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Exchange kernel of density functional response theory from the common energy denominator approximation (CEDA) for the Kohn–Sham Green's function

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A complete and explicit expression for the exchange kernel fxσ of density functional response theory (DFRT) is derived in terms of the occupied Kohn-Sham (KS) orbitals ψ. It is based on the common energy denominator approximation (CEDA) for the KS Green's function (O. V. Gritsenko and E. J. Baerends, Phys. Rev. A 64, 042506 (2001)). The kernel fxσCEDA is naturally subdivided into the Slater fSσCEDA and the 'response' frespσCEDA parts, which are the derivatives of the Slater νSσ and response νrespσ potentials, respectively. While fSσCEDA is obtained with a straightforward differentiation of νSσ, some terms of frespσCEDA are obtained from the solution of linear equations for the corresponding derivatives. All components of fxσCEDA are explicitly expressed in terms of the products ψ*ψ of the occupied KS orbitals taken at the positions r1 and r2, as well as the potentials of these products at r3. The coefficients in these expressions are obtained by inversion of the matrix, associated with the overlap matrix of the products ψ*ψ and ψ*ψ. Terms are indicated, which generate in an external electric field an ultra-nonlocal potential δνxσ, counteracting an external field, and possible approximations to fxσCEDA are considered.


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