Augmented plane wave relativistic

Theileis, V. and Bross, H. (2000) Relativistic modified augmented plane wave method and its application to the electronic structure of gold and platinum. Physical Review B - Condensed Matter, 62, 13338-13346. 

Knight shift in p-type PbTe has been calculated based on relativistic augmented plane wave functions [227]. 

Full potential linearized-augmented-plane-wave calculations for 5d transition metals using the relativistic generalized gradient approximation... 

In Sect. C, the band structure data based on self-consistent relativistic augmented-plane-wave calculations performed by the author " are presented. Besides the electronic bands and the densities of states, the nature of the chemical bond is discussed. In Sect. D the electronic states in Zintl phases are compared with those having the B2 type of structure. As shown in Sect. B the B2 structure is closely related to the B32 structure. For intermetallic compounds the B2 structure seems to be the more natural because in this lattice all nearest neighbours of an atom A are B atoms. The reason why the compounds mentioned above crystallize in the B32 structure whereas similar compounds like LiTl and KTl form B2 phases has been frequently discussed in the literature 5 ... 

According to the (R)APW method the tpi(r) are linear combinations of (relativistic) augmented plane waves [Pg.100]

In this subsection band structures of B32 type compounds determined by the author using the relativistic augmented plane wave (RAPW) method are presented. For LiAl the APW results are compared with the results obtained using the LCAO variants (Zunger and Asada et al. ) mentioned above. 

The first accurate band structure calculations with inclusion of relativistic effects were published in the mid-sixties. Loucks published [64-67] his relativistic generalization of Slaters Augmented Plane Wave (APW) method. [68] Neither the first APW, nor its relativistic version (RAPW), were linearized, and calculations used ad hoc potentials based on Slaters s Xa scheme, [69] and were thus not strictly consistent with the density-functional theory. Nevertheless (or, maybe therefore ) good descriptions of the bands, Fermi surfaces etc. of heavy-element solids like W and Au were obtained.[3,65,70,71] With this background it was a rather simple matter to include [4,31,32,72] relativistic effects in the linear methods [30] when they (LMTO, LAPW) appeared in 1975. 

In this paper we discussed the status of quantum mechanical calculations focusing on solids and surfaces. In the quantum mechanics section DFT was presented with respect to the alternative approaches such as wave function based methods or many-body physics. For the solution of the DFT Kohn Sham equations we use an adapted augmented plane wave method implemented in our WIEN2k code, which can be shortly summarized as a fiiU-potential, all electron and relativistic code that is one of the most accurate for solids and is used worldwide by more than 1,850 groups in academia and industry. 

As we have seen, on the whole the agreement with theory for the localized form factor associated with the 4f electrons in lanthanide metals and compounds is satisfactory provided one is careful to use relativistic calculations. The situation for the conduction electron polarization distribution is less clear. Conduction electron form factors were obtained for Gd by Moon et al. (1972) and for Er by Stassis et al. (1976). In both cases, these were obtained by separating from the measured form factor the localized 4f contribution, and in both cases appear to be different from either a 5d or 6s atomic form factor. A spin-polarized augmented-plane-wave (APW) calculation of the conduction electron polarization in ferromagnetic Gd was performed by Harmon and Freeman (1974). Their results are, however, only in qualitative agreement with the results of Moon et al. The theoretical form factor of Harmon and Freeman is in somewhat better agreement with the experimental results of Stassis et al. on Er. 

A number of solids with heavy constituents have been treated in relativistic DFT. For Au and Pt the linearized augmented plane-wave (LAPW) method has been implemented in order to study relativistic effects in solids (relativistic versus non-relativistic, LDA versus GGA results). Similarly, effects of spin-orbit-coupling have been investigated in bulk W, Ir and Au on the basis of relativistic LDA-LAPW approaches. 

The procedure that we have described above differs from the early[3,4] TB CPA calculations in two respects. First, our SK Hamiltonians which are fit to self-consistent relativistic augmented plane wave (APW) calculations of the stoichiometric hydrides are much more accurate than those used by other workers. Our rms error is typically less than 5 mRy for the first 7 bands. Second, previous[3,4] TB-CPA calculations freeze the s- and p-bands in transition metals and apply a so-called one-level TB model which ignores the coupling of t and e orbitals. In our calculations we use five coupled CPA conditions corresponding to the self-energies of s, p, t g, Og, and s symmetry. 

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