Amorphous structures, tight-binding

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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... 

Figure 8.07 (top) One-electron tight-binding picture for Anderson transition, (a) Band width (left) and potential well structure in the absenee of disorder, (b) Variation of band disorder in site energies. The horizontal marks are the energies EjS (schematic). When the width W of the disorder exceeds the overlap bandwidth B, disorder-induced localization takes place, (bottom) Schematic density-of-states diagram for a crystalline and an amorphous semiconductor, in the vicinity of the highest occupied and lowest empty states. 

Because they are so computationally intensive, ab initio and semiempirical studies are limited to models that are about 10 rings or less. In order to study more reahstic carbon structures, approximations in the form of the Hamiltonian (i.e., Schrodinger equation) are necessary. The tight-binding method, in which the many-body wave function is expressed as a product of individual atomic orbitals, localized on the atomic centers, is one such approximation that has been successfully applied to amorphous and porous carbon systems [47]. 

Charlier et al. [48] used the tight-binding model to study distorted stacking of graphene layers, termed pregraphitic or turbostratic carbon. The turbostratic structure was obtained by generating an amorphous cluster of graphene plates that... 

Massobrio et al. (1989, 1990) studied defect-induced amorphization in NiZr2 using a constant number of particles, constant pressure and constant temperature (NPT) MD and tight-binding potentials, by randomly exchanging a number of Ni and Zr atoms. They observed a volume increase in the system. The change in volume is more pronounced as the degree of chemical disorder introduced increases. The amorphous structure is similar to a structure obtained from a quenched liquid. 

The transferability of the tight-binding model is a key issue. Among the tight-binding models proposed so far, the model for carbon developed by Xu et al. [23] is the most successful. The model has been applied to various carbon systems, ranging from clusters to crystalline structures and to the liquid and amorphous structures of carbon. The results from TBMD simulations not only agree well with available ab initio calcula-... 

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