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Correlated ab initio methods can not be used in this study because they can be applied only to relatively small molecules, and polaron- bipolaron equilibrium is not observed for small systems (such as 8T2, The DFT and HF levels of theory are the only practical options available for studying doped oligothiophenes of sufficient length to enable the transition from bipolaron to polaron-pair to be observed. The HF level is inapplicable to the study of oligothiophene dications (as well as other charged conjugated systems) due to the huge spin contamination obtained if a pure HF wave function is used.19
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We have tested the applicability of the broken-symmetry B3LYP/6-31G(d) level to appropriately describe oligothiophene dications by comparing it to CASSCF results.21 Both methods agreed qualitatively on the relative energies of singlet and triplet oligothiophene dications and on the electronic structure (bipolaron versus polaron pair) of the dications
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21 Both methods agreed qualitatively on the relative energies of singlet and triplet oligothiophene dications and on the electronic structure (bipolaron versus polaron pair) of the dications.
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The position of counterion in-plane with the oligothiophene chains was found to be true minima according to frequency analysis of 8T+Cl 3, see Supporting Information
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Wave function instability can be expected for low HOMO-LUMO gap systems as the number of conjugated double bonds increases. Wave function instability has been observed previously for bare oligothíophene dications. 18,21 Similarly, RHF-UHF wave function instability has been predicted for other types of long conjugated systems, such as oligoacenes starting from hexacene at B3LYP/6-31Gd, see Bendikov, M, Duong, H. M, Starkey, K, Houk, K. N, Carter, E. A, Wudl, F. J. Am. Chem. Soc. 2004, 126, 7416
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18,21 Similarly, RHF-UHF wave function instability has been predicted for other types of long conjugated systems, such as oligoacenes starting from hexacene at B3LYP/6-31G(d); see Bendikov, M.; Duong, H. M.; Starkey, K.; Houk, K. N.; Carter, E. A.; Wudl, F. J. Am. Chem. Soc. 2004, 126, 7416.
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81
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53549100272
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When the C1-C2 and C3-C4 bonds of a thiophene ring (Scheme 1) are shorter than the C2-C 3 bond (so producing a A-shaped pattern in the sets of three linked data points shown in Figure 3, the ring is considered aromatic. By contrast, when the C1-C2 and C3-C4 bonds of a thiophene ring are longer than the C2-C3 bond (thus, producing a V-shaped pattern in the sets of three linked data points shown the Figure 3, the ring is considered quinoid Scheme 1
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3 bond (thus, producing a V-shaped pattern in the sets of three linked data points shown the Figure 3), the ring is considered quinoid (Scheme 1).
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82
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53549085507
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BLA patterns for other isomers are available in Supporting Information
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BLA patterns for other isomers are available in Supporting Information.
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83
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53549132889
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2 are presented in Supporting Information.
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2 are presented in Supporting Information.
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84
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53549102007
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The fact that α and β orbitals are mirror images of each other resembles frontier orbital picture of long oligoacenes that correspond to disjoint diradicals; see ref 43 and references therein
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The fact that α and β orbitals are mirror images of each other resembles frontier orbital picture of long oligoacenes that correspond to disjoint diradicals; see ref 43 and references therein.
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86
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0021160782
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(a) Kobayashi, M.; Chen, J.; Chung, T. C.; Moraes, F.; Heeger, A. J.; Wudl, F. Synth. Met. 1984, 9, 77.
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(1984)
Synth. Met
, vol.9
, pp. 77
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Kobayashi, M.1
Chen, J.2
Chung, T.C.3
Moraes, F.4
Heeger, A.J.5
Wudl, F.6
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87
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7244248982
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(b) Oztemiz, S.; Beaucage, G.; Ceylan, O.; Mark, H. B. J. Solid State Electrochem 2004, 8, 928.
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(2004)
J. Solid State Electrochem
, vol.8
, pp. 928
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Oztemiz, S.1
Beaucage, G.2
Ceylan, O.3
Mark, H.B.4
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88
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53849132691
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in press DOI: 10.1002/chem.200701182
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Zade, S. S.; Bendikov, M. Chem. Eur. J. 2008, 14, in press (DOI: 10.1002/chem.200701182).
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(2008)
Chem. Eur. J
, vol.14
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Zade, S.S.1
Bendikov, M.2
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89
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53549131610
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(51 ) The shortest oligothiophene length at which a bipolaron will become unstable and dissociate into two polarons (a polaron-pair) will depend (and might even strongly depend) on the level of theory used (see Theoretical Methods and the discussion about charge distribution). However, it is clear that the bipolaron will be unstable and will dissociate into two polarons at some oligothiophene length.
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(51 ) The shortest oligothiophene length at which a bipolaron will become unstable and dissociate into two polarons (a polaron-pair) will depend (and might even strongly depend) on the level of theory used (see Theoretical Methods and the discussion about charge distribution). However, it is clear that the bipolaron will be unstable and will dissociate into two polarons at some oligothiophene length.
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90
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53549092833
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We note that the charge distribution pattern in oligothiophene cation radicals is significantly dependent on the amount of HF exchange used. Localization of charges is proportional to the amount of HF exchange with charge distribution very localized at the HF level and practically completely delocalized at pure DFT levels (Zade, S. S, Bendikov, M, unpublished. Similar conclusions were also drawn for oligo(phenylene vinylene) cation radicals; see Geskin, V. M, Grozema, F. C, Siebbeles, L. D. A, Bejonne, D, Brédas, J. L, Cornil, J. J. Phys. Chem. B 2005,109,20237, Although presently it is unclear which theoretical method reproduces the charge distribution partem correctly, it was also observed that for polyacetylene chains in the presence of counterions different levels of theory such as HF, MP2, and B3LYP provide similar bond length alternation and charge distribution patterns.25
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25
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91
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53549101742
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Unsurprisingly, extrapolation of eqs. 1 and 5 to infinite chain lengths results in an energetic degeneracy between the dication vs. two monocations and between divalent vs. two monovalent salts (Figure 5a).
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Unsurprisingly, extrapolation of eqs. 1 and 5 to infinite chain lengths results in an energetic degeneracy between the dication vs. two monocations and between divalent vs. two monovalent salts (Figure 5a).
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92
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53549130514
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Preliminary estimation of solvent effect on the electronic structure of divalent oligothiophene salts was performed using PCM approximation. Inclusion of solvent favor the polaron pair state over the bipolaron state even more strongly compared to gas phase calculations of divalent oligothiophene salts (Zamoshchik, N.; Salzner, U.; Bendikov, M., unpublished).
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Preliminary estimation of solvent effect on the electronic structure of divalent oligothiophene salts was performed using PCM approximation. Inclusion of solvent favor the polaron pair state over the bipolaron state even more strongly compared to gas phase calculations of divalent oligothiophene salts (Zamoshchik, N.; Salzner, U.; Bendikov, M., unpublished).
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