Three-dimensional band calculations

Two recent and detailed three-dimensional band calculations on trans-PA [93] and on PPV [94] yield similar results tjtn is at least 3 x 10 2, so three-dimensional behavior should be observed and no polaron state should... 

We conclude that the available band structure calculations provide the basis for a semiquantitative understanding of the absorption spectra. There are, however, quantitative discrepancies. In addition, the importance of the 1.5 eV interchain transition in [lS] (A )n indicates that more extensive three-dimensional band calculations will be required for a complete understanding of the electronic structure of the polaronic metal. 

Excitation of ClNO(Ti) in any one of the three vibrational bands yields exclusively NO products in vibrational state n — n (Qian et al. 1990). The left-hand side of Figure 9.12 depicts the results of a three-dimensional wavepacket calculation including all three degrees of freedom and using an ab initio PES (Solter et al. 1992). This calculation reproduces the absorption spectrum and the final vibrational and rotational distributions of NO in good agreement with experiment. 

The electronic properties are also modified by polymerization. Experimentally, the band gap decreases to less than 1.2 eV in the low-pressure orthorhombic phase [65], and experiments [66,88,108] and calculations [80,109-111] agree that the band gap should decrease with an increasing number of intermolecular bonds. (We note the possible exception of the high-pressure polymerized orthorhombic phase, as discussed above.) Calculations [85, 111] show that the rhombohedral phase should have a more three-dimensional band structure than the orthorhombic phase but still be a semiconductor. However, recent measurements by Makarova et al. [88] showed that oriented samples of the rhombohedral phase had an extremely large electrical anisotropy, larger than that of single-crys-... 

Band Structure Calculations and Experimental Results The spectroscopic properties discussed above are related primarily to intrachain electronic structure. One exception is the stability of gap states (e.g., polarons) versus the three-dimensional interaction effects mentioned in Chapter 11, Section IV.D. Energy and charge transport are, of course, dependent on interchain transfers. So while there are only a few three-dimensional band structure calculations (e.g., for PA [184] and PPV [185]), there are many theoretical calculations concerning infinite perfectly periodic one-dimensinal chains, the effects of local perturbations, and the elementary excitations of these chains solitons, polarons, and bipolarons. Only a few hints of that work will be given here. It has been discussed and reviewed several times (see, e.g., Refs. 186 to 188). 

The detailed discussion of band structures arising for three-dimensional materials is hardly ever attempted, due to their often incredibly high complexity it is difficult to think in terms of reciprocal space We will also leave the calculations of three-dimensional band structures and parts of their numerical analysis to fast (albeit dumb) computers. 

P. Gommes da Costa, R. G. Dandrea, and E. M. Conwell, First-principles calculation of the three-dimensional band structure of poly(phenylene vinylene), Phys. Rev. B 47 1800 (1993). 

The optimised interlayer distance of a concentric bilayered CNT by density-functional theory treatment was calculated to be 3.39 A [23] compared with the experimental value of 3.4 A [24]. Modification of the electronic structure (especially metallic state) due to the inner tube has been examined for two kinds of models of concentric bilayered CNT, (5, 5)-(10, 10) and (9, 0)-(18, 0), in the framework of the Huckel-type treatment [25]. The stacked layer patterns considered are illustrated in Fig. 8. It has been predicted that metallic property would not change within this stacking mode due to symmetry reason, which is almost similar to the case in the interlayer interaction of two graphene sheets [26]. Moreover, in the three-dimensional graphite, the interlayer distance of which is 3.35 A [27], there is only a slight overlapping (0.03-0.04 eV) of the HO and the LU bands at the Fermi level of a sheet of graphite plane [28,29],... 

Because protein ROA spectra contain bands characteristic of loops and turns in addition to bands characteristic of secondary structure, they should provide information on the overall three-dimensional solution structure. We are developing a pattern recognition program, based on principal component analysis (PCA), to identify protein folds from ROA spectral band patterns (Blanch etal., 2002b). The method is similar to one developed for the determination of the structure of proteins from VCD (Pancoska etal., 1991) and UVCD (Venyaminov and Yang, 1996) spectra, but is expected to provide enhanced discrimination between different structural types since protein ROA spectra contain many more structure-sensitive bands than do either VCD or UVCD. From the ROA spectral data, the PCA program calculates a set of subspectra that serve as basis functions, the algebraic combination of which with appropriate expansion coefficients can be used to reconstruct any member of the... 

This remark is associated with the amount of calculation performed and is not intended as a criticism. This work provides a valuable quantum mechanical analysis of a three-dimensional system. The artificial channel method (19,60) was employed to solve the coupled equations that arise in the fully quantum approach. A progression of resonances in the absorption cross-section was obtained. The appearance of these resonances provides an explanation of the origin of the diffuse bands found... 

The model solution of porous or particulate three-dimensional electrodes is obtained using the Adomian s inverse operator method (IOM) or Decomposition Method . Data calculated by the decomposition method, are comparable with that obtained by a finite difference method using the BAND program. In general the Adomian method gives faster convergence, than that of the finite difference method, for the model over a wide range of parameters. 

Stoll and Preuss (50) have examined Li clusters using a SCF-MO calculational procedure. Although they found convergence problems for the large clusters, chains were more stable than layer structures or three-dimensional crystal structures for the smaller clusters, and BE In is an increasing function of size. The width of the occupied part of the conduction band was in the order 3d>2d> 1 d, as described for silver clusters. The lowest state in the conduction band also drops in energy with increasing size. The calculated work function is within 10% of the experimental bulk work function. 

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]. 

Note that the writing down of the approximate DOS curve bypasses the band structure calculation per se. Not that that band structure is very complicated but it is three-dimensional, and our exercises so far have been... 

If the three-dimensional calculation is repeated at different interslab or P P distances, all that happens is that the localized P-P and o bands occur at different energies. Their splitting decreases with increasing P - - P separation, as one would expect from their respective bonding and antibonding nature. 

With the discovery of superconductivity (Tc = 15.5 K) in the Y-Ni-B-C system [6, 80], a new class of quaternary borocarbide superconductors has emerged. Superconductivity has been observed in several rare earth (Lu, Tm, Er and Ho) nickel borocarbides[80], and with transition metals such as Pd and Pt. The superconducting phase having the composition of YNi2B2C, crystallizes [81] in a tetragonal structure with alternating Y-C and Ni2B2 layers. Band structure calculations [82] indicate that these materials, unlike cuprate superconductors, are three-dimensional metals. 

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