Communication: 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<inf>2</inf> (X 1 Σ g +), lying only 2000 cm^-1 below the first dissociation limit, were populated by photodissociation of H<inf>2</inf>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 ab initio calculations shows a good agreement, where the present experimental accuracy of 3.5 × 10^-3 cm^-1 is more precise than theory, hence providing a gateway to further test theoretical advances in this benchmark quantum system.