Algorithms for calculating mass-velocity and Darwin relativistic corrections with n -electron explicitly correlated Gaussians with shifted centers

Algorithms for calculating the leading mass-velocity (MV) and Darwin (D) relativistic corrections are derived for electronic wave functions expanded in terms of n-electron explicitly correlated Gaussian functions with shifted centers and without pre-exponential angular factors. The algorithms are implemented and tested in calculations of MV and D corrections for several points on the ground-state potential energy curves of the H₂ and LiH molecules. The algorithms are general and can be applied in calculations of systems with an arbitrary number of electrons.