Adaptive integration of molecular dynamics

This article presents a particle method framework for simulating molecular dynamics. For time integration, the implicit trapezoidal rule is employed, where an explicit predictor enables large time steps. Error estimators for both the temporal and spatial discretization are advocated, and facilitate a fully adaptive propagation. The framework is developed and exemplified in the context of the classical Liouville equation, where Gaussian phase-space packets are used as particles. Simplified variants are discussed briefly. The concept is illustrated by numerical examples for one-dimensional dynamics in double well potential.