  We perform a suite of hydrodynamic simulations to investigate how initial
density profiles of giant molecular clouds (GMCs) affect their subsequent
evolution. We find that the star formation duration and integrated star
formation efficiency of the whole clouds are not sensitive to the choice of
different profiles but are mainly controlled by the interplay between
gravitational collapse and stellar feedback. Despite this similarity, GMCs with
different profiles show dramatically different modes of star formation. For
shallower profiles, GMCs first fragment into many self-gravitation cores and
form sub-clusters that distributed throughout the entire clouds. These
sub-clusters are later assembled ``hierarchically'' to central clusters. In
contrast, for steeper profiles, a massive cluster is quickly formed at the
center of the cloud and then gradually grows its mass via gas accretion.
Consequently, central clusters that emerged from clouds with shallower profiles
are less massive and show less rotation than those with the steeper profiles.
This is because 1) a significant fraction of mass and angular momentum in
shallower profiles is stored in the orbital motion of the sub-clusters that are
not able to merge into the central clusters 2) frequent hierarchical mergers in
the shallower profiles lead to further losses of mass and angular momentum via
violent relaxation and tidal disruption. Encouragingly, the degree of cluster
rotations in steeper profiles is consistent with recent observations of young
and intermediate-age clusters. We speculate that rotating globular clusters are
likely formed via an ``accretion'' mode from centrally-concentrated clouds in
the early Universe.
