We present new calculations of unified line profiles for hydrogen perturbed by collisions with protons. We report on new calculations of the potential energies and dipole moments which allow the evaluation of profiles for the lines of the Lyman series up to Lyman {delta} and the Balmer series up to Balmer 10. Unified calculations only existed for the lines Lyman {alpha} to Lyman {gamma} and Balmer {alpha} including the H_2_^+^ quasi-molecule. These data are available as online material accompanying this paper and should be included in atmosphere models, in place of the Stark effect of protons, since the quasi-molecular contributions cause not only satellites, but large asymmetries that are unaccounted for in models that assume that Stark broadening of electrons and that of protons are equal.