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Exact tunneling splittings from path-integral hybrid Monte Carlo with enveloping bridging potentials
Yu-Chen Wang1, Jeremy O Richardson1
1Institute of Molecular Physical Science, ETH Zürich, 8093 Zürich, Switzerland.
The Journal of Chemical Physics
|June 23, 2026
Summary
A new method, path-integral hybrid Monte Carlo with enveloping bridging potentials (PIHMC-EBP), accurately calculates molecular tunneling splittings. This approach simplifies analysis and reduces computational cost for key molecular systems.
Area of Science:
- Quantum Chemistry
- Computational Chemistry
- Molecular Dynamics
Background:
- Calculating tunneling splittings in molecular systems is crucial for understanding reaction mechanisms.
- Existing methods like path-integral molecular dynamics with thermodynamic integration can be computationally intensive and require significant manual analysis.
Purpose of the Study:
- To develop a more efficient and accurate method for calculating numerically exact tunneling splittings.
- To reduce the computational cost and manual effort associated with analyzing results.
Main Methods:
- Introduction of a path-integral hybrid Monte Carlo approach with enveloping bridging potentials (PIHMC-EBP).
- Construction of an approximately barrierless bridging potential to connect ring-polymer phase space regions.
- Design of tailored nonlocal updates to improve sampling of collective motions.
Main Results:
- PIHMC-EBP obviates the need for quadrature and time step convergence checks, simplifying analysis.
- Achieved the most precise tunneling splittings to date for malonaldehyde and the HCl dimer.
- Reduced computational cost by several times for malonaldehyde and three orders of magnitude for the HCl dimer.
- Enabled the first numerically exact path-integral calculations of ground-state tunneling splittings for the water dimer using reweighting.
Conclusions:
- PIHMC-EBP offers a significant advancement in the accurate and efficient calculation of tunneling splittings.
- The method provides substantial computational savings and reduces the complexity of data analysis.
- Demonstrated broad applicability across various molecular systems and potential energy surfaces.
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