NMR Chemical Shifts Based on Band Theory

Abstract

Nuclear shielding offers microscopic information about the stereochemical and crystal structures of polymers which in turn are important factors in understanding physical properties. Details of electronic structure can also be deduced from nuclear shielding data, and this is also important in controlling physical properties [1]. In order to obtain the information about the electronic structure of polymers from nuclear shielding, it is necessary to use a theoretical approach in addition to an experimental one. In general, there are two possibilities to obtain such information by theoretical methods. One is to use a fragment of a polymer such as a dimer, trimer, etc. for theoretical calculations. Such an approach is useful because the nuclear shielding is sometimes governed by the local electronic structure. However, there is doubt whether the electronic structure obtained from the model compound appropriately reproduces that of the polymer chain. Another approach is to employ directly an infinite polymer chain with periodic structure. This leads to the application of the tight-binding (TB) molecular orbital approximation, which was developed in the field of solid-state physics [2]. Its advantages are that it treats the polymer directly and that relatively long-range interactions such as hydrogen bonding in the α-helix form of the polypeptide may be included. In using the model compound approach, the electronic structure of large chains can be visualized by drawing the orbital energies associated with chains of increasing length. On the other hand, for an infinite polymer chain, the energy levels are built up as a continuous band structure. As rotation about the bond is strongly restricted in solid polymers, the periodicity of a polymer chain is retained. From the point of view of calculating nuclear shielding, use of the TB model for the calculation of the electronic structure of polymers has been successful. Herein we described the basic ideas for deducing the electronic structure and the nuclear shielding of solid polymers by the TB approximation. Theoretical Aspects of Electronic State and Nuclear Shielding in Solid Polymers