  The ability of metal free gas to cool by molecular hydrogen in primordial
halos is strongly associated with the strength of ultraviolet (UV) flux
produced by the stellar populations in the first galaxies. Depending on the
stellar spectrum, these UV photons can either dissociate $\rm H_{2}$ molecules
directly or indirectly by photo-detachment of $\rm H^{-}$ as the latter
provides the main pathway for $\rm H_{2}$ formation in the early universe. In
this study, we aim to determine the critical strength of the UV flux above
which the formation of molecular hydrogen remains suppressed for a sample of
five distinct halos at $z>10$ by employing a higher order chemical solver and a
Jeans resolution of 32 cells. We presume that such flux is emitted by PopII
stars implying atmospheric temperatures of $\rm 10^{4}$~K. We performed
three-dimensional cosmological simulations and varied the strength of the UV
flux below the Lyman limit in units of $\rm J_{21}$. Our findings show that the
value of $\rm J_{21}^{crit}$ varies from halo to halo and is sensitive to the
local thermal conditions of the gas. For the simulated halos it varies from
400-700 with the exception of one halo where $\rm J_{21}^{crit} \geq 1500$.
This has important implications for the formation of direct collapse black
holes and their estimated population at z > 6. It reduces the number density of
direct collapse black holes by almost three orders of magnitude compared to the
previous estimates.
