Given their utility in a variety of electronic devices, conjugated oligomers and polymers have attracted considerable research interest in recent years. Because polymeric materials consist of very large molecules with a range of molecular weights (that is, they are polydisperse), predicting their electronic properties is a complicated task. Accordingly, their properties are typically estimated by extrapolation of oligomeric properties to infinite chain lengths. In this Account, we discuss the convergence behavior of various electronic properties of conjugated oligomers, often using thiophene oligomers as a representative example. We have observed some general trends in our studies, which we briefly summarize below for five properties. Most of the calculated values are method dependent: the absolute values can be strongly dependent on the computational level used. Band Gap. The generally accepted approximation used to estimate polymer band gap, whereby a plot of HOMO - LUMO gap versus 1/n (where n is the number of monomer units) is extrapolated to infinite n, fails for long oligomers, because convergence behavior is observed for band gaps. At the B3LYP/6-31G(d) level, it is possible to extrapolate oligomer HOMO - LUMO gaps with a second-order polynomial equation. Alternatively, PBC/B3LYP/6-31G(d) is a very good method to reliably predict the band gap of conjugated polymers. Reorganization Energy. Values of the internal reorganization energy (λ) do not scale linearly with 1/n, instead exhibiting an inverse correlation with the square-root of the number of monomer units for n = 2 - 12. For larger n (10 - 50), a linear relationship is observed between reorganization energy and the reciprocal chain length, and the extrapolation approaches λ ≈ 0 for infinite numbers of oligomer rings. Ionization Potential. The relationship between the first adiabatic ionization potential IP1a of oligothiophenes and oligoselenophenes and chain length linearly correlates with an empirically obtained value of 1/(n 0.75). The first vertical ionization potential (IP1v) linearly correlates with a similarly empirically obtained value of 1/(n 0.70). Polaron - Bipolaron Balance. The contribution of a polaron pair to the electronic structure of the short oligothiophene dication is small; for medium-length oligothiophene chains, the contribution from the polaron pair state begins to become significant. For longer (above 20-mer) oligothiophenes, the polaron pair state dominates. A similar picture was observed for multications as well as doped oligomers and polymers. The qualitative polaron - bipolaron picture does not change when a dopant is introduced; however, quantitatively, the bipolaron - polaron pair equilibrium shifts toward the bipolaron state. Disproportionation Energy. The stability of a single oligothiophene dication versus two cation radical oligothiophene molecules increases with increasing chain length, and there is an excellent correlation between the relative disproportionation energy and the inverse of chain length. A similar trend is observed in the disproportionation energies of oligothiophene polycations as well as doped oligomer and polymers. We also examine doped oligothiophenes (with explicitly included counterions) and polymers with a repeating polar unit. From our experience, it is clear that different properties converge in different ways, and long oligomers (having about 50 double bonds in the backbone) must often be used to correctly extrapolate polymer properties.
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