  Multi-mode expansions in computational quantum dynamics promise convergence
toward exact results upon increasing the number of modes. Convergence is
difficult to ascertain in practice due to the unfavourable scaling of required
resources for many-particle problems and therefore a simplified criterion based
on a threshold value for the least occupied mode function is often used. Here
we show how the separable quantum motion of the center of mass can be used to
sensitively detect unconverged numerical multi-particle dynamics in harmonic
potentials. Based on an experimentally relevant example of attractively
interacting bosons in one dimension, we demonstrate that the simplified
convergence criterion fails to assure qualitatively correct results.
Furthermore, the numerical evidence for the creation of two-hump fragmented
bright soliton-like states presented by Streltsov \emph{et al.} [PRL 100,
130401 (2008)] is shown to be inconsistent with exact results. Implications for
our understanding of dynamical fragmentation in attractive boson systems are
briefly discussed.
