Tight-binding method introduced

In the present contribution, we will examine the fundamentals of such an approach. We first describe some basic notions of the tight-binding method to build the COs of an infinite periodic solid. Then we consider how to analyze the nature of these COs from the viewpoint of orbital interaction by using some one-dimensional (ID) examples. We then introduce the notion of density of states (DOS) and its chemical analysis, which is especially valuable in understanding the structure of complex 3D sohds or in studying surface related phenomena. Later, we introduce the concept of Fermi surface needed to examine the transport properties of metallic systems and consider the different electronic instabilities of metals. Finally, a brief consideration of the more frequently used computational approaches to the electronic structure of solids is presented. 

In the next section we will start with a short theoretical intermezzo to show the approximations involved in the use of the Bxtended-Huckel and related methods and introduce some basic theoretical analytical tools. Then the tight-binding method will be applied to study changes in electronic structure in a one-dimensional system... 

Subsequent cellular methods, on which there is an enormous literature, will not be described here. We shall, however, need to introduce- certain ideas, particularly that of the pseudopotential. We begin by introducing the concept of the muffin-tin potential due to Ziman (1964a). This is illustrated in Fig. 1.9. The tight-binding approximation is appropriate for states with energies below the muffin-tin zero ( bound bands in Ziman s notation). If the energy is above the... 

As an example of the study of vacancies and self-interstitial impurities by the continued fraction expansion of Eq. (S.2S), we mention the work of Kauffer et al. These authors consider impurities in silicon and set up a model tight-binding Hamiltonian with s p hybridization, which satisfactorily describes the valence and conduction bands of the perfect crystal. A cluster of 2545 atoms is generated, and vacancies (or self-interstitial impurities) are introduced at the center of the cluster. One then takes as a seed state an appropriate orbital or symmetrized combination of orbitals, and the recursion method is started. Though self-consistent potential modifications are neglected in this paper, the model leads to qualitatively satisfactory results within a simple physical picture. 

Since the brilliant conceptual proposal by Warshel and Levitt [1], the hybrid method of QM/MM has been extensively applied to simulate some very large systems, such as enzymes, nano-scale materials etc. The purpose of this chapter is not to give a complete review of the QM/MM methods, because the developments and applications of QM/MM methods have been well documented and reviewed in many previous articles, for example. Refs. [2-5]. We try to in this manuscript introduce one of recent developed semi-empirical methods, self consistent charge density tight binding (SCC-DFTB) method [6], and its applications to enzymatic processes when integrated with CHARMM force field. 

To deal with the electronic structure of surfaces within the framework of the spin-polarized relativistic KKR formalism, the standard layer techniques used for LEED and photoemission investigations (Pendiy 1974) have been generalized by several authors (Fluchtmann et al. 1995 Scheunemann et al. 1994). As an alternative to this, Szunyogh and co-workers introduced the so-called screened version of the KKR method (Szunyogh et al. 1994, 1995). A firm basis for this approach has been supplied by the tight-binding (TB) KKR scheme introduced by Zeller etal. (1995). The corresponding spin-polarized relativistic version has been applied by various authors to multilayer and surface-layer systems (Nonas et al. 2001). 

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]. 

In the following section (II) an outline stressing the key features of the model, such as the tight binding formalism and the zeroth order Hamiltonian the CPA method and the way in which disorder is introduced will be given. Based on this outline, ways of improving the model will be considered in section III, followed by several selective results in section IV. Some of the latest developments 4,8 allowing the calculation of several... 

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