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The abundance of molecular hydrogen (H2), the primary coolant in primordialgas, is critical for the thermodynamic evolution and star-formation historiesin early protogalaxies. Determining the photodissociation rate of H2 by anincident Lyman-Werner (LW) flux is thus crucial, but prohibitively expensive tocalculate on the fly in simulations. The rate is sensitive to the H2rovibrational distribution, which in turn depends on the gas density,temperature, and incident LW radiation field. We use the publicly availablecloudy package to model primordial gas clouds and compare exactphotodissociation rate calculations to commonly-used fitting formulae. We findthe fit from Wolcott-Green et al. (2011) is most accurate for moderatedensities n~10^3 cm^{-3} and temperatures, T~10^3K, and we provide a new fit,which captures the increase in the rate at higher densities and temperatures,owing to the increased excited rovibrational populations in this regime. Ournew fit has typical errors of a few percent percent up to n =<10^7 cm^{-3}, T=< 8000K, and H2 column density NH2 =<10^{17} cm^{-2}, and can be easilyutilized in simulations. We also show that pumping of the excited rovibrationalstates of H2 by a strong LW flux further modifies the level populations whenthe gas density is low, and noticeably decreases self-shielding for J_21 > 10^3and n < 10^2 cm^{-3}. This may lower the "critical flux" at which primordialgas remains H2-poor in some protogalaxies, enabling massive black hole seedformation.

H2 self-shielding with non-LTE rovibrational populations: implications for cooling in protogalaxies