The vibrational excitation of molecular hydrogen $\left({\mathrm{H}}_2\right)$ by low-energy electrons is one of the most fundamental reactions in atomic and molecular physics, playing a key role in the chemistry of the interstellar medium and studies of fusion plasmas. Crossed-beam experiments and electron swarm measurements have long been used to determine scattering cross sections for vibrational excitation, but the two methods produce conflicting results, a disagreement that has persisted for more than five decades and remains unsolved. Theoretical treatments have historically relied on approximations tailored to specific processes, such as separating the direct and resonant pathways or employing model polarization potentials, with no single method accurately describing all vibrational transitions. The absence of benchmark-quality calculations, combined with decades-long disagreements between experimental methods, means that even for this simple problem, there are no definitive cross-section data, leaving the reliability of theoretical approaches applied to more complex molecules uncertain and without quantified error bounds. Here we present ab initio calculations of low-energy vibrational excitation in ${\mathrm{H}}_2$ that treat electronic and vibrational motion on equal footing, providing a unified description of direct and resonant scattering across all vibrational transitions. The results are in stark contrast with previous theoretical estimates for many vibrational transitions, revealing systematic differences in both magnitude and energy dependence. At the same time, they provide strong confirmation of the swarm-derived cross sections, unlike previously accepted calculations that favored the beam data. This reversal of the long-standing situation shifts attention away from the swarm data and back onto the interpretation of the crossed-beam measurements. By providing accurate and self-consistent cross sections for vibrational excitation of ${\mathrm{H}}_2$, the present calculations will enable more reliable modeling of low-temperature plasmas and interstellar clouds.

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• Atomic & molecular collisions
• Electron & positron scattering
• Scattering theory
• Molecules
• First-principles calculations
• Schroedinger equation