Relativistic Configuration-Interaction RCI Method

An alternative approach to the perturbation theory in treating many-electron systems is the configuration-interaction (Cl) method which is based on the variational principle. Nonrelativistic Cl techniques have been used extensively in atomic and molecular calculations. The generalization to relativistic configuration-interaction (RCI) calculations, however, presents theoretical as well as technical challenges. The problem originates from the many-electron Dirac Hamiltonian commonly used in RCI calculations  

However, the fact that the denominator can go to zero is not necessarily a problem. The same situation is encountered in the autoionization of atoms. Since an autoionizing state is embedded in the positive-energy continuum, second- and higher-order MBPT will also lead to vanishing denominators similar to those discussed above. In that case, an infinitesimal imaginary part must be added to the denominator, with the result that the principal part of the matrix elements leads to a real energy shift while the imaginary part 

Energies (eV) of the Is ground state of helium-Uke uranium as calculated with basis func- 

Energy Potential no—pair Dirac Dirac Eqed Eqed 

While there are no numerical disasters from vanishing denominators in RCI calculations when negative-energy basis functions are used, results of the full Dirac Hamiltonian, though potential independent, are nevertheless incorrect. To see this, we note that if the sum over intermediate states for the second-order energy is extended to included both positive- and negative-energy orbitals, can be rewritten as 

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