Negative energy states in relativistic quantum chemistry

The role of the negative energy states in relativistic quantum chemistry is shortly discussed. They must be included in a sum over states formula that arises for second-order properties. Relativistic calculations for the electric dipole polarizability and the diamagnetic susceptibility (with on-center and displaced gauge origins) for hydrogen-like ions are presented to illustrate the problem. Relativistic electron correlation calculations mostly use a configuration space Dirac-Coulomb operator together with the no-pair approximation, which excludes the negative energy states from the correlation treatment. Despite all efforts, no consistent theoretical description between this and a full QED treatment seems to exist.