The passivation of silicon dangling bond defects by H-2 is an important reaction in Si/SiO2 devices. The dangling bonds studied in this work are those in the a-SiO2 layers, prototype E' centers. Experimental estimates of the activation energy of this process are 0.3-0.4 eV, but theoretical calculations give energy barriers that are much larger, around 0.7-0.8 eV. It was suggested that the lack of tunneling in the energy barrier calculations is responsible for the overestimation. This paper is a systematic examination of this reaction, which includes tunneling corrections using the direct dynamics variational transition state theory. The inclusion of this effect is shown to provide an Arrhenius activation energy in good accord with the experimental values.