Test of quantum chemistry in vibrationally-hot hydrogen molecules

Precision measurements are performed on highly excited vibrational quantum states of molecular hydrogen. The $v=12,J=0-3$ rovibrational levels of H${}_2$ ($X^1{\mathrm{\Sigma }}_g^{+}$), lying only $2000$ cm${}^{-1}$ below the first dissociation limit, were populated by photodissociation of H${}_2$S and their level energies were accurately determined by two-photon Doppler-free spectroscopy. A comparison between the experimental results on $v=12$ level energies with the best $\mathit{\text{ab}}\mathit{\text{initio}}$ calculations shows good agreement, where the present experimental accuracy of $3.5\times {10}^{-3}$ cm${}^{-1}$ is more precise than theory, hence providing a gateway to further test theoretical advances in this benchmark quantum system.