Relativistic Effective Core Potentials—Formal Aspects

Relativistic Effective Core Potentials—Formal Aspects 

The method discussed here for the inclusion of relativistic effects in molecular electronic structure calculations is grounded in the Dirac-Fock approximation for atomic wave functions (29). The premise is that the major relativistic effects of the Dirac Hamiltonian are manifested in the core region, involving the core electrons, and that these effects propagate to the valence electrons. In addition, there are direct relativistic effects on valence electrons penetrating into the core region. Insofar as this is true, the valence electrons can be treated using a nonrelativistic Hamiltonian to which is added an operator, the relativistic effective core potential (REP). The REP formally, incorporates relativistic effects due to core electrons and to interactions of valence electrons with core electrons in an internally consistent way. 

The formalism parallels to some extent the nonrelativistic arguments of Kahn et al. (23). We begin with the relativistic Hamiltonian 

In an analogous fashion to the atomic Hartree-Fock equations, the angular variables can be separated and integrated out using the Wigner-Eckart theorem in the Dirac equation to yield a set of coupled differential equations depending on r (29). 

To construct the Dirac-Fock equations, it is assumed that the wave function for an atom having N electrons may be expressed as an antisymmetrized product of four-component Dirac spinors of the form shown in Eq. (9). For cases where a single antisymmetrized product is an eigenfunction of the total angular momentum operator J2, the JV-electron atomic wave function may be written 

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III. Relativistic Effective Core Potentials—Formal Aspects... 

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