Leading-order QED effects in the ground electronic state of molecular hydrogen

We perform highly accurate calculations of the leading-order QED correction to the ground electronic state of molecular hydrogen. Numerical results are obtained for a grid of the internuclear distances R = 0-10 a.u. with the relative precision of about 10-8. The major numerical uncertainty of previous QED results [K. Piszczatowski, G. Lach, M. Przybytek, J. Komasa, K. Pachucki, and B. Jeziorski, J. Chem. Theory Comput. 5, 3039 (2009)] has been eliminated. Nevertheless, the discrepancy with measurements in HD at the level of 1.9 a persists.