Adaptive Integration of Multidimensional Molecular Dynamics with Quantum Initial Conditions

The paper presents a particle method framework for resolving molecular dynamics. Error estimators for both the temporal and spatial discretization are advocated and facilitate a fully adaptive propagation. For time integration, the implicit trapezoidal rule is employed, where an explicit predictor enables large time steps. 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 shortly, which should prove to be easily implementable in commonmolecular dynamics codes. The concept is illustrated by numerical examples for one-dimensional dynamics in double well potential. AMS MSC 2000: 81S30, 65J10, 65M99