The light reactions, if seen as a whole, are basically the oxidation of water to provide energy (ATP) to fuel the Calvin Cycle. The photons provide the activation energy for the same.
How then can we say that during chemo-synthesis bacteria get ATP in the first step by oxidizing inorganic substances like $H_2S$ or $CH_4$ because ultimately, it is similar to the light reactions and will require some activation energy?
Where does this energy come from?