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We can calculate the quantum energy levels for an isolated Hydrogen atom (one proton and one electron) and that is it. Forget a Hydrogen molecule! It is called the three particle problem.
I gave up on fundamental Physics to concentrate on biological molecules as it seemed to be a far more unmined resource for self serving scientific grandeur. It may even give us some insights as nature has been running the experiments for about four billion years.
All jokes aside we nearly have the tools to make the tools to even start to solve the fundamental problems.
Looking at the problem from a perspective we cannot now imagine may solve it. Chucking in a fudge factor is a cop out. We may as well invoke the easter bunny or the tooth fairy!
Bert
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