# Fine Tuning Classical and Quantum Molecular Dynamics using a Generalized Langevin Equation

## TL;DR

This paper demonstrates how generalized Langevin equation (GLE) thermostats can be finely tuned to improve the accuracy of dynamical property predictions in molecular dynamics, including quantum effects and anharmonic systems.

## Contribution

It introduces analytical measures to predict and correct GLE-induced disturbances in dynamics, enhancing the modeling of quantum nuclear effects and vibrational dynamics.

## Key findings

- Analytical measures accurately predict GLE effects on harmonic oscillators
- Corrective methods significantly reduce GLE disturbances in microcanonical dynamics
- Tailored GLE thermostats improve vibrational dynamics modeling in complex systems

## Abstract

Generalized Langevin Equation (GLE) thermostats have been used very effectively as a tool to manipulate and optimize the sampling of thermodynamic ensembles and the associated static properties. Here we show that a similar, exquisite level of control can be achieved for the dynamical properties computed from thermostatted trajectories. By developing quantitative measures of the disturbance induced by the GLE to the Hamiltonian dynamics of a harmonic oscillator, we show that these analytical results accurately predict the behavior of strongly anharmonic systems. We also show that it is possible to correct, to a significant extent, the effects of the GLE term onto the corresponding microcanonical dynamics, which puts on more solid grounds the use of non-equilibrium Langevin dynamics to approximate quantum nuclear effects and could help improve the prediction of dynamical quantities from techniques that use a Langevin term to stabilize dynamics. Finally we address the use of thermostats in the context of approximate path-integral-based models of quantum nuclear dynamics. We demonstrate that a custom-tailored GLE can alleviate some of the artifacts associated with these techniques, improving the quality of results for the modelling of vibrational dynamics of molecules, liquids and solids.