  Hydrogen point defects in silicon still hold unsolved problems, whose
disclosure is fundamental for future advances in Si technologies. Among the
open issues is the mechanism for the condensation of atomic hydrogen into
molecules in Si quenched from above $T\sim700\,^{\circ}$C to room temperature.
Based on first-principles calculations, we investigated the thermodynamics of
hydrogen monomers and dimers at finite temperatures within the harmonic
approximation. The free energies of formation indicate that the population of
H$^{-}$ cannot be neglected when compared that of H$^{+}$ at high temperatures.
The results allow us to propose that the formation of molecules occurs during
cooling processes, in the temperature window $T\sim700\textrm{-}500\,$K, above
which the molecules collide with Si-Si bonds and dissociate, and below which
the fraction of H$^{-}$ becomes negligible. The formation of H$^{-}$ and most
notably of a fast-diffusing neutral species could also provide an explanation
for the apparent \emph{accelerated} diffusivity of atomic hydrogen at elevated
temperatures in comparison to the figures extrapolated from measurements
carried out at cryogenic temperatures. We finally show that the observed
diffusivity of the molecules is better described upon the assumption that they
are nearly free rotors, all along the minimum energy path, including at the
transition state.
