Are we saying that Mars doesn't have H2 in its atmosphere or regolith? The proton flux from the sun ought to provide a lot of H+ Ions. Especially without the sheilding that our planet enjoys. From what I've heard, H+ Ions aren't happy alone and quickly grab free electrons. Loneliness strikes again and two H atoms usually pair up to produce an H2 molecule. (Modern mores won't allow us to legislate that ALL H atoms do this, however)

As far as energy is concerned, Mars has enough of it to make all those peroxides. What's the problem?

By "Molecular Hydrogen" do you mean (H2)?
It takes energy (UV, perhaps?) to separate (H2) into free H atoms - aka monoatomic hydrogen.

Actually, though- I'd like to see us develop our asteroid steering capabilities by practicing on Mars a la Asimov's story "The Martian Way." That would solve a lot of our terraforming problems.