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0 is the constant corresponding to the band gap at infinite length, (a) Kuhn, H. J. Chem. Phys. 1949, 17, 1198.
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33845249087
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note
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For previous calculations of conjugated polymers using DFT/PBC. see refs 5c and 6 and references therein.
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21
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see
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For comparison of different theoretical levels used to predict band gaps of conducting polymers, see: Hutchison, G. R.; Ratner. M. A.; Marks, T. J. J. Phys. Chem. A 2002, 106, 10596.
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33845267154
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note
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We note that excellent agreement between the calculated and experimental band gap values is partially due to cancellation of several errors from the theoretical level used and from comparison of gas phase calculations with experimental measurements performed in solid state.
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more..
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24
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33845246535
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note
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2v symmetries for even and odd values of n, respectively. The energy difference between the symmetry constrained and non-constrained geometries is always less than 0.12 kcal/mol for oligothiophenes and 0.05 keal/mol for oligoselenophenes. The optimized geometries of 20T and 30T without symmetry constraints have planar structures which are indistinguishable from symmetry constrained geometries (energy difference is less than 0.01 kcal/mol). The geometries of oligoparaphenylenes and oligoEDOTs are optimized without symmetry constraints (geometries of oligoEDOTs are practically planar). Only in the case of oligopyrroles is the difference between constrained planar and non-constrained geometries significant (1.3 kcal/mol for the 6-mer and 9.2 kcal/mol for the 30-mer).
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27
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33845246081
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For an explanation of the asymptotic behavior of the HOMO-LUMO gap on the basis of the free electron model of the conjugated pseudo-one-dimensional π-system, see refs 6 and 7.
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39
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33845263421
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note
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1 symmetry) were also studied, and their HOMO-LUMO gaps showed similar behavior; see Supporting Information (Figure S1) for details.
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33746506728
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After this work had been submitted for publication, calculations on long (up to n = 40) oligothiophenes and oligopyrroles at B3P86-30%/CEP-31G* level had been published. Salzner, U.; Karalti, O.; Durdagi, S. J. Mol. Model. 2006, 12, 687. Convergence of HOMO-LUMO gaps can also be observed at this level (see Figure 1 in ref 28).
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50
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33845242436
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note
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We have also discovered several cases (which belong to yet experimentally unknown types of conjugated polymers) where PBC results do not match values obtained from oligomer extrapolation. The details will be reported in a future publication.
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