GROMACS Stochastic Dynamics and BAOAB are equivalent configurational sampling algorithms

TL;DR

This paper proves that the GROMACS Stochastic Dynamics integrator and the BAOAB splitting method are equivalent in sampling configurations, sharing the same configurational accuracy, with GSD/BAOA showing higher kinetic accuracy.

Contribution

It establishes the equivalence between GROMACS Stochastic Dynamics and the BAOA splitting method, clarifying their relationship and comparative accuracy in molecular simulations.

Findings

GSD and BAOAB sample the same configurations.

GSD/BAOA has higher kinetic accuracy than BAOAB.

GSD is equivalent to the BAOA splitting method.

Abstract

Two of the most widely used Langevin integrators for molecular dynamics simulations are the GROMACS Stochastic Dynamics (GSD) integrator and the splitting method BAOAB. In this letter, we show that the GROMACS Stochastic Dynamics integrator is equal to the less frequently used splitting method BAOA. It immediately follows that GSD and BAOAB sample the same configurations and have the same high configurational accuracy. Our numerical results indicate that GSD/BAOA has higher kinetic accuracy than BAOAB.