Extended Hiickel Tight Binding method

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... 

Nonself-consistent Extended Hiickel—Tight-binding Method... 

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]. 

In Sect. 5.3 that follows, we report on the electronic structural characteristics of the C-based hexagonite structure from the point of view of the extended Hiickel molecular orbital method (EHMO), which is an approximate solid state electronic structure algorithm based upon the tight binding methodology (Hoffmann 1963 ... 

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 molecnlar orbital as the number of repeat units in the crystal lattice is increased to infinity. This process is widely known to the chemical conununity as extended Hiickel theory (see Extended Hiickel Molecular Orbital Theory). It is also called tight binding theory by physicists who apply these methods to calcnlate the band structures of semiconducting and metallic solids. 

The empirical (semiquantitative) methods are based on a one-electron effective Hamiltonian and may be considered as partly intuitive extended Hiickel theory (EHT) for molecules [204] and its counterpart for periodic systems - the tight-binding (TB) approximation. As, in these methods, the effective Hamiltonian is postulated there is no necessity to make iterative (self-consistent) calculations. Some modifications of the EHT method introduce the self-consistent charge-configuration calculations of the effective Hamiltonian and are known as the method of Mulliken-Rudenberg [209]. 

The inverse design of molecular structures is a related problem that can make use of the same computational machinery to guide the synthesis or to predict new systems with a desired property. The tight-binding linear combination of atomic potentials (LCAP) is a framework that can be directly applied in combination with the Extended Hiickel Theory. The inverse design by the LCAP method can also be implemented in conjunction with the density functional theory. ... 

---