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

TL;DR

This paper explores optimized splitting methods for rigid body integration in molecular dynamics, demonstrating that certain schemes outperform traditional velocity Verlet at various accuracy levels, especially when avoiding kinetic energy splitting.

Contribution

It identifies the best combination of optimized splitting and gradient methods for rigid body simulations, highlighting the effectiveness of specific schemes at different accuracy thresholds.

Findings

Velocity Verlet is optimal for >1.5% accuracy.

Modified Verlet (HOA) is optimal up to 0.4% accuracy.

Fourth order gradient scheme (GIER4) is best for high accuracy.

Abstract

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