It is very difficult to absorb H2 but lots of researcher have tried anyway. Metal Hydrides appear to be the leading method.(Mg, Na or Li). Graphene has also been used. Liquid H2 srorage in tanks and caverns is a competing technology
Here are a few examples of metals that can absorb hydrogen to form metal hydrides:
Sodium (Na) to form sodium hydride (NaH)
Calcium (Ca) to form calcium hydride (CaH2)
Magnesium (Mg) to form magnesium hydride (MgH2)
Lithium (Li) to form LiH
Aluminum (Al) which forms aluminum hydride or alane (AlH3)
There are also mixtures of metals that can form complex metal hydrides such as NaAlH4 which is called sodium aluminum hydride which is also called alanate.
I've authored several peer-reviewed papers and report for the department of Energy when I was their Principal Investigator on hydrogen storage materials reactivity and safety. You can download these papers from my profile under researchgate.net