Time-Dependent Density Functional Theory Study of Low-Lying

Article pubs.acs.org/JPCA

Time-Dependent Density Functional Theory Study of Low-Lying Absorption and Fluorescence Band Shapes for Phenylene-Containing Oligoacenes Ye Jun* Institute of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, #16-16 Connexis North, Singapore 138632, Singapore S Supporting Information *

ABSTRACT: Low-lying band shapes of absorption and fluorescence spectra for a member of a newly synthesized family of phenylene-containing oligoacenes (POA 6) reported in J. Am. Chem. Soc. 2012, 134, 15351 are studied theoretically with two different approaches with TIPS−anthracene as a comparison. Underlying photophysics and exciton−phonon interactions in both molecules are investigated in details with the aid of the time-dependent density functional theory and multimode Brownian oscillator model. The first two low-lying excited-states of POA 6 were found to exhibit excitation characteristics spanning entire conjugated backbone despite the presence of antiaromatic phenylene section. Absorption and fluorescence spectra calculated from both time-dependent density functional theory and multimode Brownian oscillator model are shown to reach good agreement with experimental ones. The coupling between phonon modes and optical transitions is generally weak as suggested by the multimode Brownian oscillator model. Broader peaks of POA 6 spectra are found to relate to stronger coupling between low frequency phonon modes such as backbone twisting (with frequency 1000 cm−1 are used to reproduce experimental absorption spectrum of TIPS− Anth shown in Figure 4a, while only two phonon modes (one in the frequency range of 0−300 cm−1 and the other one in the range of that higher than 1000 cm−1) were used for calculating

Figure 3. Absorption and fluorescence spectra for (a) TIPS−Anth and (b) POA 6 calculated with the IMDHOT model and TDDFT. For TIPS−Anth, only one excited-state was considered, while two excitedstates (S1 and S2) were considered for POA 6. Homogeneous and inhomogeneous broadening parameters, i.e., Γ and Θ used for obtaining spectra are listed in Table 2. Experiment data were retrieved from ref 1.

Table 2. Parameters Used for TDPBE0 Absorption and Fluorescence Spectra of TIPS−Anth and POA 6 To Fit with Experimental Results TIPS−Anth (Abs) TIPS−Anth (FL) POA 6 S1 (Abs) POA 6 S2 (Abs)a POA 6 S1 (FL)b POA 6 S2 (FL)

Γ/cm−1

Θ/cm−1

Δ/nm

200 340 200 300 200 400

20 20 20 20 20 20

3.0 16.5 −23 −19 15 12

a

A weighting factor of 0.53 was applied to the TDPBE0 S2 absorption spectrum of POA 6 before summed with the S1 spectrum. bA weighting factor of 0.30 was applied to the TDPBE0 S1 fluorescence spectrum of POA 6 before summed with the S2 spectrum.

Good agreement between calculated and experiment results are achieved as shown in the figures. However, we would like to add a few comments to our results. It can be learned from the results in Table 1 that the S1 state of TIPS−Anth with energy of 2.927 eV is an optically allowed electronic transition with strongest oscillator strength. Therefore, the S1 state contributes most to the observed spectra. It is also indicated in the Table 1 that differences in excitation energies between calculation and experiment are very small but non-negligible. In order to achieve good fits with experimental spectra, additional small E

DOI: 10.1021/acs.jpca.5b09788 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

modes are mostly strongly coupled to the electronic transitions, with their S values greater than 1.0 except for the one used in obtaining the absorption spectrum of TIPS−Anth. To gain more insights into the physics of the fitting parameters used in the MBO model and compared to DFT calculations, we plotted the individual Huang−Rhys factors of different normal modes of both molecules in Figure 5. Careful comparison between other MBO parameters and those obtained from DFT suggest it is possible to use a few effective phonon modes to reproduce experimental spectra with good accuracy. Taking the simple case of TIPS−Anth as a staring example, where distinct regions corresponding to modes around 400 and 1400 cm−1 are observed in Figure 5a. If we summed the S values for the high frequency regime in Figure 5a, the resultant SDFT high = 0.6 can be obtained, which is close to the MBO value of SMBO high = 0.9. Similarly, if we sum the S values for the medium frequency regime, we can have SDFT mid = 0.3, which is almost identical to the MBO value of SMBO mid = 0.33. In the MBO fitting, a low frequency phonon mode ( 1000 cm , so as to facilitate further discussions. The exciton−phonon coupling strengths in both molecules fall within the weak range based on the values of S listed in Table 3 for high frequency modes. The medium frequency modes are also weakly coupled to electronic transition with their S values lower than 0.5. The low frequency

Table 3. Fitted Multi-Mode Brownian Oscillator Model Parameters for Absorption and Fluorescence Spectra of TIPS−Anth and POA 6 in Chloroforma TIPS−Anth (Abs) TIPS−Anth (FL) POA 6 S1 (Abs) POA 6 S2 (Abs)b POA 6 S1 (FL)c POA 6 S2 (FL)

ωMBO high

ωMBO mid

ωMBO low

γMBO high

γMBO mid

γMBO low

SMBO high

SMBO mid

SMBO low

Eeg/eV

1440 1360 1640 1540 1400 1360

440

100 115 80 80 80 100

100 200 240 220 240 350

70

200 200 100 100 100 100

0.90 0.65 0.54 0.77 0.42 0.65

0.33

0.4 1.4 2.5 2.2 2.0 2.5

2.795 2.785 2.805 2.996 2.590 2.833

500 650

100 100

0.1 0.1

Here both ω and γ take the unit of cm−1. Unless otherwise mentioned, the inhomogeneous broadening parameters Θ = 70 cm−1 were used in all MBO spectra. bA weighting factor of 0.53 was applied to the MBO S2 absorption spectra of POA 6 before summed with the S1 spectrum. cA weighting factor of 0.30 was applied to the MBO S1 fluorescence spectra of POA 6 before summed with the S2 spectrum. a

F

DOI: 10.1021/acs.jpca.5b09788 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Figure 5. Frequency-dependent Huang−Rhys factors of normal modes for (a) TIPS−Anth S1, (b) POA 6 S1, and (c) POA 6 S2. The in-plane breathing modes at 1687 cm−1 are also plotted in parts b and c.

softening to the high frequency modes in TIPS−Anth owing to local excitation feature based on the analysis of frontier orbitals above. However, a smaller SMBO high is found for the high frequency mode coupled to the optical transition for the fluorescence process, indicating weaker exciton−phonon coupling. It is also was found for the worth noting that a much higher SMBO low fluorescence process, which yielded broader bandwidth for the fluorescence spectrum compared to the absorption one. POA 6. Comparing the MBO results to TDPBE0 results for POA 6, the lowest excitation energy obtained through MBO fitting of the absorption spectrum is determined as 2.798 eV, which is close to the DFT value of 2.709 eV (S1) and experiment value of 2.827 eV. From the case of TIPS−Anth, it is possible to use a few effective phonon modes to represent collective effects of modes in different frequency region. Thus, it is also interesting to look into the more complicated molecule POA 6 regarding this possibility. Similar to the approach in obtaining the IMDHOT spectra, we also summed two individual MBO spectra corresponding to S1 and S2 excitation to generate final MBO absorption or fluorescence spectra. We used the same weighting factors as those in generating IMDHOT spectra to get final MBO spectra. Individual MBO spectra are shown in Figure 4 with dash and dotted lines under the summed spectra. The individual MBO spectra are closely

approximated the IMDHOT ones, thus making the comparison of parameters meaningful. In Figure 5, parts b and c, we display the distribution of S with respect to phonon frequency for both S1 and S2 states of POA 6. In the MBO fitting of S1 and S2 absorption spectra for POA 6, three phonon modes in the high, medium and low frequency regimes were included. From Figure 5, it is noticed that the S values have similar distribution for both S1 and S2 states. In the S1 and S2 states, strong exciton−phonon coupling can be found in the low and high frequency regimes, but much smaller values of S are observed in DFT the medium frequency regime. The summed value of SDFT high , Smid and SDFT for S1 of POA 6 calculated from TDPBE0 is 0.48, low 0.11 and 2.62, respectively according to Figure 5b. In MBO MBO comparison, the SMBO high , Smid and Slow values from the MBO fitting of POA 6 absorption spectrum are 0.54, 0.1 and 2.5, respectively, which are in good agreement with the summed values obtained through the TDPBE0 calculations. Summation of the S values in the three frequency regimes for the S2 of DFT POA 6 in Figure 5c gives value of SDFT high = 0.69, Smid = 0.12, and DFT MBO MBO Slow = 0.88. In comparison, the Shigh , Smid , and SMBO low values from the MBO fitting of the S2 absorption spectrum are 0.77, 0.10 and 2.2, respectively, which are also in agreement with the MBO TDPBE0 results. But the value of SDFT low is lower than Slow for S2 of POA 6. G

DOI: 10.1021/acs.jpca.5b09788 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A The fluorescence spectrum of POA 6 is also well reproduced by the MBO method following the approach applied in obtaining the IMDHOT spectrum. Similarly, only two phonon modes are needed to achieve such good agreement. Compared to the MBO parameters obtained through the POA 6 absorption spectrum, both ωMBO high from S1 and S2 derived from the fluorescence spectrum fitting are lower by about 200 cm−1, indicating possible phonon softening owing to optical excitation. But SMBO high are not significant changed compared to those for the absorption spectrum. In contrast, both ωMBO low and SMBO low values for the fluorescence spectrum are not significantly changed compared to the ones for the absorption spectrum. Further comparison of the MBO SMBO high values for the S1 states of TIPS−Anth and POA 6 obtained either from absorption or fluorescence spectra showing lower value of MBO SMBO high for POA 6. The lower value of Shigh suggested weaker exciton−phonon coupling in POA 6, which may interpreted as more rigid backbone of the molecule owing to the presence of the phenylene that connects oligoacene segments. Similarly, much smaller MBO SMBO mid is also obtained for POA 6 from its absorption spectrum, which may be also linked to more rigid backbone. In contrast, SMBO values of POA 6 are generally low higher than those for TIPS−Anth, rendering stronger exciton− phonon coupling of the low frequency modes. Such stronger exciton−phonon coupling can be understood as the results of rotating motion of additional phenyl rings attached to the naphthalene backbone in POA 6, as suggested by the vector figures in Figures S2−S5 of the Supporting Information. It is also revealed from Figures S2−S5 that twisting motions of the fused backbone (with frequency around 22.4, 26.0, and 186.0 cm−1) may also play a major role as more optical transitions are localized in the backbone rather than the other functional groups attached. In addition, it is worth noting from Figure 5, parts c and d, on a new high frequency mode at 1687 cm−1 that is strongly coupled to the S1 or S2 transition of POA 6. It is noted from the figure that this mode is directly related to the antiaromatic phenylene section, which exhibits localized inplane breathing motion of the carbon atoms. Line Broadening. Interestingly, if we compare the homogeneous broadening parameters Γ recorded in Table 2 for the IMDHO model and γ in Table 3 for the MBO model, the values are in qualitative agreement with each other. But owing to the fact that 2 to 3 phonon modes are involved in the MBO model, γ values varies with respect to the frequency of the modes. In the MBO model, the γ values for the high and medium frequency modes are generally around 200−300 cm−1, indicating these modes are under-damped. But in all cases studied, the γ values for low frequency modes are generally equivalent or higher than the respective phonon modes, suggesting over-damped feature of these modes. The underdamped values of γ for both high frequency and medium frequency modes resulted in vibronic resolved line shapes for both molecules. But it is also worth mentioning the role of the strongly coupled low frequency mode. In our previous study, it was found that strongly coupled low frequency modes are necessary to reproduce experimental fluorescence spectra of conjugated polymers.22,37 In this study, we also observed similar phenomenon, especially for the larger POA 6 molecule. As discussed above, the low frequency modes in POA 6 that are strongly coupled to optical transition are those related to twisting motions of conjugated backbone. Similar situation was also found in conjugated polymers.21,22 Owing to the presence of strong coupling between low frequency modes to optical

transitions, the full width at half maximum (FWHM) of the zero-phonon line (ZPL) for POA 6 absorption and fluorescence spectra becomes 0.10 and 0.16 eV, respectively. Clearly, these peaks are much broader compared to the corresponding values for TIPS−Anth absorption and fluorescence spectra with 0.04 and 0.09 eV, respectively.

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CONCLUSIONS The low-lying excited-states in both TIPS−Anth and POA 6 are revealed to be localized excitation by the TDDFT calculations. Presence of antiaromatic phenylene section has induced slight charge transfer characteristic in the S2 state of POA 6 while S1 state is less affected. The absorption and fluorescence spectra calculated from both TDDFT and MBO model are shown to reach good agreement with experiment. Further analysis based on the MBO model combined with TDDFT results indicate broader spectra of POA 6 are mainly related to stronger coupling between optical transition and the phonon modes with frequency 1000 cm−1) compared to TIPS−Anth, which can explain the small Stokes shift observed experimentally. Compared to TIPS−Anth, a significant coupling between an in-plane breathing mode at 1687 cm−1 for the antiaromatic phenylene segment and optical transitions of the first two excited-states is also observed for POA 6.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b09788. Cartesian coordinates of the optimized geometries using Jmol and a list of vibrational frequencies (ZIP) Excited-states energies and oscillator strengths of TIPS− Anth and POA 6 with solvent effect, brief description of the MBO model, and vector plots of normal modes with significant Huang−Rhys factors for both molecules (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(Y.J.) E-mail: [email protected]. Telephone: +65 64191352. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author would like to thank A*Star Computational Resource Center (A*CRC) for the support of computing resources.

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DOI: 10.1021/acs.jpca.5b09788 J. Phys. Chem. A XXXX, XXX, XXX−XXX