One of the things that amazes me is that it is still not possible to do an ab initio quantum mechanics calculation of the rotational spectrum of even a diatomic

One of the things that amazes me is that it is still not possible to do an ab initio quantum mechanics calculation of the rotational spectrum of even a diatomic molecule with sufficient accuracy to allow identification from measured spectra. Two atoms, and we can't precisely calculate the spectrum. There's lots of room for more computing power.