Algorithms for constrained molecular dynamics

TLDR: The form of the nonlinear equations is examined in detail and used to give convergence results for the traditional nonlinear solution technique SHAKE iteration and for a modification based on successive overrelaxation (SOR).

Abstract: In molecular dynamics simulations, the fastest components of the potential field impose severe restrictions on the stability and hence the speed of computational methods. One possibility for treating this problem is to replace the fastest components with algebraic length constraints. In this article the resulting systems of mixed differential and algebraic equations are studied. Commonly used discretization schemes for constrained Hamiltonian systems are discussed. The form of the nonlinear equations is examined in detail and used to give convergence results for the traditional nonlinear solution technique SHAKE iteration and for a modification based on successive overrelaxation (SOR). A simple adaptive algorithm for finding the optimal relaxation parameter is presented. Alternative direct methods using sparse matrix techniques are discussed. Numerical results are given for the new techniques, which have been implemented in the molecular modeling software package CHARMM and show as much as twofold improvement over SHAKE iteration. © 1995 John Wiley & Sons, Inc.