... what?! We can accurately predict hydrogen (and helium!) energy characteristics to _absurd_ accuracy levels. The issue is that even a system as simple as a single helium atom is prohibitively computationally expensive.
There's more to quantum chemistry (and hydrogen atoms) than what you're saying. If you define chemistry tautologically as what we know, then sure I guess.
To be clear, I'm not disputing unknowns in quantum chemistry in general (I lack the requisite background). But I was definitely of the understanding that single atom (and possibly somewhat larger) systems are thoroughly understood from a mathematical perspective at this point. I would appreciate concrete examples of open questions, either for hydrogen atoms specifically or for quantum chemistry more generally.
