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Dimension-free path-integral molecular dynamics without preconditioning.

Roman Korol1, Jorge L Rosa-Raíces1, Nawaf Bou-Rabee2

  • 1Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.

The Journal of Chemical Physics
|March 16, 2020
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Summary
This summary is machine-generated.

New dimension-free integration schemes for path-integral molecular dynamics (MD) ensure accurate sampling and avoid divergence issues. The BCOCB method improves stability and efficiency for simulations like liquid water.

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Area of Science:

  • Computational Chemistry
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Path-integral molecular dynamics (MD) requires convergence with imaginary-time discretization (ring-polymer beads).
  • Existing non-preconditioned schemes like ring-polymer molecular dynamics (RPMD) and thermostatted RPMD (T-RPMD) exhibit zero overlap in the infinite-bead limit, causing issues with sampling and kinetic energy calculations.
  • These limitations impact hybrid Monte Carlo/MD schemes and lead to divergences in primitive path-integral kinetic-energy expectation values.

Purpose of the Study:

  • To introduce novel "dimension-free" numerical integration schemes for path-integral MD.
  • To overcome the limitations of existing methods, ensuring non-zero overlap with the exact distribution in the infinite-bead limit.
  • To develop schemes that provide finite error bounds and improve computational efficiency.

Main Methods:

  • Development of dimension-free integration schemes, including the BCOCB method, which uses symmetric splitting and a modified Cayley transformation.
  • Mollification of forces from the external physical potential to achieve dimension freedom.
  • Theoretical analysis for harmonic potentials and numerical validation for anharmonic systems, including liquid water.

Main Results:

  • Dimension-free schemes maintain non-zero overlap with the exact distribution in the infinite-bead limit for harmonic potentials.
  • The BCOCB integrator allows for a nearly three-fold increase in the stable MD time step for liquid water simulations compared to OABAB and BAOAB.
  • These new schemes introduce negligible errors in statistical properties and absorption spectra, preserve ergodicity and second-order accuracy, and are simple, black-box methods.

Conclusions:

  • Dimension-free path-integral numerical integration schemes effectively address convergence and sampling issues in MD simulations.
  • The BCOCB method represents a significant advancement, enhancing computational efficiency and accuracy for complex systems.
  • These methods offer a robust and practical solution for path-integral molecular dynamics, avoiding additional costs or complex implementations.