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Band-gap calculations for squarelene-based polymers
Synthetic
ELSEVIER
Metals 85 (1997)
1153-l 154
Band-gap calculations for squarelene-based polymers Xiaofeng
Duan”, Ryoichi Kawaib, Alan T. Yeates and Douglas S. Dudi? “Systran Corporation, Dayton, OH 45432 bDepartment of Physics, University of Alabama, Birmingham, AL 35294 %L/MLBP, Wright-Patterson AFB, OH45433 USA
----------------------------------------------------------------------------------Abstract The electronic structures and band-gaps, modeled as the energy difference between ground singlet state and excited triplet state, for a series of oligomers of a polymer based on squarelene and fused thiophenes were investigated. AM1 and PM3 semi-empirical, Extended Htickel Theory (ETH), Hartree-Fock (HF) and second-order Moller-Plesset perturbation (MP2) ab initio, numerical atomic orbital basis set density functional theory (DFT) and ab initio molecular dynamics (AIMD) calculations are employed. The results indicate that a narrow gap less than 0.5 eV could be reached in a long polymer . Keywords:
Ab initio quantum chemical methods and calculations; synthesis; Low-bandgap conjugated polymers ___-____________------------------------------------------------------------------I. INTRODUCTION
Conjugated organic polymers, which are more like metals in their intrinsic electrical properties than any previously known polymers, combine important electronic and optical properties of semi-conductors and metals with the attractive mechanical properties and processing advantages of polymers, Designing new n-conjugated polymers with very small band gaps that exhibit intrinsic conductivities has attracted many experimentalle6 and theoretica17-12 efforts. The intrinsic electronic and optical properties of a material is governed by the band gap and therefore it is essential in successfully designing such polymers to understand the evolution of the band gaps of conjugated polymers in connection with their chemical structures. The most studied conjugated polymers include polythiophene, poly-aniline, poly-phenylene-vinylene, polypyrrole, polyacetylene and their derivatives. Most recently, a new class of polymers incorporating squaric acid has attracted strong interest. Poly-squaraine is the representative of the class and it is reportedI that its band gap is as small as 0.5 eV. In poly-squaraine there exist alternate electron-accepting (the squaraine moiety) and electron-donating (the nitrogen containing moiety) groups. It has been suggested that this alternating pattern causes a broadening of the energy bands which, in turn, leads to a narrow band gap. Recently, a new polymer based on the squarelene and fused thiophene (thienothiophene, TTN) rings (as shown in figure 1) has been synthesized14. In this polymer, the two fused thiophene rings act as the electron donor and a strong n-conjugated electron structure exist , therefore a narrow band gap is predicted. In this project, we investigate the electronic structures and band-gaps as modeled by the energetic difference between 03796779197617.00
0 1997 Ekevier
PII SO379-6779(96)04308-l
Science S.A All rights reserved
Semi-empirical
models and model calculations;
Heterocycle
ground singlet state and excited triplet state of a series of oligomers of the polymer. AM1 and PM3 semi-empirical, Extended Htickel Theory (EHT), Hartree-Fock (HF) and secondorder Moller-Plesset perturbation (MP2) ab initio using SBK double zeta valence basis set with effective core potentials, numerical atomic orbital basis set density functional theory (DFT) calculations and calculations planewave local (spin) density functional based ab initio molecular dynamics calculations are employed to conduct the research.
Fig. 1. Squarelene and fused thiophene based polymer.
II.
RESULTS
1. Optimized
AND
DISCUSSION
Geometries
The structural parameters for the monomer of the polymer calculated from three methods are displayed in figure 2. The three methods give similar results. Although, no constraints were imposed, the optimized structure is planar and has a mirror symmetry through the OCCO plane of the squarelene. The conformation with one TTN ring rotated 90” to the rest of the molecule is about 10 kcal/mol higher in energy at the AM1 level than the minimum energy structure. This indicates a ‘planar and rigid polymer of this type and are consistent with other theoretical workst5-16. The lengths of C-C bonds in squarelene are all in the range of 1.46 - 1.48 A. The sums of Mulliken charges on the group of squarelene and on the
X. Duan etal. /SptheticMetals
Fig. 2. Optimized
85 (1997) 1153-1154
monomer structure with different methods: Bold: RHF/SBK,
group of fused thiophene rings (excluding end CH, group) are -2.064 and 0.665 respectively and therefore demonstrate the donor/acceptor character of this molecule. The structures of the polymer containing repeat units from n=2 to n=4 were optimized based on the monomer structure at the AM1 level. These structures are consistent with that of the monomer with expected differences from end effect. For example, the C-C bond which links squarelene and fused thiophene rings is about 0.018, longer in the middle unit than that in the side unit. In the structure of ‘ITN rings, the largest variance is about 0.058, for a C-S bond, 2. Electronic Structure and Band Gap Based on the AM1 structures of the oligomers, we calculated the electronic structures and energetics for singlet and triplet states using several methods: AMl, PM3, EHT, ab initio HF, ab initio MP2, numerical basis set LDA and AIMD. With MP2 and AIMD method, because of their computational intensity, only energetics of monomers and dimmers were calculated,
-lot.,,,..,,,,,,,,,,,,,,,,,i 0.2 0.4 0.6
0.8
1
1.2
l/n Fig. 3. Energy Gaps vs. repeat unit of the polymer calculated with different methods. The singlet-triplet energy difference vs. reciprocal of the number of the repeat unit n is shown in figure 3 for all methods employed. The best values, from the ab initio RHF and DFT methods, extrapolate to a polymeric band-gap of - 0.2-0.3 eV. The semi-empirical AM1 and PM3 methods actually predict ground state triplets for these molecules, but we believe this is problematic to either (a) the parametrization or (b) the triplet computational methodology. This point is under further investigation, but underscores the importance of using first principle methods, such as the ab initio HF, where possible to (in)validate parametrized approaches. Surprisingly, the
Italic:
LDA; Plain: AMI.
simplest method, EHT, gives a result close to that from much more sophisticated method.
III.
CONCLUSION
The band-gap calculated for the present polymer is among the lowest known. Preliminary efforts to prepare this material have produced products which have not yield readily characterizable film14. This is consistent with the high rigidity calculated for this molecule. Accordingly, material with solubilizing side groups are in preparation. The experimental results do suggest a low optical transition energy. A number OF related polymers are also being investigated theoretically.
Reference 1. W. C. Chen and S. A. Jenekhe, Macromolecules 28, 454, 465, 1995 2. J. Ohshita, D. Kanaya, M. Ishikawa, T. Koieke and T. Yamanaka, Macromolecules 24, 2106, 1991. 3. E. E. Havinga, W. Hoeve and H. Wynber, Synth. Met. 55, 299, 1993. 4. M. Pomerantz, J. Wang, S. Seong, K. P. Starkey, L. Nguyen and D. S. Marynick, Macromolecules 27, 7478, 1994. 5. M. Hanak, K. M. Mangold, U. Rohrig and C. MaichleMossmer, Synth. Met. 60, 199, 1993. 6. A. 0. Patil and F. Wudle, Macromolecules 21, 540, 1988. 7. J. M. Toussaint and J. L. Bredas, J. Chem. Phys. 94, 8122, 1991. 8. S. Y. Hong and D. S. Marynick, Macromolecules 25, 4652, 1992. 9. C. Quattrocchi, R. Lazzaroni, J. L. Bredas, R. Zamboni and C. Taliani, Macromolecules 26, 1260, 1993. 10. P. Otto and J. Ladik, Synth. Met. 36, 327, 1990. 11. K. Tanaka, S. Wang, and T. Yamabe, Synth. Met. 39, 225, 1990. 12. S. Y. Hong, S. J. Kwon, S. C. Kim and D. S. Marynick, Synth. Met. 69, 701, 1995. 13. E. E. Havinga, W. ten Hoeve and H. Wijnberg, Polym. Bull. (Berlin) 29, 119, 1992. 14. M. Dotrong, R. McKellar and R. C. Evers, unpublished results. 15. A. J. W. Tol, J. Chem. Phys. 100,8463, 1994. 16. G. Brocks, J. Chem. Phys. 102, 2522, 1995.
ELSEVIER
Metals 85 (1997)
1153-l 154
Band-gap calculations for squarelene-based polymers Xiaofeng
Duan”, Ryoichi Kawaib, Alan T. Yeates and Douglas S. Dudi? “Systran Corporation, Dayton, OH 45432 bDepartment of Physics, University of Alabama, Birmingham, AL 35294 %L/MLBP, Wright-Patterson AFB, OH45433 USA
----------------------------------------------------------------------------------Abstract The electronic structures and band-gaps, modeled as the energy difference between ground singlet state and excited triplet state, for a series of oligomers of a polymer based on squarelene and fused thiophenes were investigated. AM1 and PM3 semi-empirical, Extended Htickel Theory (ETH), Hartree-Fock (HF) and second-order Moller-Plesset perturbation (MP2) ab initio, numerical atomic orbital basis set density functional theory (DFT) and ab initio molecular dynamics (AIMD) calculations are employed. The results indicate that a narrow gap less than 0.5 eV could be reached in a long polymer . Keywords:
Ab initio quantum chemical methods and calculations; synthesis; Low-bandgap conjugated polymers ___-____________------------------------------------------------------------------I. INTRODUCTION
Conjugated organic polymers, which are more like metals in their intrinsic electrical properties than any previously known polymers, combine important electronic and optical properties of semi-conductors and metals with the attractive mechanical properties and processing advantages of polymers, Designing new n-conjugated polymers with very small band gaps that exhibit intrinsic conductivities has attracted many experimentalle6 and theoretica17-12 efforts. The intrinsic electronic and optical properties of a material is governed by the band gap and therefore it is essential in successfully designing such polymers to understand the evolution of the band gaps of conjugated polymers in connection with their chemical structures. The most studied conjugated polymers include polythiophene, poly-aniline, poly-phenylene-vinylene, polypyrrole, polyacetylene and their derivatives. Most recently, a new class of polymers incorporating squaric acid has attracted strong interest. Poly-squaraine is the representative of the class and it is reportedI that its band gap is as small as 0.5 eV. In poly-squaraine there exist alternate electron-accepting (the squaraine moiety) and electron-donating (the nitrogen containing moiety) groups. It has been suggested that this alternating pattern causes a broadening of the energy bands which, in turn, leads to a narrow band gap. Recently, a new polymer based on the squarelene and fused thiophene (thienothiophene, TTN) rings (as shown in figure 1) has been synthesized14. In this polymer, the two fused thiophene rings act as the electron donor and a strong n-conjugated electron structure exist , therefore a narrow band gap is predicted. In this project, we investigate the electronic structures and band-gaps as modeled by the energetic difference between 03796779197617.00
0 1997 Ekevier
PII SO379-6779(96)04308-l
Science S.A All rights reserved
Semi-empirical
models and model calculations;
Heterocycle
ground singlet state and excited triplet state of a series of oligomers of the polymer. AM1 and PM3 semi-empirical, Extended Htickel Theory (EHT), Hartree-Fock (HF) and secondorder Moller-Plesset perturbation (MP2) ab initio using SBK double zeta valence basis set with effective core potentials, numerical atomic orbital basis set density functional theory (DFT) calculations and calculations planewave local (spin) density functional based ab initio molecular dynamics calculations are employed to conduct the research.
Fig. 1. Squarelene and fused thiophene based polymer.
II.
RESULTS
1. Optimized
AND
DISCUSSION
Geometries
The structural parameters for the monomer of the polymer calculated from three methods are displayed in figure 2. The three methods give similar results. Although, no constraints were imposed, the optimized structure is planar and has a mirror symmetry through the OCCO plane of the squarelene. The conformation with one TTN ring rotated 90” to the rest of the molecule is about 10 kcal/mol higher in energy at the AM1 level than the minimum energy structure. This indicates a ‘planar and rigid polymer of this type and are consistent with other theoretical workst5-16. The lengths of C-C bonds in squarelene are all in the range of 1.46 - 1.48 A. The sums of Mulliken charges on the group of squarelene and on the
X. Duan etal. /SptheticMetals
Fig. 2. Optimized
85 (1997) 1153-1154
monomer structure with different methods: Bold: RHF/SBK,
group of fused thiophene rings (excluding end CH, group) are -2.064 and 0.665 respectively and therefore demonstrate the donor/acceptor character of this molecule. The structures of the polymer containing repeat units from n=2 to n=4 were optimized based on the monomer structure at the AM1 level. These structures are consistent with that of the monomer with expected differences from end effect. For example, the C-C bond which links squarelene and fused thiophene rings is about 0.018, longer in the middle unit than that in the side unit. In the structure of ‘ITN rings, the largest variance is about 0.058, for a C-S bond, 2. Electronic Structure and Band Gap Based on the AM1 structures of the oligomers, we calculated the electronic structures and energetics for singlet and triplet states using several methods: AMl, PM3, EHT, ab initio HF, ab initio MP2, numerical basis set LDA and AIMD. With MP2 and AIMD method, because of their computational intensity, only energetics of monomers and dimmers were calculated,
-lot.,,,..,,,,,,,,,,,,,,,,,i 0.2 0.4 0.6
0.8
1
1.2
l/n Fig. 3. Energy Gaps vs. repeat unit of the polymer calculated with different methods. The singlet-triplet energy difference vs. reciprocal of the number of the repeat unit n is shown in figure 3 for all methods employed. The best values, from the ab initio RHF and DFT methods, extrapolate to a polymeric band-gap of - 0.2-0.3 eV. The semi-empirical AM1 and PM3 methods actually predict ground state triplets for these molecules, but we believe this is problematic to either (a) the parametrization or (b) the triplet computational methodology. This point is under further investigation, but underscores the importance of using first principle methods, such as the ab initio HF, where possible to (in)validate parametrized approaches. Surprisingly, the
Italic:
LDA; Plain: AMI.
simplest method, EHT, gives a result close to that from much more sophisticated method.
III.
CONCLUSION
The band-gap calculated for the present polymer is among the lowest known. Preliminary efforts to prepare this material have produced products which have not yield readily characterizable film14. This is consistent with the high rigidity calculated for this molecule. Accordingly, material with solubilizing side groups are in preparation. The experimental results do suggest a low optical transition energy. A number OF related polymers are also being investigated theoretically.
Reference 1. W. C. Chen and S. A. Jenekhe, Macromolecules 28, 454, 465, 1995 2. J. Ohshita, D. Kanaya, M. Ishikawa, T. Koieke and T. Yamanaka, Macromolecules 24, 2106, 1991. 3. E. E. Havinga, W. Hoeve and H. Wynber, Synth. Met. 55, 299, 1993. 4. M. Pomerantz, J. Wang, S. Seong, K. P. Starkey, L. Nguyen and D. S. Marynick, Macromolecules 27, 7478, 1994. 5. M. Hanak, K. M. Mangold, U. Rohrig and C. MaichleMossmer, Synth. Met. 60, 199, 1993. 6. A. 0. Patil and F. Wudle, Macromolecules 21, 540, 1988. 7. J. M. Toussaint and J. L. Bredas, J. Chem. Phys. 94, 8122, 1991. 8. S. Y. Hong and D. S. Marynick, Macromolecules 25, 4652, 1992. 9. C. Quattrocchi, R. Lazzaroni, J. L. Bredas, R. Zamboni and C. Taliani, Macromolecules 26, 1260, 1993. 10. P. Otto and J. Ladik, Synth. Met. 36, 327, 1990. 11. K. Tanaka, S. Wang, and T. Yamabe, Synth. Met. 39, 225, 1990. 12. S. Y. Hong, S. J. Kwon, S. C. Kim and D. S. Marynick, Synth. Met. 69, 701, 1995. 13. E. E. Havinga, W. ten Hoeve and H. Wijnberg, Polym. Bull. (Berlin) 29, 119, 1992. 14. M. Dotrong, R. McKellar and R. C. Evers, unpublished results. 15. A. J. W. Tol, J. Chem. Phys. 100,8463, 1994. 16. G. Brocks, J. Chem. Phys. 102, 2522, 1995.