Generalized Fockian

According to Eq. (63), the 1-RDM and the generalized Fockian F commute at the extremum hence the NSOs are the solutions of the eigenproblem (60) with the nonlocal potential defined by the identity (64). One should note, however, that Eq. (64) does not completely define v e- In fact, the diagonal elements... 

In the more general case, i.e., when the fockian contains a nonlocal exchange operator, like in hybrid DFT and in Hartree-Fock calculations, the relation seen Eq. 73 does not hold any more and the commutator of the position operator with the fockian contains an exchange contribution [76, 77], which gives rise to an additional term ... 

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