Extended Huckel method band calculations

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 ( ). 

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. 

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 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. 

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