Tight-binding molecular orbital theory

Two theoretical approaches for calculating NMR chemical shift of polymers and its application to structural characterization have been described. One is that model molecules such as dimer, trimer, etc., as a local structure of polymer chains, are in the calculation by combining quantum chemistry and statistical mechanics. This approach has been applied to polymer systems in the solution, amorphous and solid states. Another approach is to employ the tight-binding molecular orbital theory to describe the NMR chemical shift and electronic structure of infinite polymer chains with periodic structure. This approach has been applied to polymer systems in the solid state. These approaches have been successfully applied to structural characterization of polymers... 

Sometimes the estimation of the electronic structures of polymer chains necessitates the inclusion of long-range interactions and intermolecular interactions in the chemical shift calculations. To do so, it is necessary to use a sophisticated theoretical method which can take account of the characteristics of polymers. In this context, the tight-binding molecular orbital(TB MO) theory from the field of solid state physics is used, in the same sense in which it is employed in the LCAO approximation in molecular quantum chemistry to describe the electronic structures of infinite polymers with a periodical structure -11,36). In a polymer chain with linearly bonded monomer units, the potential energy if an electron varies periodically along the chain. In such a system, the wave function vj/ (k) for electrons at a position r can be obtained from Bloch s theorem as follows(36,37) ... 

Chapter 2 introduces the band theory of solids. The main approach is via the tight binding model, seen as an extension of the molecular orbital theory familiar to chemists. Physicists more often develop the band model via the free electron theory, which is included here for completeness. This chapter also discusses electronic condnctivity in solids and in particular properties and applications of semiconductors. 

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 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. 

Although ab initio molecular orbital theory and density functional theory can be used to systematically improve the accuracy of X-Pol results for large systems, it is still impractical to use these methods to perform molecular dynamics simulations for an extended period of time. With increased computing power, this will become feasible in the future however, at present, it is desirable to use semiempirical molecular orbital models such as the popular approaches based on neglect of diatomic differential overlap (NDDO) or the more recent self-consistent-charge tight-binding density functional (SCC-method to model condensed-phase and biomacromolecules. 

In Eq. (10.9), is the overlap energy and S the corresponding overlap between adsorbate and surface atomic orbitals. Approximate Eq. (10.9) applies when ad molecule orbitals are s-symmetric and the metal electrons are also described by s-atomic orbital. Equation (10.9) is a familiar expression within molecular orbital theory and is deduced from tight binding theory including overlap of the atomic orbitals as in extended Hiickel theory (Hoffmann) is used [9]. 

The outline of the paper is the following section II presents a brief retrospective of the semiempirical molecular orbital theories, section III comments about molecular quantum dynamics, section IV describes the development of effective hamiltonians based on the tight-binding Extended Huckel Theory, section V describes the implementation of... 

Figure 5. Molecular modeling methods at various scales. MO-miolecular orbital DFT-density functional theory TB-tight binding QM/MM-4iybrid quantum mechanics/molecular mechanics MD nolecnlar dynamics.

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