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We have reported a study of the relative importance of self-exchange and inter-orbital exchange interactions in both the local spin density (LSDA) and Hartree Fock (HFA) approximations. Central to our considerations was that intra-orbital self-exchange, which in HFA is the Coulomb integral, F(0), is a major part of the spin polarization energy in both HFA and LSDA. We illustrate the role of self-exchange in LSDA with the extreme example of the hydrogen atom where it is responsible for the entire spin polarization energy.

Stollhoft et al in their comment, contend that the LSDA exchange integrals contain only inter-orbital exchange. We do not agree with this interpretation of LSDA. The total energy in LSDA contains a contribution which is quadratic in the total spin density. The spin density is, just as in HFA, constructed from the contribution from the individual orbitals in a spherical expansion. .

Additional information

Authors: SEVERIN L, Technische Hochschule Darmstadt, Institut für Festkörperphysik (DE);BROOKS M S S, JRC Karlsruhe (DE);JOHANSSON B, University of Uppsala, Institute of Physics (SE)
Bibliographic Reference: Article: Physical Review Letters (1996)
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