Excited-State Absorption of Conjugated Polymers in the Near-Infrared

Mar 12, 2013 - Department Physik and Center for Optoelectronics and Photonics Paderborn (CeOPP), Universität Paderborn, Warburger Strasse. 100, 33098...
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Excited-State Absorption of Conjugated Polymers in the NearInfrared and Visible: A Computational Study of Oligofluorenes Sanliang Ling,†,‡ Stefan Schumacher,§ Ian Galbraith,∥ and Martin J. Paterson*,† †

Institute of Chemical Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, U.K. Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, U.K. § Department Physik and Center for Optoelectronics and Photonics Paderborn (CeOPP), Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany ∥ Institute of Photonics and Quantum Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, U.K. ‡

S Supporting Information *

ABSTRACT: Excited-state properties of conjugated polymers play a central role in applications ranging from organics-based photovoltaics to nonlinear photonics. From a theoretical and computational point of view, however, an accurate first-principles description poses a formidable task. Typical molecule sizes go well beyond the size limits for which highly reliable wave function based electronic-structure methods can be applied. In the present work, we demonstrate that nonlinear-response density functional theory can be used to accurately model the excited state absorption process in an important class of conjugated materials. We compute transitions between up to 100 excited states for fluorene oligomers containing up to about 100 conjugated atoms. Furthermore, we demonstrate that this approach can explain the nature of absorption bands in the ESA in near-infrared and visible spectral range. These systems are large enough that we approach the polymer limit in terms of electronic properties of excited states. The results obtained are in good agreement with available experimental data.

1. INTRODUCTION Organic semiconductors show great potential for optoelectronic applications. For example, it has been demonstrated that such conjugated polymers can be used in organic solar cells,1 lasers,2 light-emitting diodes,3 optical amplifiers,4 and chemical sensors.5 Excited states play a central role in the operation of these devices, either directly or indirectly through various loss channels. Moreover, optoelectronic devices are driven devices and so operate far from equilibrium where transitions among excited states are integral to the device operation. A number of detrimental processes involve higher lying excited states and their interactions, such as exciton−exciton annihilation,6 exciton−polaron quenching,7 electric-field-induced ionization of excitons,8 and reabsorption of emitted light by polarons.9 A better understanding of the excited states and their interactions with charge carriers and light fields will therefore directly inform mitigation strategies enabling systematic design of new conjugated polymer devices and materials with improved performance. To improve performance of conjugated polymers in these applications, one of the most important tasks is to understand the underlying electronic structures at both molecular and polymeric levels. The latter is often achieved through an extrapolated procedure based on studies of simpler molecular oligomers.10 The oligomer approach has been quite successful in elucidating the electronic structures of conjugated polymers, © 2013 American Chemical Society

and many experimental and theoretical studies have been reported.10−14 However, with increasing number of repeat units, the size of the molecular oligomers becomes extremely large, and a comprehensive theoretical description of the excited states becomes increasingly challenging. Therefore, many existing studies stop at a point where only the linear optical properties with respect to the electronic ground state are included and even semiempirical methods are still being used to reduce numerical complexity.15−18 Even fewer studies have reported on nonlinear optical properties of conjugated polymers,19 in which quite often sum-over-states approaches were employed.20−24 Polyfluorenes are one of the prototypical semiconducting conjugated polymers that show promising properties for applications in optoelectronic devices. For example, it has been shown that polyfluorenes are efficient blue emitters with high photoluminescence quantum efficiencies.25 Moreover, one can tune the emission wavelength over the entire visible range through chemical modifications of main or side chains.26 Oligofluorenes have been a highly investigated model system in ab initio studies of the photophysics of conjugated polymers. In a previous study,27 we have investigated optical transitions Received: February 6, 2013 Revised: March 11, 2013 Published: March 12, 2013 6889

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between the ground and lowest energy singlet excited state in fluorene oligomers using both experiment and theoretical simulations. In the current contribution, we extend our calculations to dipole-allowed optical transitions that occur between the lowest and higher-lying singlet excited states of fluorene oligomers. As mentioned above, such transitions are important to understand some of the dominant loss channels for optoelectronic devices constructed from such materials. While the transition energies and transition dipoles for onephoton absorption (OPA) from the ground state are readily obtained as the poles and residues of linear response functions for a given quantum chemical model, calculations of the transition dipole moments for OPA from excited states (ESA) require a higher computational effort and are obtained as the double residue of the quadratic response function with dipole operators. With the recent developments in both computational software and hardware, first-principles ESA calculations for medium sized molecules (∼100 conjugated atoms) have become feasible. These theoretical calculations can provide additional details (e.g., the nature of the excited states involved in the excited state absorption) that cannot be directly gleaned from experiment. In the current study, we take fluorene oligomers as an example and show that nonlinear response time dependent density functional theory (TD-DFT) can successfully be applied to even relatively large systems, approaching the polymer limit in terms of electronic and optical properties. In experiments, excited state absorption can often not be easily separated from other photoinduced signatures that contribute in the same spectral range (e.g., polaron and triplet absorption). 9,28,29 In our calculations, the excited-state absorption alone is obtained over a wide spectral range. We believe that such calculations will be a very valuable tool to more reliably disentangle photoinduced spectral signatures of different origin in future studies.

Figure 1. (a) Molecular structure of fluorene heptamer and schematic illustration of (b) one-photon transitions and (c) excited-state absorption. Subscripts in (b) and (c) refer to state numbers for fluorene heptamer. (d) Molecular-orbital characteristics of selected higher-lying excited states that are predominantly involved in the excited-state absorption from S1 in fluorene heptamer. We find that these excited states S6, S8, S81, and S82 have strongly mixed excitation character with different orbital contributions as indicated.

for nonlinear optical properties in small systems35 and has been applied to a diverse range of large conjugated systems.36−38 As we show below, the use of the CAM-B3LYP functional is crucial in finding ESA spectra in agreement with experiments. To obtain further insight on how geometry relaxation affects excited states, we computed ESA spectra of both the ground (S0) and optically active lowest excited (S1) state geometries, obtained using analytical CAM-B3LYP gradient optimization on the excited potential energy surface. On the basis of our previous studies that were performed for fluorene oligomers27 and star-shaped fluorene molecules,34 we used the 6-31G basis set throughout the present work. We also tested 3-21G and 631G* basis sets for F2 and F3, and we found that positions of the first peak in ESA spectra differ by less than 0.02 eV. Such relatively minor sensitivity to the one-electron basis set has been observed previously in the TD-DFT calculation of nonlinear optical properties.37 The calculated excitation energies and transition dipoles were used to calculate the oscillator strengths for electronic transitions from both the ground state (OPA) and optically active lowest excited state (ESA) to higher lying excited states (cf. Figure 1). A homogeneous broadening is included in all the spectra plotted and is chosen to be 0.2 eV. The main tool we use to visualize the character of electronic transitions is the introduction of natural transition orbitals (NTOs).39 The NTOs cast each electronic transition into a minimum number of pairs of effective single-particle orbitals. Ideally, a reduction to only one relevant pair of NTOs can be achieved for each transition. If correlations play a significant role, however, a larger number of NTOs remain to be analyzed. A number of the more commonly used canonical Kohn−Sham molecular orbitals are additionally visualized in Supporting Information. All geometry optimizations and linear response calculations were performed with the Gaussian 09 package.40 All ESA calculations were performed with a parallel version of the Dalton2011 package.41

2. METHODOLOGY Theoretical calculations at the density functional theory level have been performed for a set of fluorene oligomers, including the fluorene dimer (F2), trimer (F3), tetramer (F4), pentamer (F5), hexamer (F6), and heptamer (for F7, see Figure 1), and for molecular geometries in both the α-phase (twisted backbone)30 and β-phase (planar backbone)31,32 conformations. While an alternating structure was considered for all oligomers in the α-phase, we also considered a helical structure for several oligomers, including F3, F4, and F5, to investigate how the calculated excited-state absorption spectra are affected by oligomer conformation. The ground-state geometries were optimized with the Coulomb-attenuated B3LYP (CAM-B3LYP) exchange-correlation functional, and all other calculations involving excited states were based on time-dependent DFT, via the response function formulation.33 We calculate excitation energies and transition dipoles with CAM-B3LYP, which was designed to better describe the long-range contributions to the electronic exchange interaction and give a more accurate description for charge-transfer contributions to electronic excitations. While B3LYP shows good agreement with experiments in predicting linear optical properties,34 its performance in prediction of nonlinear optical properties has been criticized.35 CAM-B3LYP has been used successfully in the prediction of two-photon absorption, which is obtained as the single residue of the quadratic response function. Indeed it was found that CAMB3LYP accuracy could approach that of coupled cluster theory 6890

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Figure 2. Calculated excited-state absorption spectra for fluorene oligomers with (a) S0 (left panel) and (b) S1 (right panel) geometries. Both broadened (black curves, left vertical axis) and stick (red sticks, right vertical axis) spectra are shown. The same scales are used for absorptivity (arbitrary units) of broadened spectra and oscillator strength (atomic units) of stick spectra.

measured at a finite temperature, where multiple conformations might coexist for a single oligomer. The ESA spectra in this energy range are not sensitive to small conformational changes as obtained from our theoretical calculations, which we will discuss in more detail below. Thus, the neglect of finite temperature effects can be justified. In Figure 2, we show that the effect of geometry relaxation on ESA is significant for F2; the energy of the first peak in the ESA spectrum for S0 geometry is red-shifted by about 0.2 eV from the corresponding spectral feature in S1 geometry. For longer oligomers (F3−F7) we find that this effect is much less pronounced such that the lowest optically active ESA transitions for S0 and S1 geometries almost coincide. For all molecules we only find a very small change in oscillator strength upon relaxation from S0 to S1 geometry. In the following we further analyze the nature of the lowenergy spectral features in the ESA. For the F4 oligomer as an example, the first peak in the ESA spectrum in S1 geometry has two contributions (Figure 2b) belonging to the S1 → S5 and S1 → S7 transitions. In the discussion below we focus on the character of S1 → S5, as it clearly dominates in terms of oscillator strength. The nature of the lowest excited state (S1 state) of the oligomer can be easily characterized, as it is dominated (>80%, cf. Figure 3a) by a single electronic transition from the highest occupied molecular orbital

3. RESULTS AND DISCUSSIONS 3.1. Excited State Absorption Spectra. In one of our previous studies, we have calculated the OPA spectra of a series of fluorene oligomers at the B3LYP/6-31G level, and excellent agreement with experiment was obtained for the vertical transition energies. In the present study, we focus on excitedstate absorption. We have calculated the ESA spectra for the series of fluorene dimer to fluorene heptamer. To begin with, in Figure 2, we concentrate on the low-energy range in the calculated ESA spectra because this can be directly compared with available experimental data. Results are shown for both S1 and S0 geometries. As experimentally the excited-state absorption is likely to be measured dominantly in the S1 geometry (as sufficiently fast time resolution in the detection is typically not obtained), the computed ESA spectra in the S1 geometries ought to be comparable with the experimental data. The ESA spectra of F2 and F3 were measured by Hayes and Silva in a transient absorption spectroscopy experiment.42 They observed photoinduced low-energy absorption peaks attributed to excited-state absorption from the S1 electronic state into higher-lying states at 1.87 and 1.66 eV, respectively, for F2 and F3. These absorption bands were assigned to the mAg ← 1Bu transitions. We find that our calculated excitation energies for the lowest optically active transition from S1 for the F2 and F3 oligomers are in very good agreement with these experimental data. The calculated positions of the first peaks in the ESA spectra in Figure 2 are 1.65 and 1.45 eV for F2 and F3 oligomers, respectively. Compared with experiment, our calculations underestimate the transition energies by only about 0.2 eV. The 0.2 eV red shift between F2 and F3 observed experimentally is also well reproduced in our calculations. Although the availability of further significant experimental data is limited, from this comparison we conclude that a slight underestimation of the transition energy of the lowest absorption feature in the calculated ESA spectra is systematic in the calculations. In this context it is important to note that we found that the use of the very popular B3LYP functional completely fails in predicting the ESA spectra correctly. It underestimates the positions of the first peaks in the ESA spectra by more than 1 eV (deviating by about 200% from the experimental values and CAM-B3LYP results). We note here that the experimental ESA spectra, referred to above, were

Figure 3. Natural transition orbitals for relevant excited states involved in the ESA peak of F4: (a) HONTO → LUNTO (88.2%) of S1; (b) HONTO → LUNTO (48.3%) of S5; (c) HONTO−1 → LUNTO+1 (41.6%) of S5. The percentages indicate relative weight of each set of NTOs. 6891

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With respect to the oligomer length dependence, we find that there is a small red shift of the energies of the first peak in the ESA spectra of the S1 geometries with increasing oligomer length. For the S0 geometries, this shift is less pronounced. On the basis of the convergence visible for the peak positions in Figure 2 when moving to longer oligomers, it is reasonable to conclude that for the ESA we are already approaching the polymer limit with the F7 oligomer. This claim can also be verified in comparison with experimental ESA data for polyfluorene. The experimental value of the vertical transition energy of the first peak in the ESA spectra of polyfluorene is about 1.5 eV.46 The computed value for F7 differs by less than 0.2 eV from this value. Considering that we have found CAMB3LYP to systematically underestimate the transition energy of the first peak in the ESA spectra as discussed above by about 0.2 eV, our theoretically calculated transition energy for F7 is thus in excellent agreement with the experimental value for polyfluorene.46 3.2. Conformational Dependence. As mentioned above, in addition to the alternating structure, we also considered a helical structure for several of the oligomers studied here. For F3 we also considered a helical structure with C1 symmetry to study the effect of the lowered symmetry on the computed ESA spectra. We find that all these different molecular conformations give very similar ESA. Small conformational changes do not seem to significantly influence the ESA spectra in the lowenergy range discussed so far. We further considered the differences between S0 and S1 geometries, in which the dihedral angles between adjacent fluorene units are significantly different because the oligomers planarize in the center upon geometry relaxation. While the dihedral angles between adjacent fluorene units in S0 geometry of all oligomers considered are around 38°, relaxation from S0 to S1 geometry leads to significant planarization of the oligomers in the center. Such planarization has also been found in previous experiments on photoexcited oligofluorenes47 and polyfluorene47,48 as well as other similar conjugated oligomers.49,50 We did not find this geometry transformation to influence the appearance of the ESA in the energy range around 1.5 eV much. In particular for the longer oligomers, we find very similar overall ESA in S0 and S1 geometries as shown in Figure 2. However, for S0 we consistently find that this feature is only related to a single electronic transition, whereas in the S1 geometry the total oscillator strength gets split up between one and three electronic transitions depending on the oligomer length. This can be seen in the stick spectra included in Figure 2. We recall that adjacent fluorene units have very similar dihedral angles in the S0 geometry, while dihedral angles between central fluorene units become smaller in the S1 geometry. Therefore, it is reasonable to assume that in the S0 geometry only a single higher-lying excited state is delocalized over the entire oligomer, whereas in the S1 geometry, multiple higher-lying excited states with near degenerate excitation energies contribute to the overall absorption feature. To conclude the study on conformational changes, we studied the ESA in a series of fluorene oligomers in the important planar β phase conformation.31,32 Results are shown in Figure 4. As in the nonplanar fluorene oligomers, for the βphase we also find a dominant ESA feature at about 1.5 eV. This is further evidence that conformational effects in fluorenes are not of particular importance for ESA spectral signatures in the low-energy range around 1.5 eV.

(HOMO) to the lowest unoccupied molecular orbital (LUMO). In contrast, the electronic nature of the higherlying S5 excited state is less simple, as multiple electronic contributions are involved. We find the dominant contributions to be HOMO−1 → LUMO and HOMO → LUMO+1 for the S5 excited state. We find that the dominant S1 → S5 transition cannot be represented by a pure single-particle electron−hole excitation picture. If we analyze the relevant natural transition orbitals, we need to take into account both the HONTO → LUNTO and the HONTO−1 → LUNTO+1 transitions. These are depicted in Figure 3 for F4 as an example. In this case for the S1 → S5 transition, HONTO → LUNTO and HONTO−1 → LUNTO +1 have almost the same weight, namely, 48.3% and 41.6%, respectively. We find that the excitation of S1 has no obvious charge transfer character (cf. Figure 3a). For S5, however, two complementary charge transfers occur, one (HONTO → LUNTO; see Figure 3b) from the periphery of the oligomer to the center, and another (HONTO−1 → LUNTO+1; see Figure 3c) from the center of the oligomer to the periphery. Although the overall transfer of charges in the S1 → S5 transition is small because the two contributions partly cancel each other, the charge transfer character clearly visible in the orbital picture of the high-lying S5 excited state (cf. Figure 3b and Figure 3c) appears to be very relevant. Here we emphasize again that it is only with the long-range corrected DFT functional CAM-B3LYP that these excitations are correctly represented in our calculations and compare well with experiment. This also explains why the conventional B3LYP fails to give an accurate prediction on the peak energy in the ESA spectra; B3LYP cannot capture the nature of excited states with pronounced charge transfer character. Such failure of more conventional DFT functionals in TD-DFT calculations of excited-state properties has previously been discussed in a number of other polyaromatic hydrocarbons.43−45 In these systems, there are two simultaneous low-lying π → π* transitions, one with S1-like HOMO → LUMO excitation character, commonly denoted as 1La, and another with S5-like mixed HOMO−1 → LUMO and HOMO → LUMO+1 excitation characters, commonly denoted as 1Lb. It has been suggested that the 1La state is of “ionic” nature and the 1Lb state is of “covalent” nature.45 Usually the 1La excitation energy is substantially underestimated and the 1Lb excitation energy is very-well predicted by TD-DFT using the conventional B3LYP hybrid functional.44 In addition, Wong et al. argued that CAMB3LYP is not sufficient to give an accurate description of both states either.45 However, our good agreement with experiment seems to indicate that CAM-B3LYP is indeed capable of describing both states correctly for the oligofluorenes studied here. A possible explanation could likely be that in other polyaromatic hydrocarbons such as those that Wong et al. discussed previously,45 both states are low-lying excited states and they are not well separated in energy but only by about 0.2 eV. In our fluorene oligomers, the 1Lb state is a higher-lying excited state and it is well separated from the 1La state, with an excitation energy of >1 eV. For the other oligomers studied here, upon closer inspection of the dominant transitions that constitute the low-energy ESA, we find that the nature of the higher-lying excited states contributing to the ESA is very similar to what we have discussed above in detail for F4, and most of the relevant excitations are dominated by HOMO−1 → LUMO and HOMO → LUMO+1 transitions. 6892

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the total oscillator strength. Taking the F7 oligomer as an example, these two transitions correspond to transitions from S1 into the high-lying excited states S81 and S82. As for the lowenergy ESA feature, these high-lying excited electronic states cannot be well represented by a simple single-particle electron− hole excitation picture. Multiple orbitals contribute significantly to these transitions. In contrast to the S5 state of the F4 oligomer, which is dominated by HOMO−1 → LUMO and HOMO → LUMO+1 transitions, the S81 state of the F7 oligomer is dominated by several electronic transitions, with major contributions from HOMO−9 → LUMO and HOMO− 10 → LUMO+3 transitions. The situation for the S82 state of F7 is even more complicated. We find 10 different orbital contributions to this electronic transition, all of similar weight. We show the most relevant natural transition orbitals of the S81 state of F7 in Figure 6, from which we can find that similar to

Figure 4. Theoretical excited state absorption spectra for fluorene oligomers with planar β phase conformation. The same style as Figure 2 is used.

3.3. Excited State Absorption in the High Energy Range. We have shown excited state absorption in fluorene oligomers in the low energy range (∼1.5 eV). While this energy range can be easily accessed by experiment, excited-state absorption in the higher energy range (e.g., up to 4 eV) is also of considerable interest. At high excitation densities in extended fluorene systems, the spectral density in the ESA at higher energies contributes to reabsorption of emitted photons and more importantly is a crucial ingredient to understand efficiency of Auger-type exciton−exciton annihilation processes, a major loss mechanism in, for example, optical amplifiers. To access the high-energy range, a large number of excited states has to be included in the calculations which greatly increase the numerical cost in particular for the longer oligomers studied. In Figure 5 we present the ESA spectra calculated for a greatly extended spectral range for F4, F5, and F7. For the

Figure 6. Natural transition orbital for S81 state of F7 oligomer which is involved in excited state absorption in the high energy range: (a) HONTO → LUNTO (λ = 21.2%); (b) HONTO−1 → LUNTO+1 (λ = 19.3%); (c) HONTO−2 → LUNTO+2 (λ = 16.8%); (d) HONTO−3 → LUNTO+3 (λ = 13.5%). The value of λ indicates relative weight of each set of NTOs.

the S5 state of F4 (see Figure 3), this high-lying excited state also shows significant long-range charge transfer character; e.g., HONTO−2 → LUNTO+2 (Figure 6c) involves charge transfer from the periphery to the middle of the oligomer, and HONTO−3 → LUNTO+3 (Figure 6d) involves charge transfer from the middle to the periphery of the oligomer. These results indicate that electronic excitations from deeper-lying occupied electronic orbitals to higher-lying unoccupied electronic orbitals might play an important role in excited state absorption in the high energy range. The convergence and nature as well as the underlying principle of excited state absorption in fluorene oligomers in the highenergy range are still being investigated and will be discussed in our future work. We note that despite the obvious trend in the high-energy ESA feature visible in Figure 5 for the series of F4, F5, and F7, we did not find similar high-energy ESA features for F3 and F6. So far we were not able to trace the absence of this peak in some of the oligomers back to symmetry or conformational issues. We hope to be able to shed some more light on this aspect in a future study. We also note that computational cost for the calculation of the ESA spectra greatly increases with oligomer length. Additionally, the longer the oligomers are, the more excited states need to be included in the calculations to cover the entire spectral range of interest up to about 4 eV in the ESA in the present study. For the

Figure 5. Calculated excited-state absorption spectra in the energy range of 0.5−4.0 eV. Results are shown for F4, F5, and F7 in the S1 geometry. The same style as Figure 2 is used.

heptamer 60 states with symmetry element A′ needed to be included to cover the spectral range shown because of the fact that the density of excited states is much higher in F7 compared with those in small fluorene oligomers. Clearly visible is a pronounced ESA feature at energies of about 3.3 eV. This high-energy peak in the ESA spectra in Figure 5 involves one or two high-lying electronic transitions that share 6893

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Notes

longest oligomer studied here, we are at about the limit of what is computationally feasible with current HPC clusters.

The authors declare no competing financial interest.

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4. CONCLUSIONS We performed a systematic computational study on the excited state absorption spectra of a series of fluorene oligomers. Our calculated ESA spectra of F2 and F3 oligomers are in very good agreement with previously reported experiments. Our results demonstrate that excited-state absorption occurs in fluorene polymers at a low excitation energy of around 1.5 eV. The nature of excited state absorption in this energy range is characterized as an electronic transition from the lowest excited state with a single HOMO → LUMO excitation character to high-lying excited states with mixed HOMO−1 → LUMO and HOMO → LUMO+1 excitation characters that involve simultaneous complementary intramolecular charge transfer processes. Moreover, our system represents one of the largest systems for which nonlinear optical properties have been investigated by theory so far, even taking into consideration those studies that were based on semiempirical methods.18 Taking fluorene oligomers as an example, the longest oligomer that we have studied, F7, has a total of 149 atoms and 935 basis functions when the 6-31G basis set is employed. Our results show that nonlinear response TD-DFT with CAM-B3LYP functional can be applied to large conjugated systems, for which high-level wave function based quantum chemical methods cannot be employed because of the high computational cost. In addition, we demonstrate that excited state absorption can also be expected for some of the fluorene oligomers in the high energy range, around 3.5 eV. Although measurements in this energy range are challenging with current pump−probe techniques, it certainly has technological relevance due to the proximity of this energy to the one photon absorption and emission resonances. It should also be pointed out here that high-lying excited states are extremely difficult to describe accurately via the (temporally) adiabatic TD-DFT in its present implementations, employed throughout the current work, and our current results on excited state absorption in the high energy range should be further verified by more advanced theoretical methods that are currently under development.51−53 Nevertheless, we anticipate such excited state absorption processes will play a very important role in performance degradation in optoelectronic devices, and thus, they should be taken into account in future design of new materials for such applications.

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ACKNOWLEDGMENTS I.G. acknowledges financial support from the Engineering and Physical Sciences Research Council (U.K.). M.J.P. acknowledges the European Research Council (ERC) for funding under the European Union’s Seventh Framework Programme (FP7/ 2007-2013)/ERC Grant No. 258990.

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ASSOCIATED CONTENT

S Supporting Information *

Cartesian coordinates (including F2−F7), calculated excitation energies, and oscillator strengths of both the low-energy (including F2−F7) and the high-energy (including F4, F5, and F7) peaks in ESA spectra of S0 and S1 minima of fluorene oligomers; a comparison of the calculated excitation energies and oscillator strengths of some of the low energy ESA transitions with 6-31G and 6-31G* basis sets at CAM-B3LYP level (F2 at S0 geometry and F3 at S1 geometry); relevant canonical molecular orbitals involved in the low energy peak in the ESA spectrum of F4 at S1 geometry. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 6894

dx.doi.org/10.1021/jp401359a | J. Phys. Chem. C 2013, 117, 6889−6895

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dx.doi.org/10.1021/jp401359a | J. Phys. Chem. C 2013, 117, 6889−6895