Corrections to the Relativistic LDA

While the RLDA for Exc[j] is based on the xc-energy density of the RHEG, Eq.(288), the expansions (308) and (314) allow the derivation of systematic corrections to the RLDA. Restricting the discussion to the linear response contributions, Eq.(308) reduces to 

After insertion of the result (278) for the inverse response function, 

The first order terms in (323) vanish due to norm conservation, Eq.(309). The second order terms can be rewritten by use of the compressibility sum rule (284), 

The second order terms in (324) thus have to be subtracted from (322) as they are already contained in the RLDA, 

(325) explicitly demonstrates the current-dependence of relativistic density functionals. However, at this point and 6E] are given as functionals of Q (inside H /j-) and 5 f but not yet as functionals of the complete density f — 

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