By considering chains of hydrogen and helium atoms with one Gaussian function centered on each atomic sites, i.e., the simplest possible metallic and insulating model systems retaining all the characteristics of the restricted Hartree–Fock–Roothaan method for extended chains, a scheme is proposed to carry out accurately and efficiently both Coulomb and exchange lattice sums which occur in a Gaussian basis set environment.

Ab initio RHF/sTO-3G band structure calculations are carried out on extended regular polypropylene chains (isotactic helical, syndiotactic helical, and zigzag planar) to assess qualitatively the dependence of the energy band structure and density of states on the molecular geometry. It is found that discrimination between the two syndiotactic forms should be possible from spectral features in the valence region of corresponding Ps spectra.

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