An efficient algorithm for equations of motion of molecular dynamical systems

Abstract

This paper presents a new efficient sequential O ( N ) algorithm for computer modelling of the motion behaviours of molecular dynamical systems. The method is based on the frozen lightly-excited degrees of freedom of an atom in a molecular system, such as inter-atomic oscillations and rotation about double bonds with high frequencies, so that a reduced molecular system with rigid subsets and joints is formed. Then Kane’s dynamical equations and the internal coordinate method (ICM) are applied to the reduced model for recursive formation and solution of equations of motion of the atomistic molecular system. The increased computational efficiency is accomplished through three sequential computing sweepings along the structure of the molecular system so that the equations of motion are solved when they are being formed at a fixed computing cost. The algorithm provides a sequential O ( N ) computational performance for a molecular system with an open-loop structure. Here N is the total number of subsets.