Band dispersion structure

Moreover, it was shown that the presence of Hal Hal interactions between the partially oxidized molecules also contribute to the electronic delocalization. Indeed, the presence of non-zero atomic coefficients on the halogen atoms in the HOMO of EDT-TTF-Br2 or EDT-TTF-I2 [66], together with the short Hal Hal contacts, leads to a sizeable increase of the band dispersion and stabilizes a rare (V structure through the side-by-side arrangement of the inversion-centred dyads connected by Hal- Hal interactions. Both 13 salts are semiconductors with room temperature conductivities around... 

Graphite possesses highly anisotropic layered crystal structure, which translates to a quasi-2D electronic structure with electronic bands dispersing linearly near Ep and forming point-like Fermi surfaces. Visible light induces... 

The theory of band structures belongs to the world of solid state physicists, who like to think in terms of collective properties, band dispersions, Brillouin zones and reciprocal space [9,10]. This is not the favorite language of a chemist, who prefers to think in terms of molecular orbitals and bonds. Hoffmann gives an excellent and highly instructive comparison of the physical and chemical pictures of bonding [6], In this appendix we try to use as much as possible the chemical language of molecular orbitals. Before talking about metals we recall a few concepts from molecular orbital theory. 

Let us start by considering a 2D lattice for which the band dispersion is given by E(k) = Ea + lEpa coskaU + 2Epb coskhb. Figure 1.34 shows 3D band structure... 

Fig. 83. (a) Schematic electronic structure of a ion in a MnOg octahedron with IT distortion. The in-plane eg band in the layered manganite shows a different band dispersion and bandwidth depending on the respective orbital states, (b) Doping-level dependence of lattice distortion at room temperature in La2 2jSr +2jMii207. Thick arrows on the right hand of respective crystal structures indicate the spin structures within a bilayer unit at low temperatures. After Kimura et al. (1998). 

Although the overall semiconducting nature remains unchanged upon orientational ordering, the details of the band dispersion show an interesting change. In Fig. 4, the band structure of the orientationally ordered sc solid C60 and that... 

Fig. 12 a, b Electronic band structure of the rhombohedral C60 polymer with a ACB stacking and b ABC stacking, respectively. In each case, the electronic density of states is shown (in arbitrary units) energy is measured from the valence band top. The two systems show very similar valence-band dispersions, while the conduction-band states show a little difference in their dispersion. The fundamental gap of the ABC stacking polymer (lower panels) is found to be narrower than that of the ACB stacking polymer (upper panels) [39]... 

The electronic properties of organic conductors are discussed by physicists in terms of band structure and Fermi surface. The shape of the band structure is defined by the dispersion energy and characterizes the electronic properties of the material (semiconductor, semimetals, metals, etc.) the Fermi surface is the limit between empty and occupied electronic states, and its shape (open, closed, nested, etc.) characterizes the dimensionality of the electron gas. From band dispersion and filling one can easily deduce whether the studied material is a metal, a semiconductor, or an insulator (occurrence of a gap at the Fermi energy). The intra- and interchain band-widths can be estimated, for example, from normal-incidence polarized reflectance, and the densities of state at the Fermi level can be used in the modeling of physical observations. The Fermi surface topology is of importance to predict or explain the existence of instabilities of the electronic gas (nesting vector concept see Chapter 2 of this book). Fermi surfaces calculated from structural data can be compared to those observed by means of the Shubnikov-de Hass method in the case of two- or three-dimensional metals [152]. 

The energy band structures are qualitatively very similar for all four PDA backbones. The four core bands of practically zero width are situated around —299 eV. The other nine doubly occupied bands lie in the region of —4 to — 30 eV. Both the highest filled and lowest unfilled (valence and conduction) bands have n symmetry and both are crossed by the nearest band dispersions are also relatively stable against various approximations and some quantitative differences between them may play an important role in transport calculations on these polymers ... 

The band dispersion depends on the atomic arrangement in the unit cell. Having discussed the SC system the focus will now evaluate some other structure types. For the time being, consideration will be restricted to a one-atom basis of s atomic orbitals. The BCC lattice contains eight first-nearest neighbors located, relative to the atom in... 

Last, ReOs has the octahedral framework of the SrTiOs structure minus the 12-coordinate atom in the center of the unit cell. However, the orbitals on this atom ate of such high energy (Sr electron configuration = 4s 4p 5s ) that they do not hybridize with the Ti 3d-02p bands. In the perovskite stmcture, this atom simply provides electrons to the system that can occupy the valence or conduction bands. Hence, there is little change to the band dispersion directly resulting from the presence of the A cation. 

How both the density and mobility of charge carriers in metals and band semiconductors (i.e. those in which electrons are not localized by disorder or correlation) are influenced by particular features of the electronic structure, namely band dispersion and band Ailing, will now be examined. Taking mobUity first, this book will briefly revisit the topic of band dispersion. Charge carriers in narrow bands have a lower mobility because they... 

Generally, the assumption is made that scattering does not depend on the wavenumber so that the conversion of the measured reflectance spectrum R by means of the Kubelka-Munk function F R), results in an absorption-proportional representation. As for ATR and reflection-absorption spectroscopy, also the diffuse-reflectance spectmm does not consist of dispersion features but band-like structures. For changes in low absorption, the sensitivity of diffuse reflectance is greater than the one of transmittance, while strong absorption bands are less pronounced in the diffuse-reflection (see Fig. 6.4-18). Therefore, diffuse-reflection spectra resemble poorly resolved transmittance spectra. For diffuse reflectance spectra where R is in the order of 0.01 or below, the function -log R or just I / R is equally well suited for conversion (Olinger and Griffiths, 1988). Such level are found with compact samples such as polymer foams or varnishes with filler (Otto, 1987 Korte and Otto, 1988). 

As discussed earlier, it is now possible to make and study deposits of monosized, highly dispersed, transition metal clusters.(S) In this section we summarize results from the first measurements of the valence and core level photoemission spectra of mass selected, monodispersed platinum clusters. The samples are prepared by depositing single size clusters either on amorphous carbon or upon the natural silica layer of a silicon wafer. We allow the deposition to proceed until about 10 per cent of the surface in a 0.25 cm2 area is covered. For samples consisting of the platinum atom through the six atom duster, we have measured the evolution of the individual valence band electronic structure and the Pt 4f... 

The final results of the electronic structure of the nanocrystals depend on the type of the orbital basis chosen to build the TB Hamiltonian. The first-principle band structure calculation of the bulk material gives a good indication of the choice of the basis set and the interactions. For example, the density of states (DOS) and the partial DOS (PDOS) for the bulk system clearly illustrate the various orbitals involved in bonding at any given energy. The character of various bands in the band dispersions can also be analyzed to obtain similar, but even more detailed information. Thus, one can appropriately select the orbital basis to perform the TB... 

Details of the calculational technique, the resulting band dispersions, and comparisons with other (SN)x band structures have... 

Ceo fullerides exhibit several interesting phenomena related with the presence of strong correlations such as high temperature superconductivity or antiferromagnetism. The existence of non-conventional behaviors can be anticipated from the fact that both the electron-phonon and electron-electron interactions are, respectively, comparable and much larger than the narrow bandwidth predicted by standard electronic structure calculations (a few hundreds of meV). These systems are therefore close to a metal-insula-tor transition of the Mott-Hubbard type and the validity of the adiabatic approximation, assumed in most electronic structure calculations, can be questioned. From the experimental point of view the band derived from the molecular LUMO is usually seen as a quite broad feature, much wider that the theoretical estimates, in photoemission experiments. However, the observation of the band dispersion has proven elusive in ARPES studies until very recently. In a recent joint experimental and theoretical paper, Yang et al. [158] have reported the first photoemission measurement of the band dispersion for a K-doped Qo monolayer deposited on a Ag(lll) substrate. The results have been compared with ab initio calculations performed with SIESTA. In those calculations the Ag substrate was modeled by a slab con-... 

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