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

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