The Hamiltonian and relativistic effective core potentials

For a polyatomic molecule with valence electrons, the two-component molecular electronic Hamiltonian [17] can be expressed (in atomic units) as 

In most practical applications in quantum chemistry, the radial part of the AREP, Eq. (5), and the ESO, Eq. (7), is expanded most conveniently in terms of Gaussian functions. Present two-component schemes also use such analytic expansions of the potential. As a result, two component RECP calculations will be possible as long as the AREP and ESO are provided in a form which can be used in available integral packages such as ARGOS [5,21]. It is noted, however, that the separation of spin-orbit coupling from the rest of the relativistic terms is not uniquely defined [22]. Some classes of ESO may lack a theoretical basis for a variational treatment, and should not be applied in two-component approaches. 

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