Relativistic calculations for highly charged ions

Relativistic calculations for highly charged ions require the use of the Dirac operator that has both positive and negative energy continua. Since variational methods search for stationary solutions, the presence of the negative energy continuum and the associated problem of “continuum dissolution” has been of concern for more than 20 years. The development of general purpose codes depends critically on a detailed understanding of the variational problem. We will show that the correlation orbitals in the natural orbital expansion of the 1s2 ground state for 2-electron systems represent configuration state functions in the positive continuum. An interpretation of the diagonal energy parameters will be presented and the implication for the calculation of the frequency-dependent Breit correction discussed.