Fundamental Transitions and Ionization Energies of the Hydrogen Molecular Ions with Few ppt Uncertainty

Abstract

We calculate ionization energies and fundamental vibrational transitions for H2+, D2+, and HD+ molecular ions. The nonrelativistic quantum electrodynamics expansion for the energy in terms of the fine structure constant α is used. Previous calculations of orders mα6 and mα7 are improved by including second-order contributions due to the vibrational motion of nuclei. Furthermore, we evaluate the largest corrections at the order mα8. That allows us to reduce the fractional uncertainty to the level of 7.6×10-12 for fundamental transitions and to 4.5×10-12 for the ionization energies.