  The effect of line overlap in the Lyman and Werner bands, often ignored in
galactic studies of the atomic-to-molecular transition, greatly enhances
molecular hydrogen self-shielding in low metallicity environments, and
dominates over dust shielding for metallicities below about 10% solar. We
implement that effect in cosmological hydrodynamics simulations with an
empirical model, calibrated against the observational data, and provide fitting
formulae for the molecular hydrogen fraction as a function of gas density on
various spatial scales and in environments with varied dust abundance and
interstellar radiation field. We find that line overlap, while important for
detailed radiative transfer in the Lyman and Werner bands, has only a minor
effect on star formation on galactic scales, which, to a much larger degree, is
regulated by stellar feedback.
