Knowledge Bank

With two electrons and two protons, molecular hydrogen is the simplest molecule displaying all features of a chemical bond. H$2$ is therefore a fundamental system for testing molecular quantum mechanics and quantum electrodynamics in molecules. The test can be performed by comparing measured and calculated intervals between different rovibronic states of H$2$ \textbf{107} (4), 043005 (2011).}. Two further quantities that can be used for this test are the dissociation and ionization energies of H$2$, and considerable efforts have been invested over more than 80 years to improve the precision and accuracy of experimental and theoretical determination of these two quantities. The current status of the comparison is that the theoretical \textbf{5} (11), 3039 (2009).} and experimental \textbf{130} (17), 174306 (2009).} values of the ionization and dissociation energies of H$2$ agree within the combined uncertainty of 30~MHz (see also \textbf{150}, 51 (2011).}). The factors currently limiting the precision of the experimental determination will be discussed and the strategies that are being implemented towards overcoming these limitations will be presented. A long-term goal is to achieve a precision of better than 15~kHz, which is the ultimate limit imposed on the accuracy of the theoretical determination by the current uncertainty of the proton-to-electron mass ratio.