Electronic Structure of Polymers

The chemical shift is one of most important NMR parameters(l). The NMR chemical shifts provide detailed information on the structure and electronic structures of polymers in the crystalline state and amorphous state(2). 

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) ... 

Wilson reviews in detail many-body perturbation theory of molecules, which is one very useful technique for the inclusion of electron correlation in molecular calculations for small molecules. Ladik and Suhai at the other extreme describe the important advances which have recently been made in the study of the electronic structure of polymers, with emphasis on the use of ab initio methods, which have become practicable in recent years following the development of new computational schemes. Finally, March surveys the current status of the density functional approach, which gives an alternative approach to the description of atoms and molecules. 

For review see e.g. Fabish, T.J., "Electronic Structure of Polymers," Critical Reviews in Solid State Sciences, CRC Press, 1979, 8(4), 383, and references therein. 

X-ray photoelectron spectroscopy used to study the electronic structure of polymers through the analysis of their valence band spectra was found to present very interesting potentialities, but also some limits. 

D. R. Armstrong et al. have a paper on polymers The electronic structure of polymers by FSGO . ... 

Such a situation applies to many polymers and, in order to establish the relationship between the NMR chemical shift and the electronic structure of polymers, it is necessary to use a sophisticated theoretical method which takes account of the characteristics of polymers. 

Some methodologies for obtaining structures and the electronic structures of polymers, both in the solution and solid state, involve a combination of the observation and calculation of NMR chemical shifts. This approach has been applied to various polymer systems. Theoretical calculations of NMR chemical shifts for polymer systems have been achieved using two main approaches. One approach is that model compounds, such as the dimer,... 

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