By Victor Antonov
The purpose of this booklet is to check fresh achievements within the theoretical investigations of the digital constitution, optical, magneto-optical (MO), and x-ray magnetic round dichroism (XMCD) homes of compounds and Multilayered constructions.
Chapter 1 of this ebook is of an introductory personality and offers the theoretical foundations of the band concept of solids resembling the density practical idea for flooring kingdom houses of solids together with neighborhood density approximation (LDA). It additionally offers a few ameliorations to the LDA, comparable to gradient correction, self-interaction correction, LDA+U process, orbital polarization correction, GW approximation, and dynamical mean-field idea. the outline of the magneto-optical results and linear reaction concept also are offered.
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In the following we will refer to calculations performed using the LDA+U method with U eff = 0 as LDA+U (OP) calculations. The most important property of the LDA+U functional is the discontinuity of the potential and the maximum occupied orbital energy as the number of electrons increases through an integer value, the absence of which is the main deficiency of the local-density approximation compared with the exact density functional [126] as far as band gaps are concerned. It should be mentioned that whereas the SIC equations are derived within the framework of homogeneous-electron-gas theory and the method is therefore a logical extension of LDA, this is obviously not the case for the LDA+U method.
The GW A has been successful in treating the quasiparticle systems such as free-electron like metals and semiconductors [171–178]. However the plane wave expansion is impractical for the description of the systems with strong correlations such as Mott insulators and d- and f -band materials. For such systems a method for calculating the self-energy in the GW approximation has been proposed in [179]. The method based on the LMTO-TB representation for wave functions, was applied for strongly correlated systems like NiO.
69) Esp 4 l,l where Jll are the LSDA exchange interactions between shells l and l . 67) the contributions which would correspond to Hund’s first and second rules, since the former is well accounted for in LSDA. 1 mlm This is achieved by writing mlm = ml + δmlm . where ml = 2l+1 m is the average spin moment for a shell whereas δmlm represents the deviation of the moments from the average and thus represents the energy gain due to orbital polarization. 71) k TLFeBOOK 26 ELECTRONIC STRUCTURE AND MO PROPERTIES OF SOLIDS C(lm; l m ) is a Gaunt coefficient.