Unscreened final-state

Correlation energy differences (ion), 4f excitation energies A (4f ion) calculated for ionized (unscreened) final states, and screening energy estimates d,(band) and d,(atom). The initial states are the ground metallic configurations. All energies in eV. 

Now ( (ion) is a measure of the correlation accompanying the excitation of a 4f electron alone, while represents the correlation associated with 4f->5d conversion. The bracketed quantity in the above expression is thus an estimate of the correlation energy associated with the additional conduction electron which is present in the neutral (completely screened) final state of zl (4f" -> 4f ) and absent in the ionic (unscreened) final state of zl (4f ion). 

Fig. 15. Comparison of J (4f ion), the 4f excitation energy calculated for unscreened final states, with J (4f" 4f"" ). For both quan-...

In the right-hand side of this equation the first term takes into account the contributions to the exothermicity that are not associated with the medium, the second and the third terms the contributions from the interactions of the donor and the acceptor cores with the medium in the initial and the final states, respectively, and the fourth term the contribution from the unscreened Coulomb interaction between the donor and the acceptor, zx and z2 being the core charges of the donor and the acceptor, respectively. We must stress that, in the denominator of the last term of eqn. (59) the dielectric permeability of the medium is absent because the effect of the medium is contained in the terms E and E. If the distance between the donor and the acceptor considerably exceeds the sizes of the donor and the acceptor then, using eqn. (58), it is easy to obtain... 

The Dirac-Hartree-Fock iterative process can be interpreted as a method of seeking cancellations of certain one- and two-body diagrams.33,124 The self-consistent field procedure can be regarded as a sequence of rotations of the trial orbital basis into the final Dirac-Hartree-Fock orbital set, each set in this sequence forming a basis for the Furry bound-state interaction picture of quantum electrodynamics. The self-consistent field potential involves contributions from the negative energy states of the unscreened spectrum so that the Dirac-Hartree-Fock method defines a stationary point in the space of possible configurations, rather that a variational minimum, as is the case in non-relativistic theory. 

---