Band-structure approach

Single slab. A number of recent calculations of surface electronic structures have shown that the essential electronic and structural features of the bulk material are recovered only a few atomic layers beneath a metal surface. Thus, it is possible to model a surface by a single slab consisting of 5-15 atomic layers with two-dimensional translational symmetry parallel to the surface and vacuum above and below the slab. Using the two-dimensional periodicity of the slab (or thin film), a band-structure approach with two-dimensional periodic boundary conditions can be applied to the surface electronic structure. 

Recently, the effects of static and dynamic structural fluctuations on the electron hole mobility in DNA were studied using a time-dependent self-consistent field method [33]. The motion of holes was coupled to fluctuations of two step parameters of a duplex, rise and twist (Fig. 1), namely the distances and the dihedral angles between base pairs, respectively. The hole mobility in an ideally ordered poly(G)-poly(C) duplex was found to be decreased by two orders of magnitude due to twisting of base pairs and static energy disorder. A hole mobility of 0.1 cm V s was predicted for a homogeneous system the mobility of natural duplexes is expected to be much lower [33]. In this context, one can mention several theoretical studies, based on band structure approaches, to estimate the electrical conductivity of DNA [85-87]. 

Within a single-particle treatment of the final electron state, XANES can be considered as due to long-range order (5), and consequently band-structure calculations may be applied. The band-structure approach... 

For many problems in solid-state science, one can usefully employ either localized cluster approaches or delocalized band-structure approaches. Comparison of results between the two different approaches is sometimes straightforward, for example, in comparing equilibrium bond distances from cluster calculations on SiCOH) or band calculations on polymorphs of SiOj (although analysis of the reasons for discrepancies may be very difficult). Comparison of energy spectra obtained by the different approaches can, however, be difficult. 

In fact, because of its importance in solid-state science, a large variety of band-structure approaches have been used to calculate the electronic structure of sphalerite. These have included self-eonsistent and semiem-pirical orthogonalized-plane-wave (OPW) (Stukel et al., 1969), empirical-pseudopotential (Cohen and Bergstresser, 1966), tight-binding (Pantelides and Harrison, 1975), APW (Rossler and Lietz, 1966), and modified OPW (Farberovich et al., 1980), as well as KKR (Eckelt, 1967) methods. In a recent and extremely detailed study using a density-functional approach (specifically a method termed the self-consistent potential variation... 

In this chapter we will discuss one electron excitations in XANES. The multiple scattering theory and its applications for simple octahedral and tetrahedral clusters will be discussed. Then some cases where larger clusters contribute to the XANES spectra are considered. In the second part, the band structure approach for the study of metals will be described. 

The spectra of metallic crystals can be solved in k-space. Theoretical calculations of the partial and projected density of states of the crystal band structure were reported by several groups to interpret the XANES of metals " >. We discuss here the band structure approach developed by Muller et al. by which it is possible... 

PdjSi using a band structure approach have shown that the Lj-edge spectra can be interpreted in terms of the DOS calculated from the ground state potential without any inclusion of many body final state effects. 

XANES studies at the Mg and A1 X-edges. Phys Chem Minerals 27 20-33 Mottana A, Robert J-L, Marcelli A, Giuli G, Della Ventura G, Paris E, Wu Z (1997) Octahedral versus tetrahedral coordination of A1 in synthetic micas determined by XANES. Am Mineral 82 497-502 Muller JE, Jepsen O, Wilkins JW (1982) X-ray absorption spectra X-edges of 3d transition metals, /-edges of 3d and 4d metals, andM-edges of palladium. Solid State Commun 42 365-368 Muller JE, Wilkins JW (1984) Band-structure approach to the X-ray spectra of metals. Phys Rev B29 4331-4348... 

The predictions OS.Sgi of the correct temperature dependence of the resistivity and the correct signs for both the Hall and thermopower tensors is a remarkable accomplishment for the band structure approaches. The discrepancies in the magnitudes of the calculated transport coefficients compared with experiMnt seem to us relatively minor. We therefore wish to oppose strongly the view suggested by some that band theory is completely irrelevant. It is very important that accurate single crystal measurements on these and other materials be performed to stimulate further theoretical progress. 

A completely different viewpoint is adopted in calculations of infinite periodic structures (molecular crystals, semiconductors, large polymers). Band structure approaches that focus on the dynamics of electron-hole pairs are then used. " " Band theories may not describe molecular systems with significant disorder and deviations from periodicity, and because they are formulated in momentum (k) space they do not lend themselves very easily to real-space chemical intuition. The connection between the molecular and the band structure pictures is an important theoretical challenge. ... 

Fig. 9. Experimental (dotted lines) Lm and Lj absorption of Gd (Materlik et al. 1983a) together with spectra calculated from the band structure approach of Muller and Wilkins (1984) (solid lines). The dashed lines represent the calculated spectra obtmned by rescaling the energy axis by 1.05 (Ljjj) and 1.07 (Lj). The two spectra are lined up at the inflection points of the absorption edges , labelled Ep.

The Lj spectra from the gas can be understood in the same manner. Here the atomic resonances corresponding to the one-electron transition 2s 4f 5d 6p 6s - 2s 4f 5d 6p 6s are very weak due to the smaller oscillator stroigths of the s-p transitions. Nevertheless they are discernible from the absorption edge. Upon condensation into the metallic state, the Lj spectra lose their atomic character completely (solid line in fig. 10b). The Li absorption in the solid state is e.g. described through the band structure approach (cf. section 6.3). 

Three examples of the above approach are given in Figs. 15-17. In Fig. 15 the experimental valence-band spectrum from a Kynol novoloid fiber [481 is compared with the spectrum calculated from an ab initio calculation using the polymer repeat unit. Figure 16 shows the calculated spectra for two components of the repeat unit in a Nomex aramid fiber, w-phenylenediamine and isophth-aldehyde if the compounds are combined they produce the predicted spectrum in Fig. 17b, which compares well with the experimental spectrum 48. Figure 18 shows the predicted spectra for oxidized carbon fibers using multiple. scattered wave Xa calculations on a set of substituted coronene units (25). The use of the band structure approach in polymers has been demonstrated in a study of polystyrenes [49]. 

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