A trigonometric integrator for the constrained ring polymer Hamiltonian dynamics

TL;DR

This paper introduces a novel trigonometric integrator for constrained ring polymer Hamiltonian dynamics in path integral molecular dynamics, emphasizing structure preservation and stability.

Contribution

It develops a new integrator that combines flow composition with constraint handling, preserving symplectic structure and time-reversibility in ring polymer simulations.

Findings

The integrator maintains near-conservation of Hamiltonian.

Numerical tests show enhanced stability at 298K.

The method effectively handles holonomic constraints.

Abstract

A class of trigonometric integrator is proposed for the constrained ring polymer Hamiltonian dynamics, arising from the path integral molecular dynamics. The integrator is formulated by the composition of flows, thereby integrating the Cartesian equations of motions under normal mode representation and preserving the holonomic constraints by iterations. It is illustrated that the trigonometric method can preserve the symplectic structure and time-reversibility, and its near-conservation of Hamiltonian is analyzed in the framework of modulated Fourier expansion analysis. Numerical examples illustrating its stability are presented using the SPC/E force field at 298K.