Polynomial propagators for classical molecular dynamics

TL;DR

This paper introduces polynomial-based numerical propagators for classical molecular dynamics, offering controllable accuracy, acceptable long-term stability, and efficient scaling, as an alternative to traditional integrators like velocity Verlet.

Contribution

It presents a novel polynomial expansion approach for propagating classical molecular dynamics, enabling arbitrary order accuracy and efficient computation for large systems.

Findings

Polynomial propagators achieve acceptable long-term energy stability.

Scaling with expansion order is polynomial, with linear scaling in time step size.

Method is applicable to Lennard-Jones systems and extendable to other force fields.

Abstract

Classical molecular dynamics simulation is performed mostly using the established velocity Verlet integrator or other symplectic propagation schemes. In this work, an alternative formulation of numerical propagators for classical molecular dynamics is introduced based on an expansion of the time evolution operator in series of Chebyshev and Newton polynomials. The suggested propagators have, in principle, arbitrary order of accuracy which can be controlled by the choice of expansion order after that the series is truncated. However, the expansion converges only after a minimum number of terms is included in the expansion and this number increases linearly with the time step size. Measurements of the energy drift demonstrate the acceptable long-time stability of the polynomial propagators. It is shown that a system of interacting Lennard-Jones particles is tractable by the proposed technique and that the scaling with the expansion order is only polynomial while the scaling with the number of particles is the same as with the conventional velocity Verlet. The proposed method is, in principle, extendable for further interaction force fields and for integration with a thermostat, and can be parallelized to speed up the computation of every time step.