A complete and explicit expression for the exchange kernel f xσ of density functional response theory (DFRT) is derived in terms of the occupied Kohn-Sham (KS) orbitals ψ iσ. 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 f xσ CEDA is naturally subdivided into the Slater f Sσ CEDA and the 'response' f respσ CEDA parts, which are the derivatives of the Slater ν Sσ and response ν respσ potentials, respectively. While f Sσ CEDA is obtained with a straightforward differentiation of ν Sσ , some terms of f respσ CEDA are obtained from the solution of linear equations for the corresponding derivatives. All components of f xσ CEDA are explicitly expressed in terms of the products ψ iσ * ψ jσ of the occupied KS orbitals taken at the positions r 1 and r 2, as well as the potentials of these products at r 3. The coefficients in these expressions are obtained by inversion of the matrix, associated with the overlap matrix of the products ψ iσ * ψ jσ and ψ kσ * ψ lσ . Terms are indicated, which generate in an external electric field an ultra-nonlocal potential δν xσ , counteracting an external field, and possible approximations to f xσ CEDA are considered.
Research on Chemical Intermediates – Springer Journals
Published: Oct 20, 2004
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