Approximation Properties and Limits of theQuantum - Classical Molecular Dynamics

In molecular dynamics applications there is a growing interest in including quantum eeects for simulations of larger molecules. This paper is concerned with mixed quantum-classical models which are currently discussed: the so-called QCMD model with variants and the time-dependent Born-Oppenheimer approximation. All these models are known to approximate the full quantum dynamical evolution|under diierent assumptions, however. We review the meaning of these assumptions and the scope of the approximation. In particular, we characterize those typical problematic situations where a mixed model might largely deviate from the full quantum evolution. One such situation of speciic interest, a non-adiabatic excitation at certain energy level crossings, can promisingly be dealt with by a modiication of the QCMD model that we suggest.