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Searching for low-band-gap conjugated polymers by LHS calculations
Synthetic Metals, 49-50 (1992) 537-542
537
Searching for low-band-gap conjugated polymers by LHS calculations J. Kiirti Department of Atomic Physics, R. E6tvSs University Budapest, Puskin ~5-7, H-1088 Budapest (Hungary) Institut fiir FestkOrperphysik der Universitdt Wien, Strudlhofgasse 4, A-lOP0 Vienna (Austria) P. R. Surj~n Institute of Physics, Quantum Theory Group, Technical University of Budapest, Budapest (Hungary) Laboratory f o r Theoretical Chemistry R. EStvSs University Budapest, P.O.B. 32, H-1518 Budapest 112 (Hungary)
M. Kertesz Department of Chemistry, Georgetown University, Washington, DC 20057 (USA)
Abstract Semiempirical calculations on large cluster models of conjugated polymers have been done using a Longuet-Higgins and Salem (LHS) type model Hamiltonian. The model is tested for many conjugated polymers containing heteroatoms, obtaining good agreement with the results of more sophisticated methods and experimental results concerning the bond lengths and the electronic structure. Our calculations predict band gaps as low as 0.7 eV and 0.5 eV for poly(bi-isothianaphthene--methine) (PBITNM) and poly(isonaphthothiophene-thiophene) (PINTT), respectively.
Much a t t e n t i o n has b e e n paid r e c e n t l y to the t h e o r e t i c a l and e x p e r i m e n t a l investigation o f low-band-gap c o n j u g a t e d p o l y m e r s [ 1 - 1 0 ] . The interest in s e a r c h i n g for s u c h p o l y m e r s is stimulated b y the significant intrinsic conductivity and g o o d non-linear optical p r o p e r t i e s due to the small gap o f t h e s e systems. A m o n g c o n j u g a t e d p o l y m e r s , p o l y ( i s o t h i a n a p h t h e n e ) (PITN) is k n o w n so far to have the smallest e n e r g y gap ( E g - - 1 . 0 eV) f o u n d b o t h e x p e r i m e n t a l l y [3] and t h e o r e t i c a l l y [5 I. F o r a r e l a t e d system, p o l y t h i o p h e n e (PT), it was o b s e r v e d t h a t the e n e r g y gap c o u l d b e l o w e r e d significantly b y inserting additional CH units b e t w e e n t h e m o n o m e r s (poly(bit h i o p h e n e - m e t h i n e ) , PBTM); the gap o f PT is 2.1 eV e x p e r i m e n t a l l y [11] and 1.8 eV t h e o r e t i c a l l y [5], while the t h e o r e t i c a l e s t i m a t i o n for PBTM is 1.2 eV [61. A c c o r d i n g to the orbital i n t e r p r e t a t i o n s [5, 6, 10], the small gap o f PITN is due t o the c o m b i n e d effects o f the p e r t u r b a t i o n s c a u s e d b y h e t e r o a t o m s , side rings and C--C b o n d relaxations. In the case of PBTM a c u r i o u s c a n c e l l a t i o n o f h e t e r o a t o m i c p e r t u r b a t i o n s o c c u r s and, t h e r e f o r e , the gap r e d u c t i o n relative to p o l y a c e t y l e n e (PA) is due to the slight r e d u c t i o n
0379-6779/92/$5.00
© 1992- Elsevier Sequoia. All rights reserved
538
of the bond length alternation [6a] of the C - C - C - C backbone, as compared to PA. Since PITN has a lower gap than PT, it appears to be a straightforward idea to modify the structure of the former by introducing the methine linkage. The resulting polymer, poly(bi-isothianaphthene-methine), PBITNM, is shown schematically in Fig. 1. Polymers consisting of cyclic monomers can have aromatic or quinoid structure depending on the sign of the alternation between the inter-ring and the neighbouring intra-ring bond lengths. It was pointed out that in going from the aromatic to the quinoid structure, the gap v a l u e should have a minimum [1, 2]. For example, PT has aromatic structure with E ¢ = 2 eV, PITN has quinoid character with Eg = 1 eV and poly(isonaphthothiophene) (PINT) has more quinoid character with E g = 1.4 eV. The question arises of what happens in the case of the copolymer poly(isonaphthothiophene-thiophene) (PINTT) (see Fig. 2), where there is a 'quinoid-aromatic competition' due to the different characters of the two subunits. We mention that copolymers of thiophene with several substituted paraphenylenes (which axe not small-gap polymers) have been synthesized recently [12]. The two polymers investigated in this study have not yet been synthesized, but the synthesis of similar polymers [13a,b] and oligomers [13c] has been reported recently. We have done semiempirical calculations on the band structure of PBITNM and PINTT. The theoretical method we selected for this purpose is based 1,436
1.411
1.436
Fig. 1. Schematic structure and optimized bond lengths of poly(bi-isothianaphthene-methine) (PBITNM), calculated by the LHS method. 1.442
1415 1441
1.441
Fig. 2. Schematic structure and optimized bond lengths of poly(isonaphthothiophene--thiophene) (PIN'IW), calculated by the LHS method.
539
on the model of Longuet-Higgins and Salem (LHS) [14], which corresponds physically to an extended version of the SSH model [15]. In the LHS method, only the 7r-electrons are considered explicitly in a tight-binding (Htickel) approximation, while the effects of the q-core are described by an empirical potential. The model is able to describe the effects of geometry changes on the 7r-electronic structure. Recently, we have reparametrized the LHS model and extended it to heteroatoms [ 16]. The method was shown to be sufficiently accurate in predicting energy-gap values for simple ~r-electron systems (see Table 1). We have calculated the optimized bond lengths and the energy levels. The calculations have been performed for clusters up to 19 (PBITNM) or 10 (PINTT) unit cells (189 and 175 atoms, respectively). Convergence was practically reached for the gap as a function of the chain length. It is remarkable that the band gap is only --0.7 eV for PBITNM and --0.5 eV for PINTT. At the band edges the density of states is quite high, and the one-electron states are fairly delocalized. The band structures of PBITNM and PINTT are rather complicated (see the energy-level diagram in Fig. 3), but the valence and conduction bands seem to be wide enough to contribute to a significant conductivity of the system. We have to note that there are several neglected effects which can increase the real energy gap: steric effects, which may cause non planarity, short conjugated segments due to crosslinks even if the system is planar, randomly coiled segments, etc. Last but not least, electron-electron interaction and correlation effects, neglected in the present study, may also influence the band gap. Nevertheless, the parametrization of our model has been quite successful for several related systems (see Table 1), which permits us to believe that the present estimation for the band gaps of PBITNM, 0.7 eV, and PINT]?, 0.5 eV, is not far from reality. Finally, we show a diagram (see Fig. 4) in which the energy gaps of several polymers, including those investigated in the present study (PBITNM, PINTT), are plotted against the corresponding bond-length alternations. Although the perturbing role of heteroatoms and side rings can strongly TABLE 1 Reliability of the LHS method for Eg (eV), together with the Eg values of PBITNM and PINTT, calculated by the LHS method Polymer
LHS
MNDO + EH
Experiment
(CH)~ PT PITN PINT PBTM PBITNM PINTT
1.50 1.97 1.00 1.37 1.04 0.69 0.54
1.53 1:83 1.16 1.50 1.21
1.4-1.6 [17] 2.1 [111 1.0 [31 1.4-1.5 [18]
aBasis of parametrization.
[6a] [10] [10] [10] [6a]
=/
(b)
(a)
I
L
Z:::-
~
.....
--;--
---.
=.
.
~ ....
.
.
.
.
.
.
.
.
.
.
.
.
.
~ . . . . . . . .
\0 I 0
O
Fig. 3. (a) Orbital e n e r g y d i a g r a m o f PBITNM, c a l c u l a t e d b y t h e LHS m e t h o d . ( T h e H O M O a n d LUMO e n e r g i e s a r e 0 . 0 7 eV a n d 0 . 7 6 eV, respectively.) (b) Orbital e n e r g y d i a g r a m o f PINTT, c a l c u l a t e d b y t h e LHS m e t h o d . ( T h e H O M O a n d L U M O e n e r g i e s a r e 0 . 1 7 eV a n d 0.71 eV, respectively).
-9
-10
-8
-9
-7
-'7
-8
-10
-6
-6
-5
-4
-4
-2
-1
0
1
-3
0
:\o
-.J
-3
-2
- 1 L~
0
1
2
3
4
2
6
0
7
6
5
8
7
10
s(~v)
8
9
10
s(~v)
O
O1
541 i
,
1.5
,
,
I
~,
,
PT
I
,
,
L
I
x(¢H) x PI TNM TM × ×PINT
PBTM × × PITN
xpBITNM .5
xpINTT
0
-J 0
i
I
.02
,
,
,
t
.04
I
~ J
t
I
,
,
.06
~
I
.08
,
,
rin
t
.1
.12
.14
dr Fig. 4. Corr__elation b e t w e e n energy gap (Eg) and bond alternation (dr), calculated by the LHS method. (dr is the average of Irout-rinl.)
influence the gap values, one can see from Fig. 4 that a clear correlation b e t ween the energy gap and bond alternation exists. The reason for this correlation should be related to the fact that the d r values in this diagram c o r r e s p o n d to the optimized g e o m e t r y for which the effects of heteroatoms and side rings are already taken into account. This question should be investigated in mor e detail. Acknowledgements
This work was s u p p o r t e d by grants OTKA 6 4 / 1 9 8 7 (Hungary), Fonds fiir Fbrderung der Wissenschaftlichen Forschung (Austria) and NSF (INT8912665) References
1 J. L. Br4das, S p r i n g e r Series i n Solid-State Sciences, Vol. 63, Springer, Berlin, 1985, p. 166. 2 J. L. Br6das, J. Chem. Phys., 82 ( 1 9 8 5 ) 3808. 3 M. Kobayashi, N. Colaneri, M. Boysel and A. J. Heeger, J. Chem. Phys., 82 (1985) 5717. 4 (a) A. S. Jenekhe, N a t u r e (London), 322 (1986) 345; (b) see, however, A. Q. Patti and F. Wudl, Macromolecules, 21 ( 1 9 8 8 ) 540. 5 Y. S. Lee a n d M. Kertesz, Int. J. Quant. Chem. Symp., 21 (1987) 163. 6 (a) M. Kertesz and Y. S. Lee, J. Phys. Chem., 91 (1987) 2 6 9 0 ; Co) J. M. Toussaint, B. Themans, J. M. Andr~ and J. L. Br6das, Synth. Met., 28 (1989) C205.
542 7 8 9 10 11 12 13
14 15 16 17 18
Y. S. Lee and M. Kertesz, J. Chem. Phys., 88 (1988) 2609. M. Kertesz and Y. S. Lee, Sy'nth. Met., 28 (1989) C545. W. Wu and S. Kivelson, Synth. Met., 28 (1989) D575. Y. S. Lee, M. Kert~sz and R. L. Elsenbaumer, Chem. Mater., 2 (1990) 526. T. C. Chung, J. H. Kaufman, A. J. Heeger and F. Wudl, Phys. Rev. B, 30 (1984) 702. J. R. Reynolds, J. P. Ruiz, A. D. Child, K. Nayak and D. S. Marynick, Macromolecules, 24 (1991) 678. (a) R. Becker, G. B15chl and H. Br~unling, in J. L. Br~das and R. R. Chance (eds.), Conjugated Polymeric Materials, Kluwer, Dordrecht, 1990, p. 133; (b) H. Br~iunling, G. B15chl and R. Becket, Synth. Met., 41-43 (1991) 1539; (c) M. Hanack, Chem. Ber., in press. H. C. Longuet-Higgins and L. Salem, Proc. R. Soc. London, Ser. A, 251 (1959) 172. W. P. Su, J. R. Schrieffer and A. J. Heeger, Phys. Rev. B, 22 (1980) 2099. J. Kiirti and P. R. Surjfin, Springer Series in Solid-State Sciences, Vol. 91, Springer, Berlin, 1989, p. 69. C. R. Fincher Jr., D. L. Peebles, A. J. Heeger, M. A. Druy, Y. Matsumara, A. G. MacDiarmid, H. Shirakawa and S. Ikeda, Solid State Commun., 27 (1978) 489. Y. Ikenoue, Synth. Met., 35 (1990) 263.
537
Searching for low-band-gap conjugated polymers by LHS calculations J. Kiirti Department of Atomic Physics, R. E6tvSs University Budapest, Puskin ~5-7, H-1088 Budapest (Hungary) Institut fiir FestkOrperphysik der Universitdt Wien, Strudlhofgasse 4, A-lOP0 Vienna (Austria) P. R. Surj~n Institute of Physics, Quantum Theory Group, Technical University of Budapest, Budapest (Hungary) Laboratory f o r Theoretical Chemistry R. EStvSs University Budapest, P.O.B. 32, H-1518 Budapest 112 (Hungary)
M. Kertesz Department of Chemistry, Georgetown University, Washington, DC 20057 (USA)
Abstract Semiempirical calculations on large cluster models of conjugated polymers have been done using a Longuet-Higgins and Salem (LHS) type model Hamiltonian. The model is tested for many conjugated polymers containing heteroatoms, obtaining good agreement with the results of more sophisticated methods and experimental results concerning the bond lengths and the electronic structure. Our calculations predict band gaps as low as 0.7 eV and 0.5 eV for poly(bi-isothianaphthene--methine) (PBITNM) and poly(isonaphthothiophene-thiophene) (PINTT), respectively.
Much a t t e n t i o n has b e e n paid r e c e n t l y to the t h e o r e t i c a l and e x p e r i m e n t a l investigation o f low-band-gap c o n j u g a t e d p o l y m e r s [ 1 - 1 0 ] . The interest in s e a r c h i n g for s u c h p o l y m e r s is stimulated b y the significant intrinsic conductivity and g o o d non-linear optical p r o p e r t i e s due to the small gap o f t h e s e systems. A m o n g c o n j u g a t e d p o l y m e r s , p o l y ( i s o t h i a n a p h t h e n e ) (PITN) is k n o w n so far to have the smallest e n e r g y gap ( E g - - 1 . 0 eV) f o u n d b o t h e x p e r i m e n t a l l y [3] and t h e o r e t i c a l l y [5 I. F o r a r e l a t e d system, p o l y t h i o p h e n e (PT), it was o b s e r v e d t h a t the e n e r g y gap c o u l d b e l o w e r e d significantly b y inserting additional CH units b e t w e e n t h e m o n o m e r s (poly(bit h i o p h e n e - m e t h i n e ) , PBTM); the gap o f PT is 2.1 eV e x p e r i m e n t a l l y [11] and 1.8 eV t h e o r e t i c a l l y [5], while the t h e o r e t i c a l e s t i m a t i o n for PBTM is 1.2 eV [61. A c c o r d i n g to the orbital i n t e r p r e t a t i o n s [5, 6, 10], the small gap o f PITN is due t o the c o m b i n e d effects o f the p e r t u r b a t i o n s c a u s e d b y h e t e r o a t o m s , side rings and C--C b o n d relaxations. In the case of PBTM a c u r i o u s c a n c e l l a t i o n o f h e t e r o a t o m i c p e r t u r b a t i o n s o c c u r s and, t h e r e f o r e , the gap r e d u c t i o n relative to p o l y a c e t y l e n e (PA) is due to the slight r e d u c t i o n
0379-6779/92/$5.00
© 1992- Elsevier Sequoia. All rights reserved
538
of the bond length alternation [6a] of the C - C - C - C backbone, as compared to PA. Since PITN has a lower gap than PT, it appears to be a straightforward idea to modify the structure of the former by introducing the methine linkage. The resulting polymer, poly(bi-isothianaphthene-methine), PBITNM, is shown schematically in Fig. 1. Polymers consisting of cyclic monomers can have aromatic or quinoid structure depending on the sign of the alternation between the inter-ring and the neighbouring intra-ring bond lengths. It was pointed out that in going from the aromatic to the quinoid structure, the gap v a l u e should have a minimum [1, 2]. For example, PT has aromatic structure with E ¢ = 2 eV, PITN has quinoid character with Eg = 1 eV and poly(isonaphthothiophene) (PINT) has more quinoid character with E g = 1.4 eV. The question arises of what happens in the case of the copolymer poly(isonaphthothiophene-thiophene) (PINTT) (see Fig. 2), where there is a 'quinoid-aromatic competition' due to the different characters of the two subunits. We mention that copolymers of thiophene with several substituted paraphenylenes (which axe not small-gap polymers) have been synthesized recently [12]. The two polymers investigated in this study have not yet been synthesized, but the synthesis of similar polymers [13a,b] and oligomers [13c] has been reported recently. We have done semiempirical calculations on the band structure of PBITNM and PINTT. The theoretical method we selected for this purpose is based 1,436
1.411
1.436
Fig. 1. Schematic structure and optimized bond lengths of poly(bi-isothianaphthene-methine) (PBITNM), calculated by the LHS method. 1.442
1415 1441
1.441
Fig. 2. Schematic structure and optimized bond lengths of poly(isonaphthothiophene--thiophene) (PIN'IW), calculated by the LHS method.
539
on the model of Longuet-Higgins and Salem (LHS) [14], which corresponds physically to an extended version of the SSH model [15]. In the LHS method, only the 7r-electrons are considered explicitly in a tight-binding (Htickel) approximation, while the effects of the q-core are described by an empirical potential. The model is able to describe the effects of geometry changes on the 7r-electronic structure. Recently, we have reparametrized the LHS model and extended it to heteroatoms [ 16]. The method was shown to be sufficiently accurate in predicting energy-gap values for simple ~r-electron systems (see Table 1). We have calculated the optimized bond lengths and the energy levels. The calculations have been performed for clusters up to 19 (PBITNM) or 10 (PINTT) unit cells (189 and 175 atoms, respectively). Convergence was practically reached for the gap as a function of the chain length. It is remarkable that the band gap is only --0.7 eV for PBITNM and --0.5 eV for PINTT. At the band edges the density of states is quite high, and the one-electron states are fairly delocalized. The band structures of PBITNM and PINTT are rather complicated (see the energy-level diagram in Fig. 3), but the valence and conduction bands seem to be wide enough to contribute to a significant conductivity of the system. We have to note that there are several neglected effects which can increase the real energy gap: steric effects, which may cause non planarity, short conjugated segments due to crosslinks even if the system is planar, randomly coiled segments, etc. Last but not least, electron-electron interaction and correlation effects, neglected in the present study, may also influence the band gap. Nevertheless, the parametrization of our model has been quite successful for several related systems (see Table 1), which permits us to believe that the present estimation for the band gaps of PBITNM, 0.7 eV, and PINT]?, 0.5 eV, is not far from reality. Finally, we show a diagram (see Fig. 4) in which the energy gaps of several polymers, including those investigated in the present study (PBITNM, PINTT), are plotted against the corresponding bond-length alternations. Although the perturbing role of heteroatoms and side rings can strongly TABLE 1 Reliability of the LHS method for Eg (eV), together with the Eg values of PBITNM and PINTT, calculated by the LHS method Polymer
LHS
MNDO + EH
Experiment
(CH)~ PT PITN PINT PBTM PBITNM PINTT
1.50 1.97 1.00 1.37 1.04 0.69 0.54
1.53 1:83 1.16 1.50 1.21
1.4-1.6 [17] 2.1 [111 1.0 [31 1.4-1.5 [18]
aBasis of parametrization.
[6a] [10] [10] [10] [6a]
=/
(b)
(a)
I
L
Z:::-
~
.....
--;--
---.
=.
.
~ ....
.
.
.
.
.
.
.
.
.
.
.
.
.
~ . . . . . . . .
\0 I 0
O
Fig. 3. (a) Orbital e n e r g y d i a g r a m o f PBITNM, c a l c u l a t e d b y t h e LHS m e t h o d . ( T h e H O M O a n d LUMO e n e r g i e s a r e 0 . 0 7 eV a n d 0 . 7 6 eV, respectively.) (b) Orbital e n e r g y d i a g r a m o f PINTT, c a l c u l a t e d b y t h e LHS m e t h o d . ( T h e H O M O a n d L U M O e n e r g i e s a r e 0 . 1 7 eV a n d 0.71 eV, respectively).
-9
-10
-8
-9
-7
-'7
-8
-10
-6
-6
-5
-4
-4
-2
-1
0
1
-3
0
:\o
-.J
-3
-2
- 1 L~
0
1
2
3
4
2
6
0
7
6
5
8
7
10
s(~v)
8
9
10
s(~v)
O
O1
541 i
,
1.5
,
,
I
~,
,
PT
I
,
,
L
I
x(¢H) x PI TNM TM × ×PINT
PBTM × × PITN
xpBITNM .5
xpINTT
0
-J 0
i
I
.02
,
,
,
t
.04
I
~ J
t
I
,
,
.06
~
I
.08
,
,
rin
t
.1
.12
.14
dr Fig. 4. Corr__elation b e t w e e n energy gap (Eg) and bond alternation (dr), calculated by the LHS method. (dr is the average of Irout-rinl.)
influence the gap values, one can see from Fig. 4 that a clear correlation b e t ween the energy gap and bond alternation exists. The reason for this correlation should be related to the fact that the d r values in this diagram c o r r e s p o n d to the optimized g e o m e t r y for which the effects of heteroatoms and side rings are already taken into account. This question should be investigated in mor e detail. Acknowledgements
This work was s u p p o r t e d by grants OTKA 6 4 / 1 9 8 7 (Hungary), Fonds fiir Fbrderung der Wissenschaftlichen Forschung (Austria) and NSF (INT8912665) References
1 J. L. Br4das, S p r i n g e r Series i n Solid-State Sciences, Vol. 63, Springer, Berlin, 1985, p. 166. 2 J. L. Br6das, J. Chem. Phys., 82 ( 1 9 8 5 ) 3808. 3 M. Kobayashi, N. Colaneri, M. Boysel and A. J. Heeger, J. Chem. Phys., 82 (1985) 5717. 4 (a) A. S. Jenekhe, N a t u r e (London), 322 (1986) 345; (b) see, however, A. Q. Patti and F. Wudl, Macromolecules, 21 ( 1 9 8 8 ) 540. 5 Y. S. Lee a n d M. Kertesz, Int. J. Quant. Chem. Symp., 21 (1987) 163. 6 (a) M. Kertesz and Y. S. Lee, J. Phys. Chem., 91 (1987) 2 6 9 0 ; Co) J. M. Toussaint, B. Themans, J. M. Andr~ and J. L. Br6das, Synth. Met., 28 (1989) C205.
542 7 8 9 10 11 12 13
14 15 16 17 18
Y. S. Lee and M. Kertesz, J. Chem. Phys., 88 (1988) 2609. M. Kertesz and Y. S. Lee, Sy'nth. Met., 28 (1989) C545. W. Wu and S. Kivelson, Synth. Met., 28 (1989) D575. Y. S. Lee, M. Kert~sz and R. L. Elsenbaumer, Chem. Mater., 2 (1990) 526. T. C. Chung, J. H. Kaufman, A. J. Heeger and F. Wudl, Phys. Rev. B, 30 (1984) 702. J. R. Reynolds, J. P. Ruiz, A. D. Child, K. Nayak and D. S. Marynick, Macromolecules, 24 (1991) 678. (a) R. Becker, G. B15chl and H. Br~unling, in J. L. Br~das and R. R. Chance (eds.), Conjugated Polymeric Materials, Kluwer, Dordrecht, 1990, p. 133; (b) H. Br~iunling, G. B15chl and R. Becket, Synth. Met., 41-43 (1991) 1539; (c) M. Hanack, Chem. Ber., in press. H. C. Longuet-Higgins and L. Salem, Proc. R. Soc. London, Ser. A, 251 (1959) 172. W. P. Su, J. R. Schrieffer and A. J. Heeger, Phys. Rev. B, 22 (1980) 2099. J. Kiirti and P. R. Surjfin, Springer Series in Solid-State Sciences, Vol. 91, Springer, Berlin, 1989, p. 69. C. R. Fincher Jr., D. L. Peebles, A. J. Heeger, M. A. Druy, Y. Matsumara, A. G. MacDiarmid, H. Shirakawa and S. Ikeda, Solid State Commun., 27 (1978) 489. Y. Ikenoue, Synth. Met., 35 (1990) 263.