  Dissipative dark matter predicts rich observable phenomena that can be tested
with future large-scale structure surveys. As a specific example, we study
atomic dark matter, consisting of a heavy particle and a light particle charged
under a dark electromagnetism. In particular, we calculate the cosmological
evolution of atomic dark matter focusing on dark recombination and
dark-molecule formation. We have obtained the relevant interaction-rate
coefficients by re-scaling the rates for normal hydrogen, and evolved the
abundances for ionized, atomic, and molecular states using a modified version
of Recfast++ (which we have released publicly at
https://github.com/jamesgurian/RecfastJulia). We also provide an analytical
approximation for the final abundances. We then calculate the effects of the
atomic dark matter on the linear power spectrum, which enter through a
dark-photon diffusion and dark acoustic oscillations. At the formation time,
the atomic dark matter model suppresses halo abundances on scales smaller than
the diffusion scale, just like the warm dark matter models suppress the
abundance below the free-streaming scale. The subsequent evolution with
radiative cooling, however, will alter the halo mass function further.
