TB MO theory

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) ... 

Most recently, the TB MO theory for chemical shift calculation of polymer crystals with three dimensional structure within the ab initio framework has been developed and has been successfully applied to polyethylene crystals(42). 

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.

Jordan and co-workers have used similar synthetic NBO Fock matrices to analyze through-bond (TB) and through-space (TS) effects in electron-transfer and excitation-transfer processes. Other workers have similarly employed the NBO Fock matrix to examine the patterns of TB/TS interactions, demonstrating that the molecular transfer pathways are dramatically different from those envisioned in the McConnell superexchange picture. As remarked in Section 2, such improved analysis of TB/TS interactions was a primary motivation of the earlier LCBO-MO formulation that preceded NBO theory. 

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