Finite-nuclear-mass calculations of the leading relativistic corrections for atomic D states with all-electron explicitly correlated Gaussian functions

An algorithm for calculating the leading relativistic corrections for D states of atoms with an arbitrary number of electrons with all-electron explicitly correlated Gaussian functions is derived and tested in calculations for the helium and beryllium atoms. The finite-nuclear-mass approach used enables us to determine the isotopic shifts of the corrections. The results for interstate transitions for D1 states of the helium atom are compared with previous calculations. The results for the beryllium atom are compared with the experimental values, as these are high-accuracy calculations of D states of a four-electron atom performed with the inclusion of the leading relativistic corrections. The calculated and experimental values agree with each other within the experimental error bar.