  Recent observations indicate that star formation occurs only in the molecular
phase of a galaxy's interstellar medium. A realistic treatment of star
formation in simulations and analytic models of galaxies therefore requires
that one determine where the transition from the atomic to molecular gas
occurs. In this paper we compare two methods for making this determination in
cosmological simulations where the internal structures of molecular clouds are
unresolved: a complex time-dependent chemistry network coupled to a radiative
transfer calculation of the dissociating ultraviolet (UV) radiation field, and
a simple time-independent analytic approximation. We show that these two
methods produce excellent agreement at all metallicities >~10^-2 of the Milky
Way value across a very wide range of UV fields. At lower metallicities the
agreement is worse, likely because time-dependent effects become important;
however, there are no observational calibrations of molecular gas content at
such low metallicities, so it is unclear if either method is accurate. The
comparison suggests that, in many but not all applications, the analytic
approximation provides a viable and nearly cost-free alternative to full
time-dependent chemistry and radiative transfer.
