Geometries of monomers through hexamers of cylopentadiene, pyrrole, furan, silole, phosphole, thiophene, selenophene and tellurophene, and monomers through nonamers of borole were optimized employing density functional theory with a slightly modified B3P86 hybrid functional. Bandgaps and bandwidths were obtained by extrapolating the appropriate energy levels of trimers through hexamers (hexamers through nonamers for borole) to infinity. Bandgaps increase with increasing ~-donor strengths of the heteroatom. In general, second period heteroatoms lead to larger bandgaps than their higher period analogs. Polyborole is predicted to have a very small or no energy gap between the occupied and the unoccupied w-levels. Due to its electron deficient nature polyborole differs significantly from the other polymers. It has a quinoid structure and a large electron affinity. The bandgaps of heterocycles with weak donors (CH2, Sill2 and PH) are close to that of polyacetylene. For polyphosphole this is due to the pyramidal geometry at the phosphorous which prevents interaction of the phosphorus lone pair with the or-system. The bandgap of polypyrrole is the largest of all polymers studied. This can be attributed to the large w-donor strength of nitrogen. Polythiophene has the third largest bandgap. The valence bandwidths differ considerably for the various polymers since the avoided crossing between the flat HOMO-1 band and the wide HOMO band occurs at different positions. The widths of the wide HOMO bands are similar for all systems studied. All of the polymers studied have strongly delocalized or-systems.

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DFT calculations on a series of oligomers have been used to estimate band gaps, ionization potentials, electron affinities, and bandwidths for polyacetylene, polythiophene, polypyrrole, polythiazole, and a thiophenethiazole copolymer. Using a slightly modified hybrid functional, we obtain band gaps within 0.1 eV of experimental solid-state values. Calculated bond lengths and bond angles for the central ring of sexithiophene differ by less than 0.026 Å and 0.7 from those of the sexithiophene crystal structure. IPs and EAs are overestimated by up to 0.77 eV compared to experimental bulk values. Extrapolated bandwidths agree reasonably well with bandwidths from band structure calculations.

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A comparison is made of various local and gradient-corrected correlation energy functionals, Ec(n,m), for positive, neutral and negative ions with atomic numbers between 1 and 30. The improvement in the total correlation energy, in c, from the gradient corrected Ec(n,m) is not always transferred to the correlation energy differences, e.g. correlation energy contributions, Delta in c, to ionisation potentials (IP) and electron affinities (EA). Particular attention is given to the 3d transition series, where none of the presently Ec(n,m) reproduce the experimental Delta in c very well. An identity for differences in energy functionals of Vosko and Lagowski (1986) is used to express Delta Ec directly in terms of the number and spin magnetic moment density differences and 'effective potentials'. The trends in the IP and EA Delta in c for the 3d transition series elements are analysed using this identity, and the inadequacies of presently available Ec(n,m) are discussed.