Accurate calculations of free energy differences for isotopic substitutions are essential for environmental and geological chemistry. These and other properties of nuclei in condensed phases are obtained using path-integral molecular dynamics (PIMD) methods. However, previously existing PIMD integrators are plagued with resonance instabilities, requiring equations of motion to be integrated with short timesteps [J. Chem. Phys. 151, 124103 (2019)]. We propose a simple modification to the standard PIMD integrator that removes these issues at no added computational cost. Seemingly counterintuitive, the idea is to replace the exact free ring-polymer sub-step with its Cayley transform approximation. This modified PIMD integrator removes the finite timestep error for local observables in harmonic systems and allows one to take significantly larger timesteps with no loss of accuracy in general systems, as illustrated by the highly anharmonic example of liquid water [J. Chem. Phys. 152, 104102 (2020)]. Use of this improved PIMD integrator yields to date the most accurate free energy differences for isotopic substitutions in condensed phase, validating and improving on the existing experimental calibrations.

Accurate quantum statistics from improved path-integrals in imaginary time

ACS Spring 2022

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