Knowledge Bank

The ionization and dissociation energies of H$2$, HD and D$2$ are benchmark quantities in molecular quantum mechanics. Comparison between experimental and theoretical values for these quantities has a long history starting with the early measurement of Beutler, \emph{Z.~Phys.~Chem.} \textbf{29}, 315 (1935)} and the calculations of James and Coolidge., \emph{J.~Chem.~Phys.} \textbf{1}, 825 (1933)} Transition wave numbers from the \mbox{$EF1\Sigma g+(v=0,N=0,1)$} state to selected $n$p Rydberg states ($n\approx 60$) below the \mbox{$X+2\Sigma u+(v+=0,N+=0,1)$} ionization threshold have been measured in H$2$,, \emph{J.~Chem.~Phys.} \textbf{130}, 174306 (2009)} HD and D$2$, submitted to \emph{J.~Chem.~Phys.}} at a precision better than 10~MHz (0.0003~cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$). Combining the results with previous experimental and theoretical data for other energy level intervals, the ionization and dissociation energies of H$2$, HD and D$2$ could be determined at an absolute accuracy of better than 20~MHz. These new results represent an improvement over previous experimental results by more than one order of magnitude and the most precise values of dissociation and ionization energies measured to date in a molecular system. The results therefore offer the opportunity of a comparison with theoretical values. In particular they will be compared to the latest \emph{ab~initio} calculationsach, M.~Przybytek, J.~Komasa, K.~Pachucki, and B.~Jeziorski}, \emph{J.~Chem.~Theory~Comput.} \textbf{5}, 3039 (2009)} which include nonadiabatic, relativistic and radiative effects. The comparison indicates that relativistic and radiative quantum electrodynamics corrections of order up to $\alpha 4$ are needed to account for the experimental results.