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 H-2(+) and HD+ molecular ions are presented. Relativistic and radiative corrections of orders R-infinity alpha(2), R-infinity alpha(2)(m/M), R-infinity alpha(3), R-infinity alpha(3)(m/M), and, partially, R-infinity alpha(4) 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-infinity alpha(4) and higher to the reference transition frequency interval (L=0,v=0)->(0,1) is about 1 ppb.