  We consider commutator-free exponential integrators as put forward in
[Alverman, A., Fehske, H.: High-order commutator-free exponential
time-propagation of driven quantum systems. J. Comput. Phys. 230, 5930-5956
(2011)]. For parabolic problems, it is important for the well-definedness that
such an integrator satisfies a positivity condition such that essentially it
only proceeds forward in time. We prove that this requirement implies maximal
convergence order of four for real coefficients, which has been conjectured
earlier by other authors.

Numerical Analysis