Leading-order relativistic and radiative corrections to the rovibrational spectrum of H2+ and HD+ molecular ions

High-precision variational calculations for the rovibrational states in the range of the total orbital momentum L=0-4 and vibrational quantum number v=0-4 for the H2+ and HD+ molecular ions are presented. Relativistic and radiative corrections of orders R∞α2, R∞α2(m/M), R∞α3, R∞α3(m/M), and, partially, R∞α4 are taken into consideration as well as the finite size structure of proton and deuteron. It is found that the relative theoretical uncertainty due to uncalculated contributions of orders R∞α4 and higher to the reference transition frequency interval (L=0,v=0)→(0,1) is about 1 ppb