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 IP(1a) of oligothiophenes and oligoselenophenes and chain length linearly correlates with an empirically obtained value of 1/(n(0.75)). The first vertical ionization potential (IP(1v)) 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 obs...

The high reactivity of acenes can reduce their potential applications in the field of molecular electronics. Although pentacene is an important material for use in organic field-effect transistors because of its high charge mobility, its reactivity is a major disadvantage hindering the development of pentacene applications. In this study, several reaction pathways for the thermal dimerization of acenes were considered computationally. The formation of acene dimers via a central benzene ring and the formation of acene-based polymers were found to be the preferred pathways, depending on the length of the monomer. Interestingly, starting from hexacene, acene dimers are thermodynamically disfavored products, and the reaction pathway is predicted to proceed instead via a double cycloaddition reaction (polymerization) to yield acene-based polymers. A concerted asynchronous reaction mechanism was found for benzene and naphthalene dimerization, while a stepwise biradical mechanism was predicted for the dimerization of anthracene, pentacene, and heptacene. The biradical mechanism for dimerization of anthracene and pentacene proceeds via syn or anti transition states and biradical minima through stepwise biradical pathways, while dimerization of heptacene proceeds via asynchronous ring closure of the complex formed by two heptacene molecules. The activation barriers for thermal dimerization decrease rapidly with increasing acene chain length and are calculated (at M06-2X/6-31G(d)+ZPVE) to be 77.9, 57.1, 33.3, -0.3, and -12.1 kcal/mol vs two isolated acene molecules for benzene, naphthalene, anthracene, pentacene, and heptacene, respectively. If activation energy is calculated vs the initially formed complex of two acene molecules, then the calculated barriers are 80.5, 63.2, 43.7, 16.7, and 12.3 kcal/mol. Dimerization is exothermic from anthracene onward, but it is endothermic at the terminal rings, even for heptacene. Phenyl substitution at the most reactive meso-carbon atoms of the central ring of acene blocks the reactivity of this ring but does not efficiently prevent dimerization through other rings.

Recently, a family of conducting polyselenophenes was synthesized, and they were shown to have a number of interesting properties. Here we have studied oligoselenophenes, their cation radicals and dications up to the 50-mer (50 Se), as well as polyselenophene at the B3LYP/6-31G(d) level of theory, and compared them with the corresponding oligothiophenes. Although the calculations reveal many similarities between oligo- and polyselenophenes and their thiophene-based counterparts, they also show the important differences between those two types of conjugated systems. Oligo- and polyselenophenes have a more quinoid character, lower band gap, and importantly, they are more difficult to twist. The theoretical results suggest that the HOMO-LUMO gap (band gap), bond-length alternation (BLA), and charge distribution in oligo- and polyselenophenes are strongly dependent on inter-ring twisting, yet twisting costs little energy. The inter-ring distances in oligo- and polyselenophenes are shorter than the related distances in oligothiophenes, whereas the bond lengths within the selenophene rings are comparable to those of the corresponding oligothiophenes.

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The effect of counterions on the properties and structure of conducting polymers was studied by using a series of Cl3− doped polythiophenes (PTs) as a case example. Hybrid density functional theory (DFT) with periodic boundary conditions (PBC) at the B3LYP/6–31G(d) level has been used. This is the first theoretical study of infinitely long doped PT using DFT with counterions explicitly taken into account. The balance between charge carrier states was addressed by studying the singlet and triplet state unit cells of differently doped PTs. The relative isomer energies, density of states diagrams, bond length alternation, and charge distribution patterns were analyzed. Interestingly, the position of the counterion is flexible over the polymer chain and the electronic structure of the polymer and, consequently, optical properties are sensitive to the position of the counterion. A bipolaron electronic configuration is preferred at high dopant concentrations (one dopant per six or less thiophene rings) while a polaron pairs configuration is preferred at low dopant concentrations (one dopant per ten or more thiophene rings) which is in line with many experimental observations.