Tight binding polymer chains

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) ... 

In connection with studies concerning the conformational state of hydrophobic polyelectrolytes, the mode of interaction of dyes (and related compounds) with such polymers has been investigated. This matter appears to be quite complex but some aspects are to be pointed out. First, the extent of dye binding is generally related to the actual conformation of polymers chains as compared to more extended conformational states, tightly coiled polyanions can bind much more dye.15-19 This is not only observed for charged dyea-polyelectrolytes... 

This model can be applied to the ideal rans-polyacetylene chain assuming sp2 hybridization of the carbon px and py orbitals with the carbon 2s electron to form the fully occupied a bands of the polymer. The pz orbital extends perpendicular to the plane of the polymer chain. If the carbon atoms were uniformly spaced, the ideal tight-binding band with transfer integral t given by the matrix element between adjacent Pz orbitals would apply. As there is only one pz electron per carbon atom, the resulting n band would be only one-half filled with band structure and density of states shown in Figure 2. 

No correlation calculations have been performed until now on biopolymers, but such computations have been successfully executed in the cases of polymers with small unit cells (transpolyacetylene and polydiacetylene see below). The same holds for exciton spectra which have been successfully computed applying intermediate (charge transfer) exciton theory /5/ for the above mentioned two chains /6/. One should mention, however, that only the inclusion of the major part of correlation resulted in results in reasonable agreement with experiment. There is an early calculation on transport properties of periodic DNA models using simple tight binding (Huckel) band structures /7/. In the... 

They represent tight ion-pairs solvated externally by some segments of their own chains. This additional binding of the cation to the polymer accounts for the very low dissociation constants of such ion-pairs (Kdiss < 10-9 M). A similar interpretation was evoked in rationalization of the low dissociation constants of the salts of living polyvinyl pyridine 40). 

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