The quantum electrodynamic Araki-Sucher correction arising from the interaction between electrons and nuclei is calculated for rovibrational energy levels of the hydrogen molecule and its isotopologues. The corresponding expectation value $\langle r_{\mathrm{en}}^{-3}\rangle$ is evaluated across a wide range of internuclear distances using the Born-Oppenheimer approximation. The electronic wave function is represented as a linear combination of explicitly correlated Gaussian basis functions. This correction contributes approximately tenths of a megahertz (about ${10}^{-5}{\mathrm{cm}}^{-1}$) to the dissociation energy of rovibrational levels and to the transitions between them. Given recent spectroscopic measurements with an accuracy of 10 kHz, this correction is necessary to achieve sub-MHz agreement between theory and experiment.

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• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions