# Tunneling-splittings from path-integral molecular dynamics using a Langevin thermostat

## TL;DR

This paper introduces an improved path-integral molecular dynamics method utilizing a Langevin thermostat and thermodynamic integration along instanton paths to accurately compute tunneling splittings in molecules and clusters.

## Contribution

It presents a novel stochastic approach combining PIMD, thermodynamic integration, and Langevin thermostats for calculating tunneling splittings, improving accuracy and efficiency.

## Key findings

- Water dimer tunneling splittings agree within 20% of variational benchmarks.
- Smaller splittings in water dimer are within 10% of benchmark results.
- Method refines previous PIMD calculations for malonaldehyde.

## Abstract

We report an improved method for the calculation of tunneling splittings between degenerate configurations in molecules and clusters using path-integral molecular dynamics (PIMD). Starting from an expression involving a ratio of thermodynamic density matrices at the bottom of the symmetric wells, we use thermodynamic integration with molecular dynamics simulations and a Langevin thermostat to compute the splittings stochastically. The thermodynamic integration is performed by sampling along the semiclassical instanton path, which provides an efficient reaction coordinate as well as being physically well-motivated. This approach allows us to carry out PIMD calculations of the multi-well tunnelling splitting pattern in water dimer, and to refine previous PIMD calculations for one-dimensional models and malonaldehyde. The large (acceptor) splitting in water dimer agrees to within 20% of benchmark variational results, and the smaller splittings are within 10%.