  We introduce non-equilibrium molecular hydrogen chemistry into the radiation
hydrodynamics code Ramses-RT. This is an adaptive mesh refinement grid code
with radiation hydrodynamics that couples the thermal chemistry of hydrogen and
helium to moment-based radiative transfer with the Eddington tensor closure
model. The H2 physics that we include are formation on dust grains, gas phase
formation, formation by three-body collisions, collisional destruction,
photodissociation, photoionization, cosmic ray ionization, and self-shielding.
In particular, we implement the first model for H2 self-shielding that is tied
locally to moment-based radiative transfer by enhancing photodestruction. This
self-shielding from Lyman-Werner line overlap is critical to H2 formation and
gas cooling. We can now track the non-equilibrium evolution of molecular,
atomic, and ionized hydrogen species with their corresponding dissociating and
ionizing photon groups. Over a series of tests we show that our model works
well compared to specialized photodissociation region codes. We successfully
reproduce the transition depth between molecular and atomic hydrogen, molecular
cooling of the gas, and a realistic Stromgren sphere embedded in a molecular
medium. In this paper we focus on test cases to demonstrate the validity of our
model on small scales. Our ultimate goal is to implement this in large-scale
galactic simulations.
