We will discuss construction, analysis and adaptive time-stepping
of time-splitting schemes applied in large-scale simulations of
quantum systems. Local error estimates are either based on
the defect of the numerical solution or an embedding idea.
For highly nonlocal nonlinear potentials arising in model
reductions such as the multi-configuration time-dependent
Hartree-Fock (MCTDHF) method, these turn out to be outperformed
by exponential Lawson-multistep schemes. Hence methods of the latter
class will also be equipped with error estimators and tested
in particular with respect to their long-time stability.