Symplectic Multiple-Time-Stepping Integrators for Quantum-Classical Molecular Dynamics

The overall Hamiltonian structure of the Quantum-Classical Molecular Dynamics model makes — analogously to classical molecular dynamics - symplectic integration schemes the methods of choice for long-term simulations. This has already been demonstrated by the symplectic PICKABACK method [19]. However, this method requires a relatively small step-size due to the high-frequency quantum modes. Therefore, following related ideas from classical molecular dynamics, we investigate symplectic multiple-time-stepping methods and indicate various possibilities to overcome the step-size limitation of PICKABACK.