Born-Oppenheimer approximation and beyond for time-dependent electronic processes

Explicit computations of electronic motion in time and space are gradually becoming feasible and available. The knowledge of this motion is of relevance by itself but is also important for understanding available and predicting future experiments on the electronic time scale. In electronic processes of interest, usually several and even many stationary electronic states participate and the obvious question arises on how to describe the accompanying quantum nuclear dynamics at least on the time scale of the process. In this work, we attempt to study the nuclear dynamics in the framework of a fully time-dependent Born-Oppenheimer approximation. Additionally, we attempt to go beyond this approximation by introducing the coupling of several electronic wavepackets by the nuclear wavepackets. In this context, we also discuss a time-dependent transformation to diabatic electronic wavepackets. A simple but critical model of charge transfer is analyzed in some detail on various levels of approximation and also solved exactly