Band Structures Calculated

Crystal (we tested Crystal 98 1.0) is a program for ah initio molecular and band-structure calculations. Band-structure calculations can be done for systems that are periodic in one, two, or three dimensions. A separate script, called LoptCG, is available to perform optimizations of geometry or basis sets. 

Figure 5-18. UPS spectrum of the emcraidinc base form of polyanilinc is compared with the VEH calculated band structure (bottom) and the VEH DOVS.

Calculated band structures of aU these compounds feature the fermi level above a density-of-state peak that is consistent with the 3d bands for nickel. The [BN]" anion in CaNi(BN) compromises an electronic situation with a filled 3(7 (HOMO) level that is B-N anti-bonding (Fig. 8.13). Any additional electron will... 

For the conduction electrons, it is reasonable to consider that the inner-shell electrons are all localized on individual nuclei, in wave functions very much like those they occupy in the free atoms. The potential V should then include the potential due to the positively charged ions, each consisting of a nucleus plus filled inner shells of electrons, and the self-consistent potential (coulomb plus exchange) of the conduction electrons. However, the potential of an ion core must include the effect of exchange or antisymmetry with the inner-shell or core electrons, which means that the conduction-band wave functions must be orthogonal to the core-electron wave functions. This is the basis of the orthogonalized-plane-wave method, which has been successfully used to calculate band structures for many metals.41... 

Surprisingly little has been done to take advantage of these valence band spectra, perhaps because of some of the challenges in interpretation. In principle, it should be possible to fit these spectra with component peaks that correspond to contributions from individual atomic valence orbitals. However, a proper comparison of the experimental and calculated band structures must take into account various correction factors, the most important being the different photoelectron cross-sections for the orbital components. 

Figure 17. Calculated band structure for WS2 (22,0) nanotube (85). [Courtesy of G. Seifert, Paderbom University.]...

GGA property calculation on optimized bulk pyrite has been performed. The calculated band structure and frontier orbital distribution are presented in Fig. 9.3 and Fig. 9.4. The calculated band gap of FeS2 is 0.97 eV, and it is in good line... 

Figure 9 J Calculated band structure of bulk FeS2...

Fig. 25 Calculated band structure of single-layer graphene. (Reprinted with permission from [193])...

FIGURE 5. Band structure correlation for linear peralkylated polysilanes (a) (He I) PE spectra of hexamethyldisilane and octamethyltrisilane, (b) ab initio calculated band-structure dispersion (DIS) and (c) state density (DOS) for poly-dimethylsilane R(SiR2)R32... 

To relate the above results to the physical systems, we now give the comparison of the calculated band structure in the Anderson lattice-like limit of the Emery model with the ARPES data on LSCO [6]. The regime of the bare parameters is Ap[Pg.142]

Another demonstration of the validity of these calculations is provided by BEDT-TTF-based salts. The calculated Fermi surface of these materials exhibit closed orbits characteristic of two-dimensional electronic interactions and this has been confirmed experimentally. For example, in the case of (BEDT-TTF)2I3, the calculated surface of these orbits (Fig. 21) [61] agrees well with the one measured by magnetic experiments [161]. However, the overall good agreement between calculation and experiment must not hide the fact that some qualitative discrepancies may arise in some cases. For example, (TMTTF)2X salts exhibit a resistivity minimum at a temperature at which no structural transition has yet been observed. The resistivity minimum is not explained by the one-electron band structure, and to account for this progressive electron localization, it is necessary to include in the calculations the effect of the electronic correlations [162]. Another difficulty has been met in the case of the semiconducting materials a -(BEDT-TTF)2X, for which the calculated band structure exhibits the characteristic features of a metal [93,97,100] and it is not yet understood... 

Tl-2201 has high anisotropy [47-52] with two-dimensional behavior as well [50-52], The details of the crystal structure, bulk synthesis, crystal growth, calculated band structure, electronic transport properties, and pressure... 

Fig. 1. The calculated band-structure of Ti02. The left-hand side shows details of the band energies as a function of k for various directions in the Brillouin zone and the right-hand side shows the total bandwidths and orbital parentage. It can be seen that, even though Ti02 is quite ionic, the 0 2p levels are substantially broadened through 0-0 interactions and the Ti 3d levels by Ti-O-Ti interactions.

CNDO/2 calculated band structure of all-trans-polyethylene. 

Comparison with Theoretical Calculations. It appears that the polymer valence bands are (very) difficult to interpret without the aid of a theoretical basis, or a model, or of the use of a reference spectrum obtained from a model compound. Indeed, Quantum Chemical theory is nowadays able to calculate band structure and density of states for polymers, to simulate the limited resolution of the spectrometer, and to modulate these theoretical density of states to account for the photoionization cross sections that vary considerably for valence bands of polymers containing different types of atoms, and electrons with various symmetries. Consequently, one is able now to predict theoretically the energies of the various molecular orbitals, but also... 

The results listed in Table VI illustrate to what degree the band structure of polyacetylene (corresponding to Xl - X2 H in the Table VI) is affected by periodic substitution of the pendant H atoms along the chain. While substituting a pendant H by a OU appears to have a negligible effect on the values of E and BW, substitution instead by SiH or Si(CH,)2 increases E and decreases BW (suggesting poorer conductivity). A trend appears"to exist for increased E values (and decreased BW values) with an increase in the steric Bulk of the substituent X. Since in these immediate calculations all chains were considered in their trans planar zigzag conformation, it would not seem that the steric bulk of the substituent would have a major effect on the calculated band structures. 

Fig. 2.3. (a) Calculated band structure and (b) Fermi surface of (TMTSF)2AsF6 representative for all (TMTSF)2X. From [43]... 

NMR experiments it was even possible to estimate the SDW nesting vector Q — (Qa> Qb, Qc)> with Qo = 2fep, Qb 0.26, and <5c — 0> aud the amplitude a 0.08/iB of the SDW modulation, where /xb is the Bohr magneton [60, 61]. The value of a less than one means that the moments are not well localized but retain still an itinerant character. The vector Q is in good agreement with the nesting vector of the calculated band structure (see Fig. 2.3). 

As a last example for a calculated band structure in this chapter. Fig. 2.20 shows the result for an a-phase salt, namely 0 -(ET)2KHg(SCN)4, based on the crystal structure at 100K [141]. The other members of the a-(ET)2MHg(SCN)4 family are expected to have almost the same FS. Only... 

Fig. 2.20. Calculated band structure and Fermi surface of a-(ET)2KHg(SCN)4-From [141]...

The band structures of a variety of different organic metals have been investigated since 1988. The principal FS topologies have been mapped out in detail. However, for the largest number of synthetic metals the FS has not yet been verified experimentally. For some other substances the published results are partially in contrast to each other or in disagreement with the calculated band structures. 

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