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Theoretical calculations of the geometries and of the lowest optical transitions of singly and doubly charged oligodiacetylenes
Synthetic Metals 124 (2001) 179±181
Theoretical calculations of the geometries and of the lowest optical transitions of singly and doubly charged oligodiacetylenes M. Ottonellib, I. Moggiob, G.F. Mussoa,b,*, D. Comorettoa,b, C. Cunibertib, G. Dellepianea,b a
Istituto Nazionale per la Fisica della Materia, Via Dodecaneso 31, I-16146 Genova, Italy Dipartimento di Chimica e Chimica Industriale, Via Dodecaneso 31, I-16146 Genova, Italy
b
Abstract We have performed theoretical calculations on the singly and doubly charged species of the lowest unsubstituted oligodiacetylenes, with the scope of achieving information on the charged photoexcitations of polydiacetylenes. On the basis of the AM1-optimized geometries of the radical ions and of the dications we have computed their low-energy vertical transitions, using the INDO-SCI method in order to take into account the electron correlation. Extrapolated polymer results are compared with the photoinduced absorption spectra. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Polydiacetylenes; Quantum chemical calculations; Polarons; Bipolarons
1. Method and results Photoinduced absorption spectra of polydiacetylenes show, in addition to triplet exciton bands, features which can be traced back to the formation of charged species. Fig. 1 shows the steady-state long-living photoinduced absorption spectrum of polyDCHD [1]. The signals observed at 0.81 and 0.96 eV have been assigned to the high-energy peak associated with a long-lived charged state and with its vibrational structure. A very broad absorption band centred around 0.1 eV, with superimposed windows at 2000, 1400 and 1200 cm 1 related to the IRAV modes of the CBC, C=C and C±C bond stretchings, respectively, is also detected, which is assigned to the low-energy transition of the charged state. The experimental results reported in [1] show the IRAV modes to be associated with the twin bands at about 0.1 and 0.81 eV, which unambiguously signals that the above photoinduced electronic bands are due to a charged state. To achieve more information on the latter, we have undertaken theoretical calculations on the radical cation (RC) and dication (DC) species of the lowest unsubstituted oligodiacetylenes of the general form C4n2H2n2, n ranging from 2 up to 15. For the sake of comparison also radical anions (RA) up to n 7 have been
* Corresponding author. Tel.: 39-10-353-8703; fax: 39-10-353-6199. E-mail address: [email protected] (G.F. Musso).
considered. First the ion geometries have been optimized at the AM1 level, a C2h symmetry being assumed. In fact planar conformations are to be expected in the solid state due to packing effects [2]. The results for the n 5 oligomer taken as an example are reported in Table 1. For the RC and RA the geometry distortions with respect to the neutral species (N) are strictly similar and are maxima in the oligomer centre, extending over 5 units. Much stronger effects of the same form are obtained for the DC. From the study of larger oligomers the geometry changes in the DC are seen to extend over 7 units, except for n 13 and 15, in which cases the molecule experiences two de®nitely smaller distortions, each of them being located near one end and 3±4 units long. On the basis of the geometries determined as above we have computed the lowest transition energies and the related dipole oscillator strengths using the INDO-S method [3] in the SCI (single con®guration interaction) approximation in order to take into account at least part of the electronic correlation effects. The closed/open shell calculations have been done in the framework of the RHF/ROHF theory, and Mataga± Nishimoto integrals have been used throughout. The CI calculations have been performed in two ways: (a) by using all the p/p orbitals and (b) by including the single excitations involving all orbitals (occupied and virtual) lying within a given energy range (0.5 a.u. for each), to achieve size consistency as much as possible. After n 3 the difference between the excitation energies from the two
0379-6779/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 9 - 6 7 7 9 ( 0 1 ) 0 0 4 3 5 - 0
180
M. Ottonelli et al. / Synthetic Metals 124 (2001) 179±181
Fig. 1. The steady-state long-living photoinduced absorption spectrum of polyDCHD.
methods never exceeds a few hundredths of eV, indicating that for optical transitions the contributions of the p/p orbitals are the most important ones even in the presence of triple bonds. All the results reported have been computed as in b). For radical ions we obtain two low-energy transitions (peaks 1 and 2) which are to excited states that have similar structures, the main excitations for them being the HOMO-1 ! HOMO and HOMO ! LUMO ones, where the HOMO and LUMO orbitals correspond to the polaron levels. In the RC case for peak 1 the weight of the former excitation is bigger than that of the latter one, the opposite being true for peak 2. For the RA's the situation is reversed. We stress, however, that in any case the two above
excitations are strongly mixed in both peaks. The transition energies for the two ion types do not differ very much, and peak 2 is de®nitely predicted to be always the more intense one. For the DC's there is one low-energy transition, which is dominated by the HOMO ! LUMO excitation, the LUMO being now the lowest bipolaron level. In Figs. 2 and 3 the transition energies for the radical ions and for the DC's are plotted against 1/n, linear trends being obtained in all cases. For radical ions (Fig. 2) only the points n 11 and 13 show signi®cant deviations. This behaviour, which is seen to have little effect on the position of the straight lines, can be due to technical dif®culties with the INDO-S package in the open shell case, and possibly to an initial lack of size-consistency. In the DC case (Fig. 3) the points n 13 and 15 (see comments above), which are not included in the linear ®t as well as the point n 2, correspond to a nearly constant transition energy which almost coincides with the n 1 value given by the straight line. Estimated polymer (n 1) transition energies are 0.58 eV (peak 1) and 0.74 eV (peak 2) for the positive polaron, 0.55 and 0.90 eV for the negative polaron and 0.80 eV for the positive bipolaron. The agreement with experiment [1] is almost as good as that reported for charged oligophenylenes [4]. In our case the complicated lineshape of the IRAV modes gives rise to some uncertainty as to the detailed position of the low-energy band, and moreover it has been shown [1] that by changing the substituents the band itself can shift up to 0.45 eV. On
Table 1 Ê ) for the neutral, radical cation and anion, and dication n 5 oligodiacetylenea AM1 C±C bond lengths (A i
Ri(C±C)
N RC RA DC a
Ri(C=C)
Ri(CBC)
1
2
3
4
5
1
2
3
1
2
3
1.399 1.361 1.361 1.321
1.399 1.372 1.369 1.330
1.399 1.383 1.386 1.347
1.399 1.395 1.392 1.368
1.402 1.400 1.402 1.388
1.350 1.396 1.390 1.447
1.350 1.374 1.369 1.422
1.349 1.352 1.351 1.375
1.202 1.224 1.221 1.254
1.202 1.208 1.207 1.231
1.198 1.199 1.199 1.204
i denotes the order number of the actual bond of each type counted starting from the oligomer centre.
Fig. 2. INDO-SCI low-energy transitions for radical cation (open squares: peak 1; open circles: peak 2) and radical anion (full triangles: peak 1; full lozenges: peak 2) oligodiacetylenes.
Fig. 3. INDO-SCI low-energy transitions for oligodiacetylene dications.
M. Ottonelli et al. / Synthetic Metals 124 (2001) 179±181
the whole, the results appear consistent with the formation of polarons, whose spin signature has been in fact recently detected in polyCPDO through LESR experiments [5]. Acknowledgements We acknowledge support from the Italian MURST and CNR.
181
References [1] D. Comoretto, C. Cuniberti, G.F. Musso, G. Dellepiane, F. Speroni, C. Botta, S. Luzzati, Phys. Rev. B 49 (1994) 8059. [2] J.S. Patel, S. Lee, G.L. Baker, J.A. Shelburne III, Polym. Prepr. 34 (1) (1993) 757. [3] M.C. Zerner, in: K.B. Lipkowitz, D.B. Boyd (Eds.), Reviews of Computational Chemistry, Vol. 2, New York, 1991, p. 313. [4] E. Zojer, J. Cornil, G. Leising, J.L. BreÂdas, Phys. Rev. B 59 (1999) 7957. [5] C.J. Brabec, H. Johansson, A. Cravino, N.S. Sariciftci, D. Comoretto, G. Dellepiane, I. Moggio, J. Chem. Phys. 111 (1999) 10354.
Theoretical calculations of the geometries and of the lowest optical transitions of singly and doubly charged oligodiacetylenes M. Ottonellib, I. Moggiob, G.F. Mussoa,b,*, D. Comorettoa,b, C. Cunibertib, G. Dellepianea,b a
Istituto Nazionale per la Fisica della Materia, Via Dodecaneso 31, I-16146 Genova, Italy Dipartimento di Chimica e Chimica Industriale, Via Dodecaneso 31, I-16146 Genova, Italy
b
Abstract We have performed theoretical calculations on the singly and doubly charged species of the lowest unsubstituted oligodiacetylenes, with the scope of achieving information on the charged photoexcitations of polydiacetylenes. On the basis of the AM1-optimized geometries of the radical ions and of the dications we have computed their low-energy vertical transitions, using the INDO-SCI method in order to take into account the electron correlation. Extrapolated polymer results are compared with the photoinduced absorption spectra. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Polydiacetylenes; Quantum chemical calculations; Polarons; Bipolarons
1. Method and results Photoinduced absorption spectra of polydiacetylenes show, in addition to triplet exciton bands, features which can be traced back to the formation of charged species. Fig. 1 shows the steady-state long-living photoinduced absorption spectrum of polyDCHD [1]. The signals observed at 0.81 and 0.96 eV have been assigned to the high-energy peak associated with a long-lived charged state and with its vibrational structure. A very broad absorption band centred around 0.1 eV, with superimposed windows at 2000, 1400 and 1200 cm 1 related to the IRAV modes of the CBC, C=C and C±C bond stretchings, respectively, is also detected, which is assigned to the low-energy transition of the charged state. The experimental results reported in [1] show the IRAV modes to be associated with the twin bands at about 0.1 and 0.81 eV, which unambiguously signals that the above photoinduced electronic bands are due to a charged state. To achieve more information on the latter, we have undertaken theoretical calculations on the radical cation (RC) and dication (DC) species of the lowest unsubstituted oligodiacetylenes of the general form C4n2H2n2, n ranging from 2 up to 15. For the sake of comparison also radical anions (RA) up to n 7 have been
* Corresponding author. Tel.: 39-10-353-8703; fax: 39-10-353-6199. E-mail address: [email protected] (G.F. Musso).
considered. First the ion geometries have been optimized at the AM1 level, a C2h symmetry being assumed. In fact planar conformations are to be expected in the solid state due to packing effects [2]. The results for the n 5 oligomer taken as an example are reported in Table 1. For the RC and RA the geometry distortions with respect to the neutral species (N) are strictly similar and are maxima in the oligomer centre, extending over 5 units. Much stronger effects of the same form are obtained for the DC. From the study of larger oligomers the geometry changes in the DC are seen to extend over 7 units, except for n 13 and 15, in which cases the molecule experiences two de®nitely smaller distortions, each of them being located near one end and 3±4 units long. On the basis of the geometries determined as above we have computed the lowest transition energies and the related dipole oscillator strengths using the INDO-S method [3] in the SCI (single con®guration interaction) approximation in order to take into account at least part of the electronic correlation effects. The closed/open shell calculations have been done in the framework of the RHF/ROHF theory, and Mataga± Nishimoto integrals have been used throughout. The CI calculations have been performed in two ways: (a) by using all the p/p orbitals and (b) by including the single excitations involving all orbitals (occupied and virtual) lying within a given energy range (0.5 a.u. for each), to achieve size consistency as much as possible. After n 3 the difference between the excitation energies from the two
0379-6779/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 9 - 6 7 7 9 ( 0 1 ) 0 0 4 3 5 - 0
180
M. Ottonelli et al. / Synthetic Metals 124 (2001) 179±181
Fig. 1. The steady-state long-living photoinduced absorption spectrum of polyDCHD.
methods never exceeds a few hundredths of eV, indicating that for optical transitions the contributions of the p/p orbitals are the most important ones even in the presence of triple bonds. All the results reported have been computed as in b). For radical ions we obtain two low-energy transitions (peaks 1 and 2) which are to excited states that have similar structures, the main excitations for them being the HOMO-1 ! HOMO and HOMO ! LUMO ones, where the HOMO and LUMO orbitals correspond to the polaron levels. In the RC case for peak 1 the weight of the former excitation is bigger than that of the latter one, the opposite being true for peak 2. For the RA's the situation is reversed. We stress, however, that in any case the two above
excitations are strongly mixed in both peaks. The transition energies for the two ion types do not differ very much, and peak 2 is de®nitely predicted to be always the more intense one. For the DC's there is one low-energy transition, which is dominated by the HOMO ! LUMO excitation, the LUMO being now the lowest bipolaron level. In Figs. 2 and 3 the transition energies for the radical ions and for the DC's are plotted against 1/n, linear trends being obtained in all cases. For radical ions (Fig. 2) only the points n 11 and 13 show signi®cant deviations. This behaviour, which is seen to have little effect on the position of the straight lines, can be due to technical dif®culties with the INDO-S package in the open shell case, and possibly to an initial lack of size-consistency. In the DC case (Fig. 3) the points n 13 and 15 (see comments above), which are not included in the linear ®t as well as the point n 2, correspond to a nearly constant transition energy which almost coincides with the n 1 value given by the straight line. Estimated polymer (n 1) transition energies are 0.58 eV (peak 1) and 0.74 eV (peak 2) for the positive polaron, 0.55 and 0.90 eV for the negative polaron and 0.80 eV for the positive bipolaron. The agreement with experiment [1] is almost as good as that reported for charged oligophenylenes [4]. In our case the complicated lineshape of the IRAV modes gives rise to some uncertainty as to the detailed position of the low-energy band, and moreover it has been shown [1] that by changing the substituents the band itself can shift up to 0.45 eV. On
Table 1 Ê ) for the neutral, radical cation and anion, and dication n 5 oligodiacetylenea AM1 C±C bond lengths (A i
Ri(C±C)
N RC RA DC a
Ri(C=C)
Ri(CBC)
1
2
3
4
5
1
2
3
1
2
3
1.399 1.361 1.361 1.321
1.399 1.372 1.369 1.330
1.399 1.383 1.386 1.347
1.399 1.395 1.392 1.368
1.402 1.400 1.402 1.388
1.350 1.396 1.390 1.447
1.350 1.374 1.369 1.422
1.349 1.352 1.351 1.375
1.202 1.224 1.221 1.254
1.202 1.208 1.207 1.231
1.198 1.199 1.199 1.204
i denotes the order number of the actual bond of each type counted starting from the oligomer centre.
Fig. 2. INDO-SCI low-energy transitions for radical cation (open squares: peak 1; open circles: peak 2) and radical anion (full triangles: peak 1; full lozenges: peak 2) oligodiacetylenes.
Fig. 3. INDO-SCI low-energy transitions for oligodiacetylene dications.
M. Ottonelli et al. / Synthetic Metals 124 (2001) 179±181
the whole, the results appear consistent with the formation of polarons, whose spin signature has been in fact recently detected in polyCPDO through LESR experiments [5]. Acknowledgements We acknowledge support from the Italian MURST and CNR.
181
References [1] D. Comoretto, C. Cuniberti, G.F. Musso, G. Dellepiane, F. Speroni, C. Botta, S. Luzzati, Phys. Rev. B 49 (1994) 8059. [2] J.S. Patel, S. Lee, G.L. Baker, J.A. Shelburne III, Polym. Prepr. 34 (1) (1993) 757. [3] M.C. Zerner, in: K.B. Lipkowitz, D.B. Boyd (Eds.), Reviews of Computational Chemistry, Vol. 2, New York, 1991, p. 313. [4] E. Zojer, J. Cornil, G. Leising, J.L. BreÂdas, Phys. Rev. B 59 (1999) 7957. [5] C.J. Brabec, H. Johansson, A. Cravino, N.S. Sariciftci, D. Comoretto, G. Dellepiane, I. Moggio, J. Chem. Phys. 111 (1999) 10354.