Local exchange interactions

The Xa multiple scattering method generates approximate singledeterminant wavefunctions, in which the non-local exchange interaction of the Hartree-Fock method has been replaced by a local term, as in the Thomas-Fermi-Dirac model. The orbitals are solutions of the one-electron differential equation (in atomic units)... 

The calculated total moments are compared with experiment in fig. 46. Here we have added the rare earth moment to the calculated conduction-electron moment. Due to the 3d-5d hybridization a significant spin density is produced at the R sites, even when the f moments are zero. This hybridization is believed to be responsible for the important coupling between the 4f and 3d spin directions (Brooks et al. 1991a). The essential point to realize is that in the local spin density approximation the R-4f and R-5d spins are coupled by local exchange interactions to give a parallel spin alignment. The interaction between the R-4f and Fe-3d spins is mediated by the R-5d spin and it aligns the 4f and 3d spins antiparaUel. 

The two spins 5a and 5b are assumed to be local, associated with the two sites a and b, respectively. The parameter J is the so-called exchange-coupling constant, which expresses the strength of the (super)exchange interaction between the... 

In case of the charged form of chemisorption a free lattice electron and chemisorbed particles get bound by exchange interaction resulting in localization of a free electron (or a hole) on the surface energy layer of adparticles which results in creation of a strong bond. Therefore, in case of adsorption of single valence atom the strong bond is formed by two electrons the valence electron of the atom and the free lattice electron. 

To perform excited-state calculations, one has to approximate the exchange-correlation potential. Local self-interaction-free approximate exchange-correlation potentials have been proposed for this purpose [73]. We can try to construct these functionals as orbital-dependent functionals. There are different exchange-correlation functionals for the different excited states, and we suppose that the difference between the excited-state functionals can be adequately modeled through the occupation numbers (i.e., the electron configuration). Both the OPM and the KLI methods have been generalized for degenerate excited states [37,40]. 

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