Dirac function field correlations

Heavy atoms exhibit large relativistic effects, often too large to be treated perturba-tively. The Schrodinger equation must be supplanted by an appropriate relativistic wave equation such as Dirac-Coulomb or Dirac-Coulomb-Breit. Approximate one-electron solutions to these equations may be obtained by the self-consistent-field procedure. The resulting Dirac-Fock or Dirac-Fock-Breit functions are conceptually similar to the familiar Hartree-Fock functions the Hartree-Fock orbitals are replaced, however, by four-component spinors. Correlation is no less important in the relativistic regime than it is for the lighter elements, and may be included in a similar manner. 

Dirac s relativistic theory for the motion of electrons in molecules was introduced in the preceding chapters. The appearance of positron solutions and the four-component form of the wave function looks problematic at first sight but in practice it turns out that the real challenge is, like in non-relativistic electronic structure theory, the description of the correlation between the motion of electrons. The mean-field approximation that is made in the Dirac-Hartree-Fock (DHF) approach provides a good first step, but gives bond energies and structures that are often too inaccurate for chemical purposes. 

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