# Comparison of Modern Langevin Integrators for Simulations of Coarse-Grained Polymer Melts

## TL;DR

This study compares the performance of three Langevin integrators in coarse-grained polymer melt simulations, highlighting that G-JF maintains accuracy at larger time steps better than others, which is crucial for efficient molecular dynamics simulations.

## Contribution

It provides a comparative analysis of Langevin integrators for coarse-grained systems, emphasizing G-JF's superior stability at larger time steps.

## Key findings

- G-JF maintains accuracy with larger time steps.
- All integrators perform similarly at low friction.
- Large steps cause deviations in diffusivity for most methods.

## Abstract

For a wide range of phenomena, current computational ability does not always allow for fully atomistic simulations of high-dimensional molecular systems to reach time scales of interest. Coarse-graining (CG) is an established approach to alleviate the impact of computational limits while retaining the same algorithms used in atomistic simulations. It is of importance to understand how algorithms such as Langevin integrators perform on non-trivial CG molecular systems, and in particular how large of an integration time step can be used without introducing unacceptable amounts of error into averaged quantities of interest. To investigate this, we examined three different Langevin integrators on a CG polymer melt: the recently developed BAOAB method by Leimkuhler and Matthews, the Gronbech-Jensen and Farago method, or G-JF, and the frequently used Brunger-Brooks-Karplus integrator, also known as BBK. We compute and analyze key statistical properties for each. Our results indicate that the three integrators perform similarly when using a small friction parameter; however, outside of this regime the use of large integration steps produces significant deviations from the predicted diffusivity and steady-state distributions for all integration methods examined with the exception of G-JF.