Relativistic Hartree-Fock in terms of DPT

The basic idea behind the application of DPT to the relativistic Hartree-Fock (HF) equations is simple. We start from the energy expression and the stationarity condition of relativistic closed-shell Hartree-Fock theory. 

We introduce the change of the metric characteristic of DPT, and expand in powers of c. To 0(c ) we get the non-relativistic Hartree-Fock equations in Levy-Leblond form. The leading relativistic correction to the energy is then expressible in terms of nonrelativistic HF spin orbitals or rather the corresponding lower components xf - For the Dirac-Coulomb operator we get after some rearrangement [17, 18]  

In order to construct 4 and one needs the, which are obtained from a coupled Hartree-Fock type equation. 

The first formulation of relativistic HF in terms of DPT [88, 17, 18] was given in the just indicated pedestrian way . A more straightforward presentation is possible [83], if one uses the formalism of quasidegenerate DPT, presented in section 6. 

There is a minor problem with the just indicated derivation of DPT-HF. Actually the classical DPT is only valid if the are either nondegenerate or if they are chosen perturbation adapted. However, in closed-shell Hartree-Fock theory this does not matter, since everything can be 

---