Extended Huckel band structure

Can we see this local, very chemical bonding construction in a delocalized band structure Most certainly. The calculated (extended Huckel) band structure and total density of states of a single Mn2P22 layer is illustrated in Fig. 27. 

The spatial arrangement of ETs in this system is shown in Fig. 40 together with the overlap integrals leading to the extended Huckel band structures shown in Fig. 41. As seen this system is intermediate between a-(ET)2l3 and k-(ET)2X if the degree of dimerization in k-(ET)2X and the degree of the band-overlap in a-(ET)2l3 are varied, this system is realized [111]. This is schematically shown in Fig. 42(a). This affords a unified view on these three different polytypes. At the same time the phase diagram expected from this HF calculations is shown in Fig. 42(b) [111]. 

Resistivity and susceptibility measurements have been carried out for Lal2 and the electronic band structure has been calculated (Burrow et al. 1987). Extended Huckel band structure calculations were also undertaken for the remarkable cubic modification of Prl2 (Prl2-V, fig. 8, Waikentin and Bamighausen 1979). It resembles the spinel structure... 

Finally, within the crystal-orbital formalism for the valence electrons one can also use the extended Huckel method of Roald Hoffmann that leads to extended Huckel band structures of quasi-one-dimensional periodic chains. Unfortunately, we cannot here enter into the details of this method (neither in its simple nor in its iterative form). 

The dependence of the XPS of polymers on substitutions and conformational changes was examined by first performing an extended Huckel band-structure calculation on the series of linear fluoropoly-ethylenes -CH2-CH2-, -CHF-CH2-, -CF2-CH2-, -CHF-CHF-, -CHF-CFH-, -CF2-CHF-, and finally -CF2-CF2-, > taking them in the artificial planar zigzag conformation. The theoretical conclusions obtained indicate that the fluoro substituents should be observable in the XPS measurements. Subsequent experimental works have confirmed these predictions. >... 

Poly(thieno[3,4-h]thiophene), like the monomers, was the last of the thienothiophenes to be synthesized. Hong and Marynick [28] had obtained the electronic structures of poly(thieno[3,4-h]thiophene) using modified extended-Huckel band calculations and predicted that PT34bT connected through 4-and 6-positions will have a bandgap of 1.5-1.6 eV (tt-tt, comparable to that of polyacetylene. In... 

The primary reason for interest in extended Huckel today is because the method is general enough to use for all the elements in the periodic table. This is not an extremely accurate or sophisticated method however, it is still used for inorganic modeling due to the scarcity of full periodic table methods with reasonable CPU time requirements. Another current use is for computing band structures, which are extremely computation-intensive calculations. Because of this, extended Huckel is often the method of choice for band structure calculations. It is also a very convenient way to view orbital symmetry. It is known to be fairly poor at predicting molecular geometries. 

The distances found between platinum centers in these molecules have been correlated with the resonating valence bond theory of metals introduced by Pauling. The experimentally characterized partially oxidized one-dimensional platinum complexes fit a correlation of bond number vs. metal-metal distances, and evidence is presented that Pt—Pt bond formation in the one-dimensional chains is resonance stabilized to produce equivalent Pt—Pt distances.297 The band structure of the Pt(CN)2- chain has also been studied by the extended Huckel method. From the band structure and the density of states it is possible to derive an expression for the total energy per unit cell as a function of partial oxidation of the polymer. The equilibrium Pt-Pt separation estimated from this calculation decreases to less than 3 A for a loss of 0.3 electrons per platinum.298... 

The tight-binding band structure calculations were based upon the effective one-electron Hamiltonian of the extended Huckel method. [5] The off-diagonal matrix elements of the Hamiltonian were calculated acording to the modified Wolfsberg-Helmholtz formula. All valence electrons were explicitly taken into account in the calculations and the basis set consisted of double- Slater-type orbitals for C, O and S and a single- Slater-type orbitals for H. The exponents, contraction coefficients and atomic parameters were taken from previous work [6],... 

Polymer Conformation and Crystallinity. Beyond the stereoregularity and tacticity, the geometrical conformation of the polymer chain in the solid material could influence its electronic structure, through a modification of its valence band molecular orbitals. Indeed, a few years ago, very characteristic band structures were calculated for T, G, TG, and TGTG polyethylenes ( ). More recently. Extended Huckel crystal orbital calculations showed that for isotactic polypropylene, a zig-zag planar or a helical conformation resulted in significant changes in the theoretical valence band spectra, supporting the idea that conformation effects could be detected experimentally by the XPS method ( ). 

Electronic band structures were calculated for several polymeric chains structurally analogous to polyacetylene (-CH-CH) and carbyne (-CbC). Ihe present calculations use the Extended Huckel molecular orbital theory within the tight binding approximation, and values of the calculated band gaps E and band widths BW were used to assess the potential applic ilitf of these materials as electrical semiconductors. Substitution of F or Cl atoms for H atoms in polyacetylene tended to decrease both the E and BW values (relative to that for polyacetylene). Rotation about rhe backbone bonds in the chains away from the planar conformations led to sharp increases in E and decreases in BW. Substitution of -SiH or -Si(CH,) groups for H in polyacetylene invaribly led to an increase in E and a decrease in BW, as was generally the case for insertion of Y ... 

Figure 29 Band structure and Fermi surface of (TMTTF)2X calculated within the extended Huckel approximation, (taken from ref. 10)...

Fig. 2.9 Semiempirical (extended Huckel theory) band structure E ip k)) for a onedimensional chain of hydrogen atoms with H-H distances of 3 A and 2 A (in grey) and 1 A (in black). The shape of the extended wave function has been iconized for three different k points, r (left), k = n/2a (middle), and X (right).

Fig. 2.19 Semiempirical (extended Huckel theory) band structure, density-of-states, and crystal orbital overlap population for a one-dimensional chain of hydrogen atoms spaced at 2.0 A. Due to a Gaussian smoothing, DOS and COOP plots appear slightly...

The first electronic structure calculations on polyazine used the Extended Huckel method on a basis set composed only of n orbitals to establish the band structure of the polymer [11]. An al -trans structure was assumed and, as would be expected by the repeat unit. 

Tetramers of aniline (and substituted anilines) were optimized using the B3LYP functional with a 6-3IG basis set. The unit cell for polymer calculations was built from the tetramer structural data obtained above. In our calculations, a periodical, infinite and non-planar helical geometiy was assumed having the internal coordinates of one aniline unit, as shown in Fig. 2. We have studied the electronic properties of PANI only in its reduced form. Previous works have shown that PANI has a large band gap in the reduced state (around 3.6eV), which diminishes for the oxidized state. These effects were extensively analyzed using VEH and Extended HUckel methods [35]. 

We finish our discussion of this polymer by examining the band structure for the o linear, all trans structure with alternating bond lengths (Fig. 15-18a) as calculated by the extended Huckel method. 

After a number of semiempirical (extended Huckel, CNDO/2,< > INDO,< and MINDO< >) calculations in 1970, Andre performed the first ab initio band-structure computation of an infinite polyethylene chain. Since this polymer is mass-produced in the plastics industry, the theoretical study of its properties (especially of its mechanical properties, see Chapter 10) is of great practical interest, which explains the large... 

The formation of C-C chemical bonds in a variety of solids, including some refractory dicarbides, has been considered by Li and Hoffman (1989) and Wijeyesekera and Hoffman (1984) based on EHT (extended Huckel theory) calculations. To our knowledge, these works are the only ones where the band analogues of bond populations, the so-called crystal orbital overlap populations (COOPs) have been calculated for refractory compounds. The most noticeable result is that, in spite of the evident crudeness of the nonself-consistent semiempirical EHT method, the calculations allow us to understand the nature of the phase transition from cubic to hexagonal structure which occurs in the ZrC, NbC, MoC,... series as the VEC increases. The increase of metal-to-metal bonding when going from cubic (NaCl-type) to hexagonal (WC-type) becomes evident. 

Figure 10.6 a) Crystal structure of p-fBEDT-TTFljIs at room temperature. The band structure (b) and Fermi surface (c) calculated by tight-binding approximation with extended Huckel MO calculation based on the structure (a). 

Over the years, electronic band structure calculations have been made on a number of salts based on tetrachalcogenafiilvalenes and metal 1,2-dichalcogeno-lenes, mainly by applying the extended Huckel tight-... 

The intermolecular interaction is very sensitive to the anisotropy of the conduction molecular orbitals (HOMO, LUMO,. ..) and the compactness of the intermolecular contacts. So that it may be appropriate to use the anisotropy of the intermolecular overlap integral (5) of the conduction molecular orbitals as a semi-quantitative measure of the dimensionality of the system. If we adopt the simple extended Huckel approximation (transfer integral (t)(xS), we can visualize the dimensionality of the molecular conductor as a form of simple band structure (or the shape of Fermi surface (FS)). 

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