Nonadiabatic calculations on hydrogen molecule

Since its infancy quantum mechanics has treated hydrogen molecule as a test bed. Contemporary spectroscopy is able to supply the dissociation energy ($D_0$) of H$_2$ with the accuracy of $3.7\cdot 10^{-4}\ \mathrm{cm}^{-1}$, while current theoretical predictions are $10^{-3}\ \mathrm{cm}^{-1}$ in error. Both the uncertainties are already smaller than the quantum electrodynamic (QED) effects contributing to $D_0$, which poses a particular challenge to theoreticians. Undoubtedly, in order to increase the predictive power of theory one has to not only account for the multitude of the tiny relativistic and QED effects but, especially, significantly increase precision of the largest component of $D_0$---the nonrelativistic contribution. We approach the problem of solving the Schroedinger equation, equipped with new methodology, with the target precision of $D_0$ set at the level of $10^{-7}\ \mathrm{cm}^{-1}$.