Exact tunneling splittings from path-integral hybrid Monte Carlo with enveloping bridging potentials

TL;DR

This paper introduces a novel path-integral hybrid Monte Carlo method with enveloping bridging potentials for accurately computing tunneling splittings in molecular systems, reducing manual effort and computational cost.

Contribution

The method enables direct sampling of free-energy profiles for tunneling splittings without quadrature or time-step convergence, providing highly precise results efficiently.

Findings

Achieved the most precise tunneling splittings for malonaldehyde and its isotopologue.

Reduced computational cost by several times and three orders of magnitude for studied systems.

First numerically exact path-integral calculations of water dimer tunneling splittings on multiple potential surfaces.

Abstract

A path-integral hybrid Monte Carlo approach with enveloping bridging potentials (PIHMC-EBP) is proposed for calculating numerically exact tunneling splittings in molecular systems. The central idea is to construct an approximately barrierless bridging potential that smoothly connects symmetry-related regions of ring-polymer phase space, enabling direct sampling of the free-energy profile from which the relevant splittings are obtained. Two tailored nonlocal updates are designed to enhance the sampling of slow collective motions. Compared with path-integral molecular dynamics using thermodynamic integration, PIHMC-EBP requires neither quadrature nor time-step convergence checks, thereby substantially reducing the manual effort required to analyze the results. Applications to malonaldehyde (and its deuterated isotopologue) and the HCl dimer using state-of-the-art potential energy surfaces provide the most precise tunneling splittings reported to date for both systems, while simultaneously reducing the overall computational cost by several times and three orders of magnitude, respectively. Finally, application to the water dimer yields the first numerically exact path-integral calculations of the ground-state tunneling splittings on three different potential energy surfaces, all obtained simultaneously by reweighting a single set of trajectories.