BAND STRUCTURE EVOLUTION

Band structures. Evolution from tt MOs in finite polyenes to bands in an infinite TT system. 

Fig. 2-15 Band structure evolution for Poly(pyrrole) (P(Py)). The evolution from (a) to (d) is with progressively increasing doping.

Some of the most practically useful results of VEH calculations have been the band structures and the derivative band structure evolution as a function of doping, dealt with in some detail in Chapter 2 earlier, and to which reference may be made. 

From a reading of this chapter, which methods do you find are best suited, in terms of accuracy and economy of time, for computation of the following properties of CPs bandgaps band structures band structure evolutions rotational barriers UV-Vis-NIR absorption spectra far-IR absorption and Reflectance spectra Pauli susceptibility optical transition probabilities (intensities). 

Figure 1. Schematic diagram of the evolution of the band structure of a conducting polymer.

Tsuji I, Kato H, Kobayashi H, Kudo A (2004) Photocatalytic H2 evolution reaction from aqueous solutions over band structure-controlled (AgIn)xZn2(i-x)S2 solid solution photocatalysts with visible-light response and their surface nanostructures. J Am Chem Soc 126 13406-13413... 

P. Barta, P. Dannetun, S. Stafstrom, M. Zagorska, and A. Pron, Temperature evolution of the electronic band structure of the undoped and doped regioregular analog of poly(3-alkylthio-phenes) a spectroscopic and theoretical study, J. Chem. Phys., 100 1731-1741, 1994. 

The occurrence of bipolaronic states in the polymer chains promotes optical absorption prior to the n-n gap transitions. In fact, referring to the example (9.30) of the band structure of doped heterocyclic polymers, transitions may occur from the valence band to the bipolaronic levels. These intergap transitions are revealed by changes in the optical absorptions, as shown by Fig. 9.8 which illustrates the typical case of the spectral evolution of polydithienothiophene upon electrochemical doping (Danieli et al., 1985). 

The evolution of the band structure - and thus of the doping process -may be conveniently monitored by detecting in situ the optical absorption during the electrochemical process, by placing the cell directly into the spectrophotometer (Danieli et al, 1985). 

H2 evolution reaction from aqueous solutions over band structure-controlled (AgIn)xZn2(i-x)S2 solid solution... 

Transition from non-metallic clusters consisting of only a few atoms to nanosized metallic particles consisting of thousands of atoms and the concomitant conversion from covalent bond to continuous band structures have been the subject of intense scrutiny in both the gas phase and the solid state during the last decade [503-505]. It is only recently that modern-day colloid chemists have launched investigations into the kinetics and mechanisms of duster formation and cluster aggregation in aqueous solutions. Steady-state and pulse-radiolytic techniques have been used primarily to examine the evolution of nanosized metallic particles in metal-ion solutions [506-508]. 

The changes in the optical absorption spectra of conducting polymers can be monitored using optoelectrochemical techniques. The optical spectrum of a thin polymer film, mounted on a transparent electrode, such as indium tin oxide (ITO) coated glass, is recorded. The cell is fitted with a counter and reference electrode so that the potential at the polymer-coated electrode can be controlled electrochemically. The absorption spectrum is recorded as a function of electrode potential, and the evolution of the polymers band structure can be observed as it changes from insulating to conducting (11). 

H.J. Zhai et al., Probing the electronic structure and band gap evolution of titanium oxide clusters (Ti02)n (n = 1-10) using photoelectron spectroscopy. J. Am. Chem. Soc. 129, 3022-3026 (2007)... 

The observed evolution of the shape of the band-structure upon doping satisfies the Luttinger sum rule [9], It should be noted that only in the Anderson lattice-like limit of the Emery model it is possible to obtain the observed evolution of the FS upon doping. In all other cases, the oxygen symmetry of the FS can be attributed to the (non-renormalized) oxygen band and therefore the strong doping dependence of the band structure cannot be expected. 

As was discussed above, the absence of a kink in the nodal band below Ev [11] in NCCO, supports the possibility that it is also a real n-type cuprate. It is possible that the change in the sign of the TEP slope in NCCO with doping is an anomalous band-structure effect, probably associated with the peculiar evolution of its FS with doping, detected in ARPES [34], The position of the kink (below or above /q.) is determined by the inequality (11) between dq+ and d L, which is less susceptible to band-structure effects than the inequality (11) between bq+ and bq, determining the sign of the TEP slope. Anomalous behavior is observed also in the Hall constant of NCCO [32], which changes... 

The Brillouin zone, 104, has some special points labeled in it. There are conventions for this labeling.915 The zone is, of course, three-dimensional. The band structure (Fig. 37) shows the evolution of the levels along several directions in the zone. Count the levels to confirm the presence of six low-lying bands (which a decomposition of the DOS shows to be mainly S 3p) and 10 V 3d bands. The two S 3s bands are below the energy window of the drawing. At some special points in the Brillouin zone there are degeneracies, so one should pick a general point to count bands. 

Metal particles larger than about 100 atoms present an electronic band structure like in the bulk state, when the proportion of surface atoms, however, becomes non-negligible, several differences appear in the band structure. First, the width of the valence band is reduced and, second, its centre of gravity is shifted towards the Fermi level [55,56]. This evolution is a consequence of the reduction of the coordination that is equivalent to an increase in the localization of the valence electrons. This becomes more dramatic if we consider the local density of states on low-coordinated sites like edge and corner atoms. Figure 3.10 shows the calculated density of states on various atoms from a cubo-octahedron Pd cluster containing 3,871 atoms (equivalent to a radius of 5.7 nm) [40]. 

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