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

Exchange kernel of density functional response theory from the common energy denominator... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research on Chemical Intermediates Springer Journals

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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Publisher
Brill Academic Publishers
Copyright
Copyright © 2004 by VSP 2004
Subject
Chemistry; Inorganic Chemistry; Physical Chemistry
ISSN
0922-6168
eISSN
1568-5675
D.O.I.
10.1163/156856704322798070
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Research on Chemical IntermediatesSpringer Journals

Published: Oct 20, 2004

References

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