Correlation energy functional relativistic

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. 

From what has been said already with respect to the variational collapse and the minimax principle, it is clear from the beginning that the standard derivation of the Hohenberg-Kohn theorems [386], which are the fundamental theorems of nonrelativistic DFT and establish a variational principle, must be modified compared to nonrelativistic theory [383-385]. Also, we already know that the electron density is only the zeroth component of the 4-current, and we anticipate that the relativistic, i.e., the fundamental, version of DFT should rest on the 4-current and that different variants may be derived afterwards. The main issue of nonrelativistic DFT for practical applications is the choice of the exchange-correlation energy functional [387], an issue of equal importance in relativistic DFT [388,389] but beyond the scope of this book. 

For both the DZ and TZ sets a contracted function was included for the 6p orbital, but this was deleted in the QZ and 5Z sets due to near linear dependence. The contraction was also deleted from the 5Z set for the same reason. Figure 7 plots the correlation energies for both nonrelativistic and DK-relativistic CISD calculations. The CBS limits using a extrapolation of the QZ and 5Z correlation energies are -391.8 and -418.0 m /, for NR and DK, respectively. 

Table 5.6 demonstrates once more the well known fact that the nonrelativistic LDA overestimates the exact atomic correlation energies by about a factor of 2. Here, however, not the accuracy of the complete functional (4.10) is of interest, but rather the relativistic corrections AE and Ej, as the correction scheme (4.10) could be combined with more accurate nonrelativistic c[n] like GGAs. Table 5.6 shows that both AEc and Ej are much smaller than their x-only counterparts. On the other hand, AE and Ej add up constructively so that the total correction AE + Ej is somewhat closer to AE + El than the individual components For Hg one obtains AEl + Ej = — 0.49 hartree within MBPT2 compared with the exact AE + El of about 2.19 hartree. Nevertheless, in absolute values the relativistic corrections to [n] are clearly less important than those to ,t[n]. 

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