Extended tight-binding band calculations

Almost a decade ago, we wrote a report on Special Project Research on New Superconducting Materials carried out at that time [17], in which our motivation, to use a simple extended Hiickel tight-binding band calculation, was briefly described. Since the chemical viewpoint on the usefulness of the simple band examination mentioned there seems to still be valid, it might be permissible to quote some sentences from it. 

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],... 

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 ... 

The calculation of the exact band structure from first principles, however, is rather complex and requires considerable simplifications. The usual and very successful method to calculate the band structure of organic charge transfer salts is a tight-binding method, called extended Hiickel approximation. In this approximation, one starts from the molecular orbitals (MO) which are approximated by linear combinations of the constituent atomic orbitals. Each MO can be occupied by two electrons with antiparallel spins. These valence electrons are assumed to be spread over the whole molecule. Usually, only the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are relevant and are, therefore, considered in most band-structure calculations [41]. 

Based on the extended Hiickel tight-binding method the 2D energy dispersion relation and FS of k-(ET)2Cu(NCS)2 [29, 155, 161, 162] and K-(ET)2l3 [147, 163] have also been calculated. Figure 2.19 shows the results. The band structures are very similar except for the degeneracy of the two upper bands along Z-M for K-(ET)2l3. In k-(ET)2Cu(NCS)2, due to the lack of a center of... 

The molecular arrangement in the crystals of neutral [Ni(tmdt)2] is illustrated in Figure 4.28 the [Ni(tmdt)2] molecules are ideally flat and closely packed. Three-dimensional short S - S contacts develop within the structure. The conductivity at room temperature is 4 x 10 S cm and it shows metallic behaviour (Figure 4.28). The band calculations based on first principle calculations and extended Hiickel tight-binding calculation... 

The band structure of a three-dimensional solid, such as a semiconductor crystal, can be obtained in a similar fashion to that of a polyene. Localized molecular orbitals are constructed based on an appropriate set of valence atomic orbitals, and the effects of delocalization are then incorporated into the molecular orbital as the number of repeat units in the crystal lattice is increased to infinity. This process is widely known to the chemical community as extended Hiickel theory see Extended Hiickel Molecular Orbital Theory). It is also called tight binding theory by physicists who apply these methods to calculate the band structures of semiconducting and metallic solids. 

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