Semi-empirical LCAOMO theory for infinite systems. Part 1.—Application to polyethylene, polyacetylene and polyvinylchloride

Abstract

Tight-binding molecular orbital theory for infinite systems developed in terms of the SCF CNDO formalism allows for the explicit inclusion of orbital rather than atomic core Hamiltonian matrix elements and electron repulsion integrals. It also seeks to establish a relationship, in terms of parametrisation, between the molecular and the solid-state tight-binding method. By applying this theory to a regular polyethylene polymer model, the band gap has been compared with that for an ab initio calculation and optimized with respect to the Mulliken-Wolfsberg A parameter. The results suggest that parametrisation of the semi-empirical solid-state tight-binding approach can be carried through in the same way as in molecular versions of this theory. The method, applied to regular polyacetylene, reveals that the energy bands on either side of the band gap have π character and the lowest energy electronic transitions are therefore πâ†�π* in nature. The highest filled band in polyvinylchloride has chlorine 3p character; the band gap is lower than that of polyethylene. The density-of-states plots for all three systems are sharply peaked around the energy gaps.