  Gravitational collapse of a massive primordial gas cloud is thought to be a
promising path for the formation of supermassive blackholes in the early
universe. We study conditions for the so-called direct collapse (DC) blackhole
formation in a fully cosmological context. We combine a semianalytic model of
early galaxy formation with halo merger trees constructed from dark matter
$N$-body simulations. We locate a total of 68 possible DC sites in a volume of
$20\;h^{-1}\;\mathrm{Mpc}$ on a side. We then perform hydrodynamics simulations
for 42 selected halos to study in detail the evolution of the massive clouds
within them. We find only two successful cases where the gas clouds rapidly
collapse to form stars. In the other cases, gravitational collapse is prevented
by the tidal force exerted by a nearby massive halo, which otherwise should
serve as a radiation source necessary for DC. Ram pressure stripping disturbs
the cloud approaching the source. In many cases, a DC halo and its nearby light
source halo merge before the onset of cloud collapse. Only when the DC halo is
assembled through major mergers, the gas density increases rapidly to trigger
gravitational instability. Based on our cosmological simulations, we conclude
that the event rate of DC is an order of magnitude smaller than reported in
previous studies, although the absolute rate is still poorly constrained. It is
necessary to follow the dynamical evolution of a DC cloud and its nearby
halo(s) in order to determine the critical radiation flux for DC.
