AIMPs as relativistic effective core potentials

Let us start with the spin-free part of a two-component valence-only relativistic Hamiltonian of a molecule, that we will write as  

In the three mentioned spin-free Hamiltonians, the electron-electron interaction is described by the nonrelativistic Coulumb interaction, 

Cowan-Griffin-Wood-Boring AIMP molecular Hamiltonian 

In the Cowan-Griffin-Wood-Boring Hamiltonian, the 7] and operators of Eq. (4) read  

the AIMP recipe for the approximation of operators can be applied and the following substitution will be made after adding and subtracting / r i for 

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