Numerical Integrators for Quantum-Classical Molecular Dynamics

It was revealed that the QCMD model is of canonical Hamiltonian form with symplectic structure, which implies the conservation of energy. An efficient and reliable integrator for transfering these properties to the discrete solution is the symplectic and explicit PICKABACK algorithm. The only drawback of this kind of integrator is the small stepsize in time induced by the splitting techniques used to discretize the quantum evolution operator. Recent investigations concerning Krylov iteration techniques result in alternative approaches which overcome this difficulty for a wide range of problems. By using iterative methods in the evaluation of the quantum time propagator, these techniques allow for the stepsize to adapt to the classical motion and the coupling between the classical and the quantum mechanical subsystem. This yields a drastic reduction of the numerical effort. The pros and cons of both approaches as well as the suitable applications are discussed in the last part.