The dissociation energy of H2 represents a benchmark quantity to test the accuracy of firstprinciples calculations. We present a new measurement of the energy interval between the EF 1 Σ + g (v = 0, N = 1) state and the 54p11 Rydberg state of H2. When combined with previously determined intervals, this new measurement leads to an improved value of the dissociation energy D N =1 0 of ortho-H2 that has, for the first time, reached a level of uncertainty that is three times smaller than the contribution of about 1 MHz resulting from the finite size of the proton. The new result of 35 999.582 834(11) cm −1 is in remarkable agreement with the theoretical result of 35 999.582 820(26) cm −1 obtained in calculations including high-order relativistic and quantum electrodynamics corrections, as reported in the companion article (M. Puchalski, J. Komasa, P. Czachorowski and K. Pachucki, submitted). This agreement resolves a recent discrepancy between experiment and theory that had hindered a possible use of the dissociation energy of H2 in the context of the current controversy on the charge radius of the proton.The dissociation energy of molecular hydrogen, D 0 (H 2 ), has been used as a benchmark quantity for firstprinciples quantum-mechanical calculations of molecular structure for more than a century. H 2 consists of two protons and two electrons and is the simplest molecule displaying all aspects of chemical binding. Whereas early calculations were concerned with explaining the nature of the chemical bond [1-3], the emphasis later shifted towards higher accuracy of the energy-level structure, requiring the consideration of nonadiabatic, relativistic and radiative contributions [4][5][6][7][8][9][10][11].These theoretical developments were accompanied and regularly challenged by experimental determinations of D 0 (H 2 ) [12][13][14][15][16][17][18][19][20]. Periods of agreement between theory and experiment have alternated with periods of disagreement and debate. The reciprocal stimulation of theoretical and experimental work on the determination of D 0 (H 2 ) has been a source of innovation. With its ups and downs and the related controversies, it has long reached epistemological significance [21,22].In 2009, the experimental (36 118.0696(4) cm −1 ) and theoretical (36 118.0695(10) cm −1 ) values of D N =0 0 (H 2 ) reached unprecedented agreement at the level of the combined uncertainties of 30 MHz [9,19], apparently validating the treatment of the lowest-order (α 3 ) QED correction and the one-loop term of the α 4 correction, including several QED contributions that had not been considered for molecules until then. The insight that D 0 (H 2 ) is a * Present address: sensitive probe of the proton charge radius [23,24] stimulated further work.On the theoretical side, Pachucki, Komasa and coworkers have improved their calculations based on nonadiabatic perturbation theory [11,[24][25][26][27], significantly revised the 2009 result, and came to the unexpected conclusion that the excellent agreement of theoretical predicti...

The ionization energy of ortho-H_{2} has been determined to be E_{I}^{o}(H_{2})/(hc)=124 357.238 062(25)  cm^{-1} from measurements of the GK(1,1)-X(0,1) interval by Doppler-free, two-photon spectroscopy using a narrow band 179-nm laser source and the ionization energy of the GK(1,1) state by continuous-wave, near-infrared laser spectroscopy. E_{I}^{o}(H_{2}) was used to derive the dissociation energy of H_{2}, D_{0}^{N=1}(H_{2}), at 35 999.582 894(25)  cm^{-1} with a precision that is more than one order of magnitude better than all previous results. The new result challenges calculations of this quantity and represents a benchmark value for future relativistic and QED calculations of molecular energies.

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The term values of rovibrational levels of the GK 1Σ+g and H 1Σ+g states of H2 have been measured with absolute and relative accuracies down to 10−4 cm−1 (≈3 MHz) and 10−6 cm−1 (≈30 kHz), respectively, by measuring transitions to long-lived high-n Rydberg states using single-mode cw laser radiation and a collimated supersonic beam of cold H2 molecules.