Orbital-functional response theory, exchange-only

The failure of the DFT linear-response theory to reduce to the exact formalism of Dirac [13] in the exchange-only limit [12] is symptomatic of the inadequacy of the locality hypothesis. It will be shown here that on dropping this hypothesis a linear-response theory can be derived that is formally exact for both exchange and correlation. As will be discussed in more detail in the following Section, an exact but implicit orbital functional exists for the correlation energy Ec [31]. This produces a formally exact correlation term in the OEL equations, defined by the orbital functional derivative... 

On the other hand, the orbital-dependent treatment of correlation represents a much more serious challenge than that of exchange The systematic derivation of such functionals via standard many-body theory leads to rather complicated expressions. Their rigorous application within the OPM not only requires the evaluation of Coulomb matrix elements between the complete set of KS states, but, in principle, also relies on the knowledge of higher order response functions. In practical calculations, these first-principles functionals necessarily turn out to be rather inefficient, even if they are only treated perturbatively. In addition, the potential resulting from a large class of such functionals is non-physical for finite systems. Both problems are related to the presence of unoccupied states in the functionals which seems inevitable as soon as some variant of standard many-body theory is used for the derivation. 

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