Vis Spectra of Halogenated Tetraazaperopyrenes

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Understanding UV/Vis Spectra of Halogenated Tetraazaperopyrenes (TAPPs): A Computational Study Sebastian Hoefener, Benjamin Günther, Michael E. Harding, and Lutz H. Gade J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b12296 • Publication Date (Web): 14 Mar 2019 Downloaded from http://pubs.acs.org on March 15, 2019

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The Journal of Physical Chemistry

Understanding UV/Vis Spectra of Halogenated Tetraazaperopyrenes (TAPPs): A Computational Study Sebastian Höfener,∗,† Benjamin Günther,‡ Michael E. Harding,† and Lutz H. Gade∗,‡ †Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), P.O. Box 6980, D-76049 Karlsruhe, Germany ‡Anorganisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 270, 69120 Heidelberg, Germany E-mail: [email protected]; [email protected]

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ACS Paragon Plus Environment

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Abstract The UV/Vis absorption and emission spectra of halogenated tetraazaperopyrenes (TAPP) have been investigated employing second-order approximate coupled cluster (CC2) and (time-dependent) density functional theory (DFT). We have found that qualitative estimates of (vertical) absorption and excitation energies are possible within a single particle picture based on frontier orbitals, but the single particle picture is not sufficient to achieve quantitative accuracy. Going from the single-particle picture to the many-particle picture improves the agreement with experimental results but still no satisfying correspondence of theory and experiment is obtained. The comparison of CC2 and DFT-based methods reveals that the deviations from the experimental results cannot be explained by deficiencies of the electronic-structure methods but rather stem from neglecting vibrational effects. An agreement of theoretical results and experimental spectra is found for adiabatic excitation energies, which are given as energy differences of vibronic states, which are directly accessible using both theoretical and experimental methods. The most pronounced vibronic influence is found for the Stokes shifts, which are significantly overestimated by computing vertical electronic transitions only. Based on the vibronic contributions, the small Stokes shift of the TAPP compounds can be explained by the temperature dependence of the vibrationally resolved UV/Vis spectra.

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Introduction

Polycyclic aromatic compounds are used in various applications as functional dyes, which are employed as chemical sensors, in light emitting diodes, and as organic semiconductors in several electronic devices. 1 To achieve a deeper insight into the structural and electronic features of these molecular materials and to allow for a rational development of new functional molecules with tailored properties in particular with respect to energy and charge-transport properties, a detailed analysis using advanced theoretical methods is required. In recent years, the synthesis and structural as well as redox-chemical and photophysical properties of 1,3,8,10-tetraazaperopyrenes (TAPP) were reported, a new class of polyheterocyclic aromatics. Such TAPP derivatives have shown promising results as both fluorescence markers and organic semiconductors. 2–10 In particular, the tetrachlorinated as well as tetraiodinated TAPP-derivatives were found to display n-channel semiconducting behavior with electron mobilities of up to 0.17 cm2 /Vs. 4,8–11 Generally, TAPPs consist of a peropyrene core with four nitrogen atoms incorporated in the 1-, 3-, 8- and 10-positions. This leads to a stabilization of the lowest unoccupied molecular orbital (LUMO) energy and an increase of the electron affinity, both being important factors for the performance in organic field effect transistors (OFETs). 2 Treatment of the unsubstituted TAPP with an appropriate chlorine or bromine source led to the selective four folded ortho-functionalization of the peropyrene core, which has a significant influence on the photophysical and electrochemical properties. In order to fine-tune these properties further, substitution reactions of the TAPP-Br have provided access to a variety of differently substituted TAPP-derivatives. 4,11 Apart from the LUMO levels and the electron affinity, a dense packing pattern of the material is a critical parameter to assess the quality of an n-type semiconductor. The flat and rigid peropyrene core leads to dense packing motifs with intermolecular distances as short as 3.38 Ångstrom. Alteration of the substituents in 2- and 9-positions was found to have a significant influence on the packing pattern, while barely affecting the photophysical properties of the TAPP molecules, and it was found that 3



Figure 1: Tetraazaperopyrene molecules studied in this work with R = H or C3 F7 and X = H, F, Cl, Br, or I.

a perfluorinated propyl group as orientating substituent leads to the best performance in OFETs. 4 The TAPP molecules investigated are illustrated in Figure 1. Experimental results for absorption and emission spectra have been taken from Refs. 2,9 and are converted to eV for convenience. One approach to model absorption and emission spectra with theoretical methods is given by the linear-response framework, in which vertical excitations are computed as the response due to a time-dependent (or frequency-dependent) perturbation. This general scheme can be applied to both density-functional theory (DFT) 12 and wave-function based methods. 13 Although the DFT framework allows the computational modeling of molecules up to about 100 atoms conveniently, it cannot be systematically improved. This is particularly important in the case of excited states because of large errors encountered in the modeling of charge-transfer excitations. Such states can be addressed using hybrid schemes 14 or rangeseparated functionals such as the Coulomb-attenuation method (CAM) 15 , but nevertheless the accuracy has to be assessed for different molecule classes. 16,17 Wave function-based approaches do not suffer from this deficiency and allow for the accurate description of such charge-transfer states. 18 To identify possible problems due to charge-transfer character, the second-order approximate coupled cluster singles and doubles method (CC2) and the second-order algebraic diagrammatic construction method (ADC(2))

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are also employed in the present work. In both CC2 and ADC(2) excitation energies are correct to second order and thus yield similar results in many cases while for conical intersections between states of the same symmetry significant qualitative deviations are observed. 19 Additionally, deviations between these methods as large as 0.5 eV have been reported 20 so that we compare these two methods in the present work. This comparison cannot be considered a strict but rather a qualitative measure. However, even for (non-symmetric) systems with about 50 atoms, these calculations can become tedious, in particular if structures need to be optimized or even second derivatives are required. In many cases, absorption and emission spectra are computationally modeled based on the vertical transition energies taking only the electronic contribution of the wave function into account, which gives rise to results which are not observable experimentally. 21 Experimental spectra, however, do not only include the electronic contribution but also vibrational contributions, see for example Refs. 22–27. A quantity that allows for a direct comparison between experimental values and computed data is thus the adiabatic transition energy, which is obtained computationally as the energy difference of the optimized ground state and the optimized excited state geometries including the zero-point vibrational energy (ZPVE), respectively. The knowledge of the (experimental) absorption and the emission spectra and taking into account the ZPVE allows the calculation of approximate adiabatic transition energies. In order to simulate the actually observed vibrationally resolved spectra, however, not only the zero-point vibrations but also higher vibrational levels have to be included as well, which requires to compute at least the Franck-Condon (FC) factors. 25,28,29 The FC spectra may thus be obtained for different temperatures and provide insight into the broadening of absorption bands in experimental spectra, which stem from the increased occupation of higher-lying vibrations. Taking these factors into account allows for a direct comparison of the theoterically modeled electronic spectra with the absorption or emission spectra obtained experimentally.

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The article is organized as follows. First, we present the computational details of our calculations and in the results and discussion section the accuracy of different methods is assessed for the case of the unsubstituted TAPP-H (R = H) molecule using CC2 as a reference method. Based on these findings, results for absorption and emission spectra as well as adiabatic excitation energies (0–0 transitions) are presented employing the B3LYP 30–33 and PBE0 34,35 functionals.

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Methods

2.1

Electronic structure methods

For all calculations the TURBOMOLE program package V7.2 was used employing default convergence criteria for all methods, i.e., scfconv 6 in case of DFT and scfconv 7 (together with denconv 1d-7) in case of CC2. 36–38 Geometry optimizations were considered converged if the change in the Cartesian gradient norm was below 10−3 , i.e. gcart 3, and the threshold for the response equations was 10−5 , i.e. rpapconv 5. Grid m3 and the def2-TZVPP basis has been used for all calculations unless stated otherwise. 39,40 For the Hartree-Fock and DFT calculations the RI approximation was used to compute the two-electron Coulomb term (RIJ). 41,42 For the second-order approximate coupled cluster singles and doubles (CC2) and the second-order algebraic diagrammatic construction method (ADC(2)) the RI approximation was applied as well. 19,43 However, for all methods the prefix RI is dropped in the following as the RI approximation does not lead to significant numerical errors when the standard auxiliary basis sets are used. All geometries were optimized using B3LYP and PBE0 if not stated otherwise and the minima were confirmed by computing second derivatives, which were computed analytically for electronic ground states using the aoforce 44 module, while second derivatives for electronically excited states were computed semi-numerically from analytical first derivatives using the Turbomole modules egrad 45 and NumForce. CC2 geometry optimizations and 6


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semi-numerical second derivatives of excited states were not feasible for halogen substituted TAPPs with the computational resources available to us. The target excited state was chosen to be the one within the first 5 excitations with the largest oscillator strength. As the target excited state is not always the lowest singlet state, a careful analysis of the excited-state calculations was required in all cases. The largest oscillator strengths for all TAPP-X (R=C3 F7 ) compounds exhibit values of about 0.7 to about 1.1 for B3LYP, PBE0, and CC2. Radiative lifetimes estimated from the Einstein transition probabilities 46–48 are provided in the SI. If the radiative lifetime is long, competitive non-fluorescent decay pathways can dominate. In the present case no long radiative lifetimes were obtained. Due to the lack of full potential-energy surfaces (PES), the estimates of the radiationless decay times is beyond the scope of the present article. In order to obtain accurate geometries and frequencies for the Franck-Condon simulations, the halogenated TAPP-X without fluorinated alkyl substituents in 2-and 9-positions, i.e. with R=H, were optimized with tightened thresholds. For these ground-state as well as excited-state DFT optimizations the PBE0 functional was used together with Turbomole’s grid 4, while taking into account the derivatives of the quadrature weights. The SCF iterations were considered converged if the energy variation was below 10−9 (scfconv 9) and the norm of the density change was less than 10−9 (denconv 1d-9). Additionally, the point group D2h was used and the threshold for the response equations was 10−9 (rpaconv 9). The geometry was considered converged if the cartesian gradient norm was below 10−5 , i.e. gcart 5.

2.2

Franck-Condon simulations

In the present work, the HOTFCHT 29 program, which takes into account vibrational mode mixing effects (Duschinsky), 49 has been used for the calculation of the vibronic (FranckCondon) 50–52 spectra of polyatomic molecules at nonzero temperatures. In this program, 7



the number of calculated integrals is reduced by the implementation of the approach developed by Berger and co-workers. 25 This involves a prescreening of Franck-Condon profiles enabling the assessment of the discrepancies induced by the neglect of overtones beyond a given quantum number and of integrals with a high (given) number of simultaneously excited vibrational modes. Although transitions originating from vibrationally excited levels in the initial state (hot bands) are taken into account, anharmonic vibrational effects are neglected. The calculation of electronic spectra may be achieved either by time-dependent approaches or in terms of Franck-Condon overlaps of the initial nuclear wave functions with time-independent vibrational eigenfunctions of the final electronic state. For low resolution and very high densities of states, i.e. for large molecules at high temperatures, the use of time-dependent wave packets for the computation of spectra is particularly advantageous, whereas for high resolution and low temperatures time-independent approaches might be preferable. 53,54 In our computations, both approaches (time-dependent and timeindependent) were used for all spectra, whereas the time-dependent approach was used for the comparisons with experiment.

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Results

In this section, the vertical absorption and emission energies of the TAPP molecules obtained by DFT and wave function-based methods are discussed. Based on these results, the adiabatic excitation energies (0–0 transitions) are compared with experimental values. The section concludes with an analysis of the Stokes shift for which the Franck-Condon factors need to be considered.

3.1

Electronic properties in the ground state

In order to assess the accuracy of the employed PBE0 and B3LYP functionals for the target TAPP compounds, we start with the comparison of ground-state geometries computed with

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Figure 2: Comparison of the CC2 (aquamarine) and PBE0 (red) ground-state geometry of TAPP (R=H). these functionals with those obtained with the wave function-based CC2 and ADC(2) methods. For all compounds investigated an acceptable agreement of the different approaches has been obtained, which may be largely due to the rigidity of the aromatic ring system of the TAPPs. For example, a direct comparison of the PBE0 and CC2 ground-state geometries is given in Figure 2 for the TAPP (R=H) molecule. Comparing the CC2 energies computed at the CC2 and the DFT ground-state geometries, a difference as low as 0.05 eV is found for the ground-state energies of the example depicted in Figure 2, supporting the aforementioned qualitative analysis and indicating sufficiently accurate DFT geometries. While PBE0, B3LYP, and CC2 methods are established methods for the modeling of molecular properties in the many-body picture, yielding accurate data such as electronic spectra, regular ground-state DFT can also be used to qualitatively estimate molecular properties in the single-particle picture. The single-particle picture is frequently used to understand trends obtained for a fixed molecular frame, as in the TAPPs, while varying substituents, such as halogen atoms in the present case. In Tab. 1 the orbital energies of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are enlisted for the different TAPP compounds investigated in this work. As far as the ground-state geometry is concerned, the table reveals 9



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Table 1: Orbital energies of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) in eV for TAPP (R=H) and TAPP-X (R=C3 F7 ) compounds.

TAPP-X (R = H) TAPP-X (R = C3 F7 )

X H H F Cl Br I

HOMO –6.24 –6.76 –6.88 –6.81 –6.79 –6.63

Ground-state geometry B3LYP PBE0 a LUMO ∆ HOMO LUMO –3.25 2.99 –6.52 –3.24 –3.77 2.99 –7.02 –3.74 –4.08 2.80 –7.09 –4.01 –4.13 2.68 –7.03 –4.09 –4.15 2.64 –7.02 –4.12 –4.09 2.54 –6.88 –4.08

Excited-state geometry B3LYP PBE0 b X HOMO LUMO ∆ HOMO LUMO TAPP-X (R = H) H –6.13 –3.46 –2.67 –6.39 –3.46 TAPP-X (R = C3 F7 ) H –6.65 –3.98 –2.67 –6.90 –3.96 F –6.76 –4.26 –2.50 –6.96 –4.20 Cl –6.70 –4.30 –2.40 –6.92 –4.28 Br –6.69 –4.33 –2.36 –6.91 –4.31 I –6.55 –4.27 –2.28 –6.79 –4.27 a Absorption in the single-particle picture: ∆ = LUMO − HOMO . b Emission in the single-particle picture: ∆ = HOMO − LUMO .

∆a 3.28 3.28 3.08 2.94 2.90 2.80

∆b –2.93 –2.94 –2.76 –2.64 –2.60 –2.52

that for both PBE0 and B3LYP the LUMO energies agree within about 0.05 eV. However, the HOMO energies differ by about 0.2 eV between the two functionals, leading to a variation in the HOMO-LUMO gaps of about 0.25 eV. However, for the series of halogenated derivatives, ranging from fluorine to iodine, a gradual decrease in the HOMO-LUMO gap ∆ by 0.45 eV and 0.48 eV was found for B3LYP and PBE0, respectively, cf. Refs. 9,55. Such an agreement is remarkable and indeed encourages a qualitative estimate of such trends. Table 1 also includes the computed HOMO and LUMO values computed at the excitedstate geometries, vide infra. In order to indicate that for those geometries the HOMO-LUMO gap can be used to estimate the fluorescence emission, a negative sign is included in the HOMO-LUMO gap ∆. After geometry relaxation in the lowest excited state using timedependent density-functional theory (TDDFT), the HOMO energies are shifted by about

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+0.1 eV for both B3LYP and PBE0, while the LUMO energies are shifted by -0.2 eV for both B3LYP and PBE0, leading to an average decrease of the HOMO-LUMO gap of about 0.3 eV, which can be interpreted as the geometric contribution to the Stokes shift, i.e. the difference between the positions of the band maxima of the absorption and emission spectra due to structural changes when going from the ground-state to the excited state. Interestingly, this shift is indeed of the same order of magnitude as the results from the many-body picture discussed in the next section.

3.2

Vertical electronic transitions

In this section, absorption spectra as obtained after geometry optimization in the electronic ground state are discussed. Results for the unsubstituted TAPP-H (R=H) are given in Table 2. Results for the TAPP-X (R=C3 F7 ) with X = H, F, Cl, Br, and I are given in Table 3. For all TAPP compounds investigated in the study the ordering of the states was found to depend on the quantum-chemical method used and the oscillator strength was used to identify the target state. Since the comparison of the computed values should be made with the experimentally observed intense bands, those excited states with the largest oscillator strengths were selected in this work, independent of the actual ordering of the Table 2: Lowest singlet vertical excitation energy of TAPP (R=H) compounds in eV. Values in parentheses denote the state label.

a

c

Absorptiona Emissionb Stokes a Response method B3LYP PBE0 B3LYP PBE0 B3LYP PBE0 DFTc 2.91 (S3 ) 3.01 (S3 ) 2.69 (S1 ) 2.77 (S1 ) 0.22 0.24 CC2 3.21 (S1 ) 3.24 (S1 ) 2.97 (S1 ) 2.98 (S1 ) 0.24 0.26 ADC(2) 3.17 (S1 ) 3.20 (S1 ) 2.90 (S1 ) 2.92 (S1 ) 0.27 0.28 d,e d Exp. 2.86 2.75–2.80 0.06–0.10 Lowest singlet vertical excitation energy. The selected state, based on the oscillator strength with a value of 0.7 to 1.1, is given in parenthesis. b Vertical de-excitation energy from lowest singlet state. (TD-)B3LYP for (TD-)B3LYP geometries, (TD-)PBE0 for (TD-)PBE0 geometries. d Experimental value in toluene. e 434 nm.

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excited states. For the TAPP parent molecule (R=H) TD-DFT employing the B3LYP functional yielded an absorption energy of 2.91 eV, which represents a deviation of 0.05 eV compared to the experimental value of 2.86 eV, see Table 2. The value for the emission band of 2.69 eV, has a deviation of about 0.1 eV when compared to the experimental value of 2.80 eV. Using the PBE0 functional, the deviation in the absorption increases to about 0.15 eV, while the deviation in the emission decreases significantly. However, single-point CC2 calculations at the PBE0 geometry show a deviation of more than 0.2 eV. In order to exclude possible problems related to the CC2 model, Table 2 also contains ADC(2) vertical transition energies computed at the same DFT geometries. The ADC(2) transition energies agree significantly better than 0.1 eV with the CC2 energies, which can be considered to be sufficiently accurate and we believe that the wavefunction methods chosen can be considered adequately accurate for the present study. This conclusion is supported additionally when using the CC2 method to compute the geometry, which yields an absorption energy of 3.1 eV, see Table 4 and a fluorescence energy of 2.86 eV for this TAPP-H (R=H) molecule, as these values agree to better than 0.1 eV to the CC2 transitions computed at the DFT geometries. However, all methods give a Stokes shift of about 0.25 eV, which significantly deviates from the experimentally observed Stokes shift of about 0.06–0.10 eV, see Table 2. The theoretical methods are thus sufficiently consistent in their results but give rise to a pronounced and seemingly arbitrary difference with respect to the experimental results. In case of TAPP-H (R=C3 F7 ), see Table 3, the absolute values and thus also the deviations of experimental and computed absorption energies barely differ from those of the parent molecule TAPP-H (R=H), see Table 2. This can be understood readily as the new fluorinated alkyl substituents are not involved in the excited state. To illustrate this, the difference density is plotted in Figure 3 for both compounds for the electronic transition from the ground state to the first excited state. It is apparent that no difference density is located on either substituent, explaining the negligible influence.

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Figure 3: Difference density upon lowest singlet excitation for TAPP-H (R=H) and TAPPH (R=C3 F7 ), respectively, displayed using an isovalue of ±0.002, showing that the different substituents R do not influence the excited state.

Table 3: Lowest singlet vertical excitation energy of TAPP-X (R=C3 F7 ) compounds in eV. Values in parentheses denote the oscillator strengths (dimensionless). Absorption Emission Stokes Method B3LYPa PBE0b B3LYPa PBE0b B3LYPa PBE0b DFTc 2.89 (0.6) 2.98 (0.7) 2.67 (0.7) 2.75 (0.7) 0.22 0.23 CC2 3.17 (0.9) 3.19 (0.9) 2.93 (0.9) 2.94 (1.0) 0.24 0.25 H ADC(2) 3.13 (0.9) 3.26 (0.9) 2.87 (1.0) 2.89 (1.0) 0.26 0.37 Exp. 2.84 2.77 0.07 c DFT 2.72 (0.6) 2.80 (0.7) 2.53 (0.7) 2.60 (0.7) 0.19 0.20 CC2 2.97 (0.9) 2.99 (0.9) 2.75 (0.9) 2.76 (1.0) 0.22 0.23 F ADC(2) 2.93 (0.9) 2.94 (0.9) 2.69 (1.0) 2.70 (1.0) 0.24 0.24 Exp. 2.74 2.63 0.11 DFTc 2.59 (0.7) 2.67 (0.7) 2.40 (0.7) 2.46 (0.7) 0.19 0.21 CC2 2.88 (0.9) 2.88 (0.9) 2.66 (0.9) 2.66 (1.0) 0.22 0.22 Cl ADC(2) 2.83 (0.9) 2.84 (0.9) 2.60 (1.1) 2.60 (1.0) 0.23 0.24 Exp. 2.64 2.59 0.05 c DFT 2.53 (0.7) 2.62 (0.7) 2.35 (0.7) 2.41 (0.7) 0.18 0.21 CC2 2.83 (0.9) 2.84 (0.9) 2.61 (0.9) 2.62 (1.0) 0.22 0.22 Br ADC(2) 2.78 (0.9) 2.79 (0.9) 2.55 (1.1) 2.55 (1.1) 0.23 0.24 Exp. 2.61 2.55 0.06 DFTc 2.39 (0.6) 2.48 (0.7) 2.21 (0.7) 2.29 (0.7) 0.18 0.19 CC2 2.74 (0.9) 2.74 (0.9) 2.54 (0.9) 2.54 (1.0) 0.20 0.20 I ADC(2) 2.70 (0.9) 2.70 (0.9) 2.48 (1.0) 2.47 (1.0) 0.22 0.23 Exp. 2.51 2.39 0.12 a Geometry obtained using (TD-)B3LYP/def2-TZVPP. b Geometry obtained using (TD-)PBE0/def2-TZVPP. (TD-)B3LYP for (TD-)B3LYP geometries, (TD-)PBE0 for (TD-)PBE0 geometries.

TAPP-X

c

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Table 4: TAPP absorption energies in eV obtained using CC2. Values in parentheses denote the oscillator strengths (dimensionless). Compound TAPP (R=H) H TAPP-X H (R=C3 F7 ) F Cl Br I

Absorption 3.12 (0.8) 3.08 (0.9) 2.88 (0.8) 2.77 (0.9) 2.71 (0.9) 2.61 (0.9)

For the compounds with X = F, Cl, Br, or I and R=C3 F7 , i.e. the halogenated TAPPs with fluorinated alkyl substituents, a similar picture compared to X=H is obtained. B3LYP and PBE0 yield results that are similar to the experimental values. For example, the absorption energy of TAPP-Cl (R=C3 F7 ) computed with PBE0 seems to exhibit a deviation of only 0.03 eV with respect to the experimental results, while the emission energy exhibits a significantly increased deviation of almost 0.15 eV. Additionally, carrying out single-point wave function calculations employing the DFT geometries does not lead to a more balanced description but instead yields increased deviations when compared to the experimental results. Similar to the TAPP-H (R=H) compound, for the compounds with alkyl chains no significant improvement is observed by applying the wavefunction methods. Table 3 shows that, in agreement with TAPP-H (R=H), the CC2 and ADC(2) results agree better than 0.1 eV to each other while deviation of about 0.2 eV can be obtained with respect to the experimental results. In order to investigate the discrepancy of theoretical and experimental results further, the ground-state geometries of the halogenated TAPPs (R=C3 F7 ) have been optimized using the CC2 method. The results of excitation energy calculations using CC2 at CC2 geometries are provided in Table 4. The results show that the deviations from experiment are slightly decreased but still no significant improvement over DFT is obtained, e.g. for TAPP-I (R=C3 F7 ) the experimental absorption band maximum is measured to be 2.51 eV, while PBE0 yields 2.48 eV and CC2 2.61 eV at the CC2 ground-state geometry.

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X= H F Cl Br I

PBE0 2.86 2.70 2.57 2.52 2.38

with ZPVEa PBE0 B3LYP PBE0 CC2 ADC(2) B3LYP CC2 ADC(2) ZPVE PBE0 CC2 ADC(2) 2.86 2.82 2.78 2.86 2.82 –0.00 2.86 2.86 2.82 2.68 2.63 2.64 2.66 2.61 +0.15 2.85 2.83 2.78 2.67 2.62 2.52 2.66 2.61 +0.11 2.68 2.78 2.73 2.61 2.56 2.46 2.61 2.56 +0.11 2.62 2.72 2.67 2.41 2.36 2.32 2.51 2.46 +0.11 2.49 2.52 2.47 a Computed using with (TD-)PBE0 at the (TD-)PBE0 geometries. b Experimental values, see Refs. 4,9. w/o ZPVE

Exp.b 2.83 2.71 2.62 2.58 2.46

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 5: TAPP-X (R=C3 F7 ) 0–0 transition energies in eV.

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Figure 4: Vibrational spectra for TAPP-H (R=H) in the harmonic approximation obtained from PBE0. Figures for the other compounds are given in the SI.

For the absorption and emission values discussed so far, a comparison of experimental and computational results show that a qualitative agreement is obtained but the deviations with respect to experiment are not systematic. A clearer picture is obtained from the Stokes shifts because these exhibit large deviations with respect to experiment: while the experimentally determined Stokes shifts are about 0.1 eV or lower in all cases, the computations result in Stokes shifts of about 0.2 eV or even larger. The average deviation in the computed Stokes shift is therefore about 0.15 eV, which corresponds to a relative error of about 100%. The comparison of computed vertical transitions and experimentally-obtained band maxima discussed above are not systematic and thus not satisfying. This holds in particular for the Stokes shifts, which exhibit large deviations that cannot be explained using the theoretical methods used so far. We thus hypothesized that neglect of the vibronic contributions were responsible for the deviations observed rather than deficiencies in the electronic structure models. Because only adiabatic excitation energies can be compared, which are differences of vibronic states and therefore directly observable, they are investigated in the following.

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Figure 5: Selected bending (left) and symmetric stretching (right) vibrations with associated vibrational frequencies of 44 cm-1 (5 meV) and 283 cm-1 (35 meV), respectively, of TAPP-H (R=H) in the harmonic approximation obtained from PBE0 in the electronic ground state.

3.2.1

0–0 transition energies

While vertical transition energies are straightforward to calculate there is no direct analogy with experimental results. However, direct comparison is possible for adiabatic excitation energies, which correspond to energy differences of vibronic states and are directly observable in experiments. The vibrational levels in the harmonic approximation are displayed in Figure 4 with their corresponding harmonic IR intensities for the TAPP-H (R=H) compound for the ground state and the excited state. The figure also shows that for these rigid TAPP compounds ground and excited states display significant similarities, at least qualitatively. The first eight bands correspond to bending vibrations, while vibration nine is a symmetric stretching vibration. Two of those vibrations are shown in Fig. 5. Results for computed 0–0 transitions are given in Table 5, for which the harmonic ZPVEs were computed using the PBE0 functional. Notably, the computed transitions using the B3LYP functional including ZPVEs are in good agreement with the results compiled in the table. To give an example, the ZPVE for TAPP-Cl (R=C3 F7 ) is computed to be 0.10 eV using B3LYP, which exhibits a very small difference of 0.01 eV to the PBE0 result, see Table 5. The ZPVE obtained from PBE0 is employed also for the CC2 and ADC(2) values computed at the PBE0 geometries. We also find that the PBE0 functional performs well in terms of both absolute and relative errors compared to experimental results. For the 0–0

17



transitions the agreement is better than 0.06 eV for all cases but TAPP-F (R=C3 F7 ), for which an error of about 0.15 eV is observed. The wave function methods CC2 and ADC(2) agree within 0.05 eV and all results agree well within 0.1 to 0.2 eV. The agreement of experimental and computed 0–0 transitions despite the increased deviations for the difference of absorption and emission values, i.e. the Stokes shift, supports the hypothesis that the increased deviations for vertical transitions are not rooted in the electronic structure methods but only in the lack of vibronic contributions, as mentioned above. This observation pointed us to study the vibronic effects in these compounds by computing the Franck-Condon factors and, based on this, simulating the vibronically resolved spectra.

3.3

Simulation of vibrationally-resolved transitions

So far, all results including geometries, excitation energies, and ZPVEs, were obtained for R=H or R=C3 F7 , depending on the molecular system investigated. In the following, however, the simulated spectra have been computed only using R=H, in particular in case of the halogenated TAPPs, due to the computational demands of the vibronic calculations at finite temperatures. However, all simulated spectra are shifted to the computed 0-0 transitions, in order to obtain simulated spectra that are based on theoretical results only. All absorption spectra are plotted in red, all emission spectra are plotted in blue. In the main article only selected figures are presented, while figures for all compounds can be found in the SI. Simulated spectra for the TAPP-H (R=H) and TAPP-I (R=H) molecules are given in Figure 6 at zero temperature using the time-dependent and the time-independent methods. For higher temperatures, such as room temperature, the time-dependent method was chosen to compare the simulated envelope spectra to experimental spectra. In the vertical approach the Stokes shift is given as the difference of the vertical transition energies at the optimized ground-state geometry and the optimized excited-state geometry, see Tables 2 and 3. However, in the simulated spectra the Stokes shift is given as the difference of bands with large Franck-Condon factors. Figure 6 shows that the difference in 18


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Figure 6: Simulated spectra using the time-dependent method (envelope spectra), employing 100 cm-1 full width at half maximum (FWHM) for the Lorentzian convolution function, and the time-independent method (stick spectra) at zero temperature for TAPP-H (R=H) (left) and TAPP-I (R=H) (right). The numbers in parentheses denote the computed adiabatic excitation energy, see Table 5.

the bands is exactly zero for both TAPP-H (R=H) and TAPP-I (R=H) at zero temperature since the spectra are dominated by the 0–0 transition. Simulated spectra obtained for the other TAPP-X (R=H) compounds are given in the SI. While simulated Stokes shifts of zero represent a significant change compared to the Stokes shifts of about 0.2 eV using the vertical transition energies only, a deviation of about 0.05–0.1 eV with respect to the experimental results is still found. Assuming that the vibronic contributions are significant, it is likely that temperature effects must be taken into account. In comparison to 0 K at which only the zero-point vibration is active, higher vibrational states are also being populated with increasing temperature. In Fig. 7, the vibronic transitions for the TAPP-H (R=H) compound are displayed, computed with the time-independent method at different temperatures. The figure shows that in case of zero temperature only the 0–0 transition itself has a strong intensity and the second peak (with significant lower intensity) is located at about 282 cm-1 which corresponds to the lowest symmetric stretching vibration. A similar picture is obtained for the emission, where the second peak is located at about 283 cm-1 also due to the lowest symmetric stretching vibration. Increasing the temperature to 100 K and 300 K leads to two main effects. First, the

19



Figure 7: Simulated emission (left) and absorption (right) spectra around the vibronic transition involving the symmetric stretching vibration, using the time-independent method at 0 K (solid black bars), at 100 K (solid boxes), and at 300 K (light boxes) temperature for TAPP-H (R=H). The full spectra for all TAPP-X compounds are given in the SI. In case of absorption, vibrations of the final state yield a positive shift, i.e. an increase of the transition energy, and vibrations of the initial state yield a negative shift, i.e. a decrease of the transition energy. The signs are inverted in case of emission.

pure 0–0 transition is shifted slightly in energy due to a population of the vibrational states of the initial electronic state. Second, the relative intensity of the 0–0 transition is reduced since the intensity of the lowest symmetric stretching vibration increases. The population of the additional vibrational contributions eventually leads to a shift in the maximum of the simulated absorption or emission spectra, see Fig. S15 (for TAPP-H) and Figs. S16 to S19 (for the halogenated compounds) in the SI. In the following, the time-dependent method is therefore used for the simulation of envelope spectra at 300 K. Simulated envelope spectra at finite temperatures obtained using the time-dependent method are displayed in Figures 8 and 9. These calculations reveal that the Stokes shift is slightly increasing with temperature and an excellent agreement with experimental results is found (less than 0.1 eV). In order to illustrate this, the spectra at 300K in Figures 8 and 9 are directly compared with the experimental spectra, see Figures 10 and 11. In particular for TAPP-H (R=H) the agreement is striking. In Figure 10, the experimental results are in close agreement with the purely theoretical results. In particular, neither results were shifted or scaled (except for the scaling of the intensity of the largest bands to 1.0), and the 20


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Figure 8: Simulated spectra using the time-dependent method at different temperatures for TAPP-H (R=H) using 500 cm-1 full width at half maximum (FWHM) for the Lorentzian convolution function. The difference of the maxima at 300 K is 0.06 eV.

Figure 9: Simulated spectra using the time-dependent method at different temperatures for TAPP-F (R=H) using 500 cm-1 full width at half maximum (FWHM) for the Lorentzian convolution function. The difference of the maxima at 300 K is 0.02 eV.

21



Figure 10: Comparison of the experimental spectra for TAPP-H (R=C3 F7 ) and the simulated spectra for TAPP-H (R=H) at 300 K using 100 cm-1 (left) and 500 cm-1 (right) full width at half maximum (FWHM) for the Lorentzian convolution function.

Figure 11: Comparison of the experimental spectra for TAPP-Cl (R=C3 F7 ) and the simulated spectra for TAPP-Cl (R=H) at 300 K using 100 cm-1 (left) and 500 cm-1 (right) full width at half maximum (FWHM) for the Lorentzian convolution function.

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position of the theoretical spectra is given by the computed 0–0 transition. In case of the halogenated TAPP compounds experimental spectra are only available with the fluorinated alkyl substituents (R=C3 F7 ) in the axial positions and the comparison with the simulated spectra obtained for hydrogen sustituents (R=H) is therefore less direct. Additionally, no anharmonicities are taken into account in the present work. Nevertheless, in order to compare these spectra, the experimental and computed spectra were shifted relative to the 0–0 transition energy, see Figure 11. Given these results, it can therefore be concluded that the experimentally obtained absorption and emission spectra need to be simulated using vibronic methods at finite temperatures.

4

Conclusions

In the present work, tetraazaperopyrene (TAPP) compounds with different substituents have been investigated with quantum chemical methods for the theoretical modeling of electronic and vibrational spectroscopy to gain a detailed understanding of both electronic and vibrational contributions to the UV/Vis absorption and emission spectra. Concerning vertical electronic transition energies, the quantum chemical methods employed show a good consistency. For the TAPP compounds, the results of the B3LYP and PBE0 functionals are in good agreement with those obtained with the approximate secondorder wavefunction methods. Furthermore, estimating the trends for different substitution patterns is possible but only meaningful if relative energies are compared. Despite the good agreement of the theoretical methods no acceptable agreement with experimentally obtained spectra was obtained without including vibrational effects. In a first step, the 0–0 transition energies improved the agreement with the experimental results significantly. Computing the Franck-Condon factors allowed to simulate vibrationallyresolved spectra showing a significantly reduced Stokes shift for the systems under study and excellent agreement with the experimental findings.

23



The analysis of the TAPP compounds presented allows to draw two main conclusions: 1) The calculation of purely electronic contributions only is not sufficient in order to obtain an acceptable agreement with experimental results and vibrational effects need to be included. 2) For the calculation of the purely electronic contributions (time-dependent) DFT employing the PBE0 functional is sufficient as these results are in good agreement with the wave function based CC2 calculations. The present study prepared the ground for an analysis of dimer properties such as resonance coupling which is the subject of further research aimed at understanding charge and energy migration of TAPP derived materials.

5

Supporting Information

IR spectra (Fig. S1 to S4), simulated spectra at 0 K (Fig. S5 to S7), spectra obtained from the time-dependent method for 0 K, 100 K, 200 K, and 300 K (Fig. S8 to S10), comparison of experimental spectra and simulated spectra at 300 K (S11 to S14), and spectra obtained from the time-independent method for 0 K, 100 K, and 300 K (Fig. S15 to S19).

6

Acknowledgments

This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) through SFB 1249 ”N -Heteropolycycles as Functional Materials” (Projects A02 and B07).

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Graphical TOC Entry

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Vis Spectra of Halogenated Tetraazaperopyrenes

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