Relativistic DFT Results for Atoms

So far only few applications of the RKS-equations (3.25-3.29) utilising a relativistic form for E [n] have been reported (and none for the field theoretical KS-equations (3.5,3.15-3.17)). MacDonald and Vosko [19] as well as Das et al. [104] analysed the x-only RLDA for high-Z atoms and ions, emphasising the importance of relativistic corrections to [n]. This work has been extended by 

On the other hand, a large number of relativistic Slater calculations [23] (Dirac-Fock-Slater DFS), in which the RKS-equations are used with the nonrelativistic x-only LDA, can be found in the literature (see e.g. [8,9]). However, no attempt is made to review this extensive body of literature here. 

In this section we summarise the properties of the approximations to tc[M] discussed in Section 4 in applications to atoms. All results presented in the following [36] are based on the direct numerical solution of Eqs. (3.25-3.29) using a nuclear potential which corresponds to a homogeneously charged sphere [69]. Only spherical, i.e. closed subshell, atoms and ions are considered. Whenever suitable we use Hg as a prototype of all high-Z atoms. 

Av represents the percentage deviation of the selfconsistent relativistic potential I x ([ ] ) from the corresponding selfconsistent nonrelativistic potential yJ0 ([n ] r). The selfconsistent Dx([n ] f) is calculated by insertion of the self-consistent n (r) into the functional derivative (3.28) for that [n] which has been used to determine n (r). In particular, the ROPM x-only potential can, in principle, be obtained by insertion of the exact x-only density (r) into the exact Dx([n] r) = r J ([ ] r) and thus can be used as a comparative standard  

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