It is well known from nonrelativistic quantum chemistry that mean-field methods, such as the Hartree–Fock (HF) model, provide mainly qualitative insights into the electronic structure and bonding of molecules. To obtain reliable results of “chemical accuracy” usually requires models that go beyond the mean field and account for electron correlation. There is no reason to expect that the mean-field approach should perform significantly better in this respect for the relativistic case, and so we are led to develop schemes for introducing correlation into our models for relativistic quantum chemistry. There is no fundamental change in the concept of correlation between relativistic and nonrelativistic quantum chemistry: in both cases, correlation describes the difference between a mean-field description, which forms the reference state for the correlation method, and the exact description. We can also define dynamical and nondynamical correlation in both cases. There is in fact no formal difference between a nonrelativistic spin–orbital-based formalism and a relativistic spinor-based formalism. Thus we should be able to transfer most of the schemes for post-Hartree–Fock calculations to a relativistic post-Dirac–Hartree–Fock model. Several such schemes have been implemented and applied in a range of calculations. The main technical differences to consider are those arising from having to deal with integrals that are complex, and the need to replace algorithms that exploit the nonrelativistic spin symmetry by schemes that use time-reversal and double-group symmetry. In addition to these technical differences, however, there are differences of content between relativistic and nonrelativistic methods. The division between dynamical and nondynamical correlation is complicated by the presence of the spin–orbit interaction, which creates near-degeneracies that are not present in the nonrelativistic theory. The existence of the negative-energy states of relativistic theory raise the question of whether they should be included in the correlation treatment. The first two sections of this chapter are devoted to a discussion of these issues. The main challenges in the rest of this chapter are to handle the presence of complex integrals and to exploit time-reversal symmetry.
Richardson–Gaudin mean-field for strong correlation in quantum chemistry