Dimension-free path-integral molecular dynamics without preconditioning

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.