of planar rotations. Besides preserving the symplectic and reversible structures of the flow, this scheme accurately conserves the total angular momentum of a system of interacting rigid bodies. Excellent energy conservation can be obtained relative to traditional methods, especially in long time simulations. The method is implemented in a research code, ORIENT, and compared with a quaternion/extrapolation scheme for the TIP4P model of water. Our experiments show that the symplectic-reversible is far superior to the more traditional quaternion method.

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