Intermolecular diatomic energies of a hydrogen dimer with non-Born-Oppenheimer nuclear and electron wave packets

► We developed a non-Born-Oppenheimer theory for nuclear and electron wave packets. ► The theory explicitly and non-perturbatively calculated energies of a hydrogen dimer. ► Significant nuclear quantum effects were found in intra- and intermolecular energies. ► The non-Born-Oppenheimer interaction increased the intermolecular energy barriers. ► The result contrasts usual Born-Oppenheimer nuclear quantization on a given surface.