Relativistic LDA for Ec

Our review of the properties of explicit relativistic functionals is concluded by an examination of the RLDA for c[ ] (using the RPA for the relativistic corrections, Eq. (4.10), and the parametrisation of Vosko et al. [70] for The 

RLDA correlation energies obtained by solution of (3.25) (using the RLDA for the complete r ) for a number of atoms are listed in Table 5.6 and compared with the usual quantum chemical correlation energy 

The inappropriate scaling of the RLDA with Z, and thus also with j6, becomes particularly obvious for fixed electron number. In Fig. 5.5 the percentage deviations of the RLDA for and Ej are shown for the Ne isoelectronic series. The error for the correlation energy in the RLDA shows little tendency to approach zero with increasing Z, indicating that the relativistic correction factor plotted in Fig. 4.4 is inadequate for electronic structure calculations. 

In summary, the RLDA addresses relativistic corrections to Ec n on the same limited level of sophistication as the NRLDA does for the nonrelativistic correlation energy functional. Even more than in the case of exchange, nonlocal corrections seem to be required for a really satisfactory description of (relativistic) correlation effects in atoms. 

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