2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158832The major goal of the high-precision studies of ro-vibrational states in the hydrogen molecular ions is to provide an alternative way for improving the electron-to-proton mass ratio, or the atomic mass of electron. By now the complete set of relativistic and radiative corrections have been obtained for a wide range of ro-vibrational states of H_2^+ and HD^+ up to order R_\inftyα^4. In this work we complete calculations of various contributions to the R_\inftyα^4 order by computing the relativistic corrections to the binding energy of electron.4 pages, 1 figureAtomic Physicstext