The importance of ``relativistic effects'' in properly describing the electronic structure of molecules containing heavy elements is often stressed in the literature. A logical definition of these effects might be: ``The differences in molecular property predictions made by the relativistic Hamiltonian and the non-relativistic Hamiltonian''. However, this definition is impractical for several reasons. The first problem with this definition is that it requires the existence of an exact relativistic Hamiltonian. This may be resolved by choosing a single, well-accepted approximate Hamiltonian such as the Dirac-Coulomb or Dirac-Breit Hamiltonian as the relativistic Hamiltonian. Another problem stems from the extensive discussion of ``correlation effects'' in the quantum chemical literature. This term is used to describe the difference between properties predicted by the Hartree-Fock wavefunctions and the properties predicted by higher level, correlated wavefunctions. In order to study relativistic effects independently of correlation effects, it is useful to define relativistic effects as the differences between the predictions of the Hartree-Fock (HF) and Dirac-Hartree-Fock (DHF) methods. In this way, both relativistic effects and correlation effects may be viewed as corrections to the non-relativistic HF model. It is important to note, however that the two types of effects should not be regarded as separate, additive effects, and that significant interplay between the two should be expected in cases where relativistic and correlation effects are significant[35].
Unfortunately, there are other approximations inherent in the HF and DHF methods structure methods which stand in the way of isolating those differences which are purely due to the introduction of relativity. The properties predicted by a particular molecular wavefunction are often highly dependent on the quality of the finite basis set in which the wavefunction is expanded. This is especially true in the case of the DHF method, where the reliability of the predictions are not only dependent upon the size and flexibility of the basis set, but also upon the proper balance of large and small component basis sets. The extraordinarily different basis set requirements of the two methods make it difficult to determine what would constitute an equal treatment of the two.
For atomic systems, however, the issue of basis set effects may be avoided by solving the one dimensional DHF and HF radial equations[36] numerically. This makes atomic systems a good starting point for the investigation of isolated relativistic effects. Furthermore, characterization of the differences in such properties as orbital shape and extent, and orbital energies for isolated atomic systems can help to identify periodic trends in relativistic effects without the perturbation of a molecular environment. Models established in the high symmetry of the central force field of the atom may then lend structure to descriptions of the valence orbital effects in molecules, where significant orbital mixing may be encouraged by the lower symmetry molecular environment.
When molecular systems are too large to be treated with the relatively rigorous, DHF-based four-component methods, more approximate two-component methods such as relativistic perturbation theory are utilized in an attempt to include the most important relativistic effects. In these cases, it is essential to have an estimate of the magnitude of the difference between the relativistic and non-relativistic pictures in order to evaluate the validity of perturbative schemes.