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1
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33748591789
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Band gaps in polymers are identified with the onset of optical absorption due to electronic excitations. An excitation energy of 2 (3.5) eV corresponds to an absorption wavelength of 620 (350) nm
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Band gaps in polymers are identified with the onset of optical absorption due to electronic excitations. An excitation energy of 2 (3.5) eV corresponds to an absorption wavelength of 620 (350) nm.
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2
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0025498642
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Burroughes, J. H.; Bradley, D. D. C.; Brown, A. R.; Marks, R. N.; Mackay, K.; Friend, R. H.; Burns, P. L.; Holmes, A. B. Nature 1990, 347, 539.
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33748596018
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Proceedings of the 6th International Conference on II-VI Compounds and Related Optoelectronic Materials
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Nurmikko, A., Yao, T., Ruth, R., Eds.; in press
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For an overview see, for example: Proceedings of the 6th International Conference on II-VI Compounds and Related Optoelectronic Materials; Nurmikko, A., Yao, T., Ruth, R., Eds.; J. Cryst. Growth, in press.
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J. Cryst. Growth
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0027678070
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Greenham, N. C.; Moratti, S. C.; Bradley, D. D. C.; Friend, R. H.; Holmes, A. B. Nature 1993, 365, 628.
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Friend, R.H.4
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Garnier, F.; Yassar, A.; Hajlaoui, R.; Horowitz, G.; Deloffre, F.; Servet, B.; Ries, S.; Alnot, P. J. Am. Chem. Soc. 1993, 115, 8716.
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Horowitz, G.4
Deloffre, F.5
Servet, B.6
Ries, S.7
Alnot, P.8
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8
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33748630444
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As for the problem cited above: it is easier to have a polymer with high electron affinity if the band gap is small
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As for the problem cited above: it is easier to have a polymer with high electron affinity if the band gap is small.
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0000609611
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Hagler, T. W.; Pakbaz, K.; Voss, K. F.; Heeger, A. J. Phys. Rev. B 1991, 44, 8652.
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Chung, T.-C.1
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10944221105
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Katrizky, A. R., Ed.; Academic: New York
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Mason, S. F. In Physical Methods in Heterocyclic Chemistry; Katrizky, A. R., Ed.; Academic: New York, 1963; Vol II, p 1.
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Mason, S.F.1
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13
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33748592500
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Using Hückel terminology, there will be a set of β's which describe the hybridization interaction between each pair of levels
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Using Hückel terminology, there will be a set of β's which describe the hybridization interaction between each pair of levels.
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16
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0000434536
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Havinga, E. E.; ten Hoeve, W.; Wijnberg, H. Polym. Bull. 1992, 29, 119;
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Synth. Met. 1993, 55-57, 299.
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33748621409
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Aliphatic groups such as the methyl bridges in the five-membered rings in 2 do not contribute directly to the π states and are unimportant in discussing the electronic structure around the band gap of the polymer
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Aliphatic groups such as the methyl bridges in the five-membered rings in 2 do not contribute directly to the π states and are unimportant in discussing the electronic structure around the band gap of the polymer.
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24
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0002852185
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Heeger, A. J.; Kivelson, S.; Schrieffer, J. R.; Su, W.-P. Rev. Mod. Phys. 1988, 60, 781.
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0003716563
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QCPE 455; Quantum Chemistry Program Exchange: Indiana University, Bloomington, IN
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Program obtained from: Stewart, J. P. P. MOPAC (V6.0); A General Molecular Orbital Package, QCPE 455; Quantum Chemistry Program Exchange: Indiana University, Bloomington, IN.
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MOPAC (V6.0); A General Molecular Orbital Package
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Stewart, J.P.P.1
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0001172461
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The C-O bond length could in principle be improved by optimizing the oxygen pseudopotential. Cf.: Laasonen, K.; Car, R.; Lee, C.; Vanderbilt, D. Phys. Rev. B 1991, 43, 6796.
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Brédas, J.-L.; Quattrocchi, C.; Libert, J.; MacDiarmid, A. G.; Ginder, J. M.; Epstein, A. J. Phys. Rev. B 1991, 44, 6002.
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35
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33748908357
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Godby, R. W.; Schlüter, M.; Sham, L. J. Phys. Rev. B 1988, 37, 10159.
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36
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0001160675
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Baraff, G. A.; Schlüter, M. Phys. Rev. B 1984, 30, 3460. This procedure is often referred to as a scissors operator, because one can think of it as cutting the band structure through the band gap and moving the conduction bands rigidly upward.
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Phys. Rev. B
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Baraff, G.A.1
Schlüter, M.2
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40
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0345070133
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Causa, M.; Dovesi, R.; Pisani, C.; Roetti, C.; Saunders, V. R. J. Chem. Phys. 1988, 88, 3196.
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Saunders, V.R.5
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41
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0347872312
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Even for the dye molecule 8, this procedure works reasonably well. Dividing the calculated LDA HOMO/LUMO gap of 1.2 eV by 0.6 gives a fair agreement with experiment. See e.g.: Dirk, C. W.; et al. J. Am. Chem. Soc. 1995, 117, 2214.
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J. Am. Chem. Soc.
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Dirk, C.W.1
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42
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33748612121
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Bear in mind that the out-of-plane torsion in polymer 5 increases the band gap as compared to completely planar structures; cf. ref 31
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Bear in mind that the out-of-plane torsion in polymer 5 increases the band gap as compared to completely planar structures; cf. ref 31.
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43
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33748624552
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In some cases we find in our calculation oxygen lone-pair-like n levels close to HOPO π level; cf. ref 21. In order to avoid complicating the discussion, we will only discuss states of π symmetry. Since the n-π* transition is forbidden, n states will not appear in the optical spectrum at a low energy. However, they could in principle act as trap states upon p-doping of the polymer
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In some cases we find in our calculation oxygen lone-pair-like n levels close to HOPO π level; cf. ref 21. In order to avoid complicating the discussion, we will only discuss states of π symmetry. Since the n-π* transition is forbidden, n states will not appear in the optical spectrum at a low energy. However, they could in principle act as trap states upon p-doping of the polymer.
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44
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2842578995
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and references therein
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For the helical symmetry group, see e.g.: Springborg, M. Int. Rev. Phys. Chem. 1993, 12, 241 and references therein.
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Int. Rev. Phys. Chem.
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Springborg, M.1
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45
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85087191530
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x. The gap is then found at K = 0
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x. The gap is then found at K = 0.
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46
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85087190296
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H is simply that the amplitude of the LUMO on the carbon atom of the fragment coupled to the nitrogen atom is much larger than of the HOMO
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H is simply that the amplitude of the LUMO on the carbon atom of the fragment coupled to the nitrogen atom is much larger than of the HOMO.
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47
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33748597613
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In ref 16 it was speculated that the small band gaps of squaraine polymers could be the results of donor/acceptor properties of the individual fragments. That type of reasoning relies on charge transfer between the energy levels of the fragments, but one has to assume that the fragment states are not completely rehybridized (and thus remixed and reordered) in the polymer. However, as we have shown here, such hybridization effects are very large here and mask the charge transfer effects. Therefore, it seems that the donor/acceptor concept is not the key to understanding the electronic structure
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In ref 16 it was speculated that the small band gaps of squaraine polymers could be the results of donor/acceptor properties of the individual fragments. That type of reasoning relies on charge transfer between the energy levels of the fragments, but one has to assume that the fragment states are not completely rehybridized (and thus remixed and reordered) in the polymer. However, as we have shown here, such hybridization effects are very large here and mask the charge transfer effects. Therefore, it seems that the donor/acceptor concept is not the key to understanding the electronic structure.
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