Band Structure Methods

O. Jepsen, M. Snob, O.K. Andersen, Linearized Band-structure Methods in Electronic Band-structure and its Applications, Springer Lecture Note, Springer Verlag, Berlin, Germany, 1987 (d) O. K. Anderson, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571. 

Recent calculations of hyperfine parameters using pseudopotential-density-functional theory, when combined with the ability to generate accurate total-energy surfaces, establish this technique as a powerful tool for the study of defects in semiconductors. One area in which theory is not yet able to make accurate predictions is for positions of defect levels in the band structure. Methods that go beyond the one-particle description are available but presently too computationally demanding. Increasing computer power and/or the development of simplified schemes will hopefully... 

Photoelectron spectra Spin-orbit couplings Band structure methods... 

Calculation of the multiple scattering by means of a real-space cluster approach is considerably more flexible than band-structure methods. Since this technique does not rely on crystal periodicity, it can readily be applied to interpret data for materials of arbitrary atomic arrangements. The sensitivity to higher order correlations has been shown. Fujikawa et al. (94,96) favor short-range-order multiple-scattering XANES theory, in which atoms are not divided into shells but the scattered waves are classified into a direct term and a fully multiple-scattering term. 

There are a number of band-structure methods that make varying approximations in the solution of the Kohn-Sham equations. They are described in detail by Godwal et al. (1983) and Srivastava and Weaire (1987), and we shall discuss them only briefly. For each method, one must eon-struct Bloch functions delocalized by symmetry over all the unit cells of the solid. The methods may be conveniently divided into (1) pesudopo-tential methods, (2) linear combination of atomic orbital (LCAO) methods (3) muffin-tin methods, and (4) linear band-structure methods. The pseudopotential method is described in detail by Yin and Cohen (1982) the linear muffin-tin orbital method (LMTO) is described by Skriver (1984) the most advanced of the linear methods, the full-potential linearized augmented-plane-wave (FLAPW) method, is described by Jansen... 

We remark that memory function methods have been extensively applied to perfect crystals, where they are alternative tools to the traditional band structure methods. In the presence of translational symmetry and long-range order, however, the use of the memory function techniques is not essential but rather a matter of convenience (or taste) in a number of situations. We thus focus on the study of the electronic structure in systems that are aperiodic because of impurities our unorthodox way of looking at defects is to consider them as a source of a given frozen-in disorder in an otherwise perfect crystal lattice. The more general case of the presence of stochastic disorder will be discussed in Section VI. 

Another standing topic during the last two decades has been to evaluate the electronic structure of solids, surfaces and adsorbates on surfaces. This can be done using standard band structure methods [107] or in more recent years slab codes for studies of surfaces. An alternative and very popular approach has been to model the infinite solid or surface with a finite cluster, where the choice of the form and size of the cluster has been determined by the local geometry. These clusters have in more advanced calculations been embedded in some type of external potential as discussed above. It should be noted that these types of cluster have in general quite different geometries compared with... 

The electronic structure of bulk VO has been calculated by different band structure methods [110-114] and using correlated electron procedures [115]. This Mott-Hubbard metal, which forms a rocksadt type lattice, is the simplest of all single valence oxides of vanadium and has been treated theoretically already a long time ago. As an example, Neckel et al. [114] have published results from self-consistent APW calculations for the experimentally known lattice geometry... 

Based on this property, LDA band-structure methods were generated [14], in which the electronic energy levels are obtained in the reciprocal k space. Since the early 60 s, there have been developed a large number of band structure methods, differing among themselves mainly in the way the crystal potential is treated, and in the choice of expansion bases. Frequently they may be recognized in the literature by their initials APW, LMTO, FLAPW, KKR, etc. 

Crystal orbital or band structure methods consist in solving the problem of the infinite system directly by exploiting the translational symmetry in order to... 

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