  We present the results of a numerical study examining the effect of H_2-based
star formation (SF) model on the rest-frame UV luminosity function and star
formation rate function (SFRF) of z>=6 galaxies, and the implications for
reionization. Using cosmological hydrodynamical simulations outfitted with an
H_2-SF model, we find good agreement with our previous results (non-H_2 SF
model) and observations at Muv<=-18. However at Muv>-18, we find that the LF
deviates from both our previous work and current observational extrapolations,
producing significantly fewer low-luminosity galaxies and exhibiting additional
turnover at the faint end. We constrain the redshift evolution of this turnover
point using a modified Schechter function that includes additional terms to
quantify the turnover magnitude (Muv^t) and subsequent slope (Beta). We find
that Muv^t evolves from Muv^t=-17.33 (at z=8) to -15.38 (z=6), while Beta
becomes shallower by \Delta Beta=0.22 during the same epoch. This occurs in an
Muv range which will be observable by JWST. By integrating the SFRF, we
determine that even though H_2-SF model significantly reduces the number
density of low luminosity galaxies at Muv>-18, it does not suppress the total
SFR density enough to affect the capability of SF to maintain reionization.
