Efficient algorithms for rigid body integration using optimized splitting methods and exact free rotational motion

摘要

Hamiltonian splitting methods are an established technique to derive stableand accurate integration schemes in molecular dynamics, in which additionalaccuracy can be gained using force gradients. For rigid bodies, a traditionexists in the literature to further split up the kinetic part of theHamiltonian, which lowers the accuracy. The goal of this note is to comment onthe best combination of optimized splitting and gradient methods that avoidssplitting the kinetic energy. These schemes are generally applicable, but theoptimal scheme depends on the desired level of accuracy. For simulations ofliquid water it is found that the velocity Verlet scheme is only optimal forcrude simulations with accuracies larger than 1.5%, while surprisingly amodified Verlet scheme (HOA) is optimal up to accuracies of 0.4% and a fourthorder gradient scheme (GIER4) is optimal for even higher accuracies.