Vibronic spectra of organic electronic chromophores

Abstract

In this work, we illustrate how Time-Dependent Density Functional Theory (TD-DFT), that has become an everyday black-box tool for assessing the nature of electronic excited states, can be used to reach an accurate and thorough analysis of experimental optical spectra for a series of organic molecules recently proposed as building blocks for organic electronic devices. The results that yield insights regarding band shapes and extinction coefficients are shown to provide more relevant information than that obtained by the popular vertical approximation. Cases with several overlapping vibronic bands are also discussed. For the vast majority of treated molecules (10 out of 11) the agreement between the theoretical and experimental 0–0 energies and band topologies are really excellent, paving the way towards more refined theoretical designs of new organic electronic chromophores.

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1 Introduction

To complement experimental measurements, theoretical calculations have become increasingly popular tools for experimentalists. Without dispute, the most widely used theoretical model is Density Functional Theory (DFT), and, more specifically the extremely popular B3LYP approach.¹ While DFT is an adequate method to explore the geometry and reactivity of molecules in their electronic ground-states, the information given by DFT for the analysis of optical spectra or photochemical events remains insufficient. Indeed, DFT calculations provide molecular orbitals, but the use of HOMO and LUMO frontier orbitals to analyze optical signatures is not an appropriate choice. Indeed, even if the electronic transitions in the near UV and visible spectra imply almost essentially these frontier molecular orbitals rather than a complex blend, the HOMO–LUMO energy gaps provide very poor approximations of the maximal absorption (λ_max). This is due to the complete neglect of the electronic relaxation effects that always occur. These effects can be properly accounted for by TD-DFT,^2,3 which yields an approximate solution for the time-dependent (TD) Schrödinger equation. TD-DFT has become more and more used by non-specialists in the last five years to help analyze experimental spectra, and one can easily find numerous recent examples of the applications of TD-DFT in high-impact organic journals.^4–23 The large majority of these TD-DFT applications rely on the so-called vertical approximation: the transition energies to the lowest excited state(s) are computed with TD-DFT in a frozen ground-state geometry. This protocol has, however, several drawbacks: (i) absolutely no indication regarding the fluorescence properties is obtained; (ii) the neglect of the coupling terms between the vibrational and electronic motions (vibronic effects) does not allow the prediction of band shapes in a consistent way; (iii) vertical transition energies cannot be compared to experimental λ_max on a solid physical basis due to the neglect of both vibrational and geometry reorganization effects; and (iv) the same holds for the experimental molar absorption coefficients (ε) that cannot be directly obtained from vertical calculations.

During the last decade, there have been numerous theoretical developments aiming to improve TD-DFT, and these notably include the implementation of TD-DFT forces and Hessian that give, respectively, access to geometry optimization and vibrational analysis at the excited state.^24–27 In turn, these allow researchers to efficiently explore the potential energy surface of the excited states, to obtain fluorescence wavelengths and Stokes shifts, as well as to rapidly account for the most important vibronic couplings. Whilst these methodologies have already found applications for “real-life” structures,^28–40 they remain often unused by non-specialists. In the present work, we illustrate the applications of these new approaches taking as working examples several structures that have appeared in organic chemistry journals. More specifically, the molecules studied here have been selected as contributions devoted to the design of molecules with potential impacts in organic electronic devices. The accurate simulation of their optical signatures is therefore of prime importance. These compounds are represented in Fig. 1. We direct the interested reader to the original works (1,⁴¹ 2–4,⁴² 5 and 6,⁴³ 7–9,⁴⁴ 10 and 11 ⁴⁵) for synthetic and experimental details, that are clearly beyond our scope here.

Fig. 1 A representation of the set of molecules investigated in this work.

2 Computational details

All calculations have been performed with the latest version of the Gaussian 09 program package,⁵² applying a tight self-consistent field convergence criterion (10⁻⁹ to 10⁻¹⁰ a.u.) and a strict optimization threshold (10⁻⁵ a.u. on average forces). The same DFT integration grid, namely the ultrafine pruned (99 590) grid, was systematically used. Indeed, the potential energy surfaces of the excited states tend to be softer than their ground-state counterparts, and improved numerical accuracy is desirable to avoid possible instabilities. We have optimized both the ground and excited state geometries and determined their vibrational patterns using DFT and TD-DFT, respectively. Following ref. 51, we have used the 6-31+G(d) atomic basis set throughout but corrected our 0–0 energies for basis set errors using single-point 6-311++G(2df,2p) calculations. This yields converged data for low-lying excited states in organic molecules. We do not intend to discuss what is the most appropriate exchange–correlation functional here, a topic covered in details elsewhere,⁵³ and we have used Truhlar’s M06 global hybrid throughout the text,^54,55 as this hybrid often works well for organic compounds. In this work, we have modeled solvent effects through an implicit solvation approach, namely the Polarizable Continuum Model (PCM).⁴⁶ While for ground-state properties, the use of PCM is rather straightforward, PCM-TD-DFT calculations should be performed more carefully. Indeed, there exists two different PCM regimes for excited states: equilibrium (eq) and non-equilibrium (neq) limits.⁴⁶ In the former, the solvent has time to fully adapt to the new state of the chromophore and this approximation is adequate for slow phenomena (e.g., optimizing the geometry of the excited states). In the latter, only the electrons of the solvent have time to react to the change of states of the solute, a limit suitable for fast phenomena (e.g., vertical absorption and emission). For assessing the polarization of the cavity in the excited states, there exists several PCM schemes: linear response (LR),^47,48 corrected linear response (cLR)⁴⁹ and state specific (SS).⁵⁰ To make a long story short, the traditional LR approach is suitable for absorption spectra and for optimizing excited-state structures but cannot be rigorously applied to compute both emission and 0–0 energies of solvated species. We have therefore used the cLR scheme here to compute all excited-state energies. We direct interested readers to a recent contribution for a complete discussion of the computation of cLR 0–0 energies.⁵¹

Vibrationally resolved spectra within the harmonic approximation were computed using the FCclasses program (FC).^30,56,57 The reported spectra were simulated using a convoluting Gaussian function presenting a half width at half maximum (HWHM) that was adjusted to allow direct comparisons with experiments (typical value: 0.08 eV). A maximal number of 25 overtones for each mode and 20 combination bands on each pair of modes were included in the calculation. The maximum number of integrals to be computed for each class was first set to 10⁶. In the cases where convergence of the FC factor [≥0.9] could not be achieved with this number of integrals, a larger value (up to 10¹²) was used to pass the 0.9 limit.

3 Results

3.1 Molecule 1

Let us start with the nitrogen-bridged terthiophene 1 proposed by Mitsudo and coworkers.⁴¹ A comparison between the theoretical and experimental band shapes is shown in Fig. 2. The computed positions of the peaks are at 372, 354 and 337 nm. These fit well with the experimental data of 354, 339 and 320(sh) nm but for a nearly constant offset of ca. 17 nm.⁵⁸ Probably more impressive is the fact that the log(ε) computed for the two first peaks are 4.70 and 4.74, very close to the experimental data of 4.62 (for both peaks), nicely illustrating the accuracy of the vibronic calculations. For the record, as the absorption between 380 and 260 nm is due to only one electronic excitation, the vertical TD-DFT approximation level would have led to a single band at 357 nm with an oscillator strength of 0.9, and would have been much less relevant.⁵⁹

Fig. 2 Comparison between the experimental (red) and theoretical (blue) band shapes for the absorption spectra of 1 in dichloromethane. The intensities have been normalized to 1 in both cases, but no offset was applied on the energy scale. Experimental spectra adapted with permission from Mitsudo et al. Org. Lett. 2012, 14, 2702–2705, Copyright 2012 American Chemical Society.

As can be seen in Fig. 2, the agreement between the theoretical and experimental band shapes is very good, though the computed data slightly overshoot the relative intensities of the second and third bands, the errors being ca. 10%, which is the expected error range for relative vibronic intensities.⁶⁰ More importantly, the stick spectrum shown in Fig. 2 allows us to determine the vibrational modes (in the excited state here as we consider absorption) significantly contributing to the specific band shape of the system. Here, mode 71 is particularly important. This mode, that can be found in the ESI,† corresponds to the stretching at 1678 cm⁻¹ of the C–C bond of the central thiophene connecting the two pyrroles (see Fig. 1). This suggests that the central pattern of this chromophore is responsible for the band shapes, and that substitution of the external thiophene would only slightly affect this specific topology.

3.2 Molecules 2–4

Let us now continue with rather similar structures but bearing substituents on the sides and presenting a central thienothiophene unit, namely, dyes 2–4 of Bäuerle and collaborators (see Fig. 1). The position, intensity and shape of both the absorption and emission bands are significantly dependent on the side groups.⁴² A comparison between the theoretical and experimental data can be found in Fig. 3, and the agreement is obvious at first glance. The computed data restore the bathochromic shifts that occurred upon substitution for both the absorption and emission, and accurately reproduce the relative intensities related to the two phenomena. For absorption, the measured ε_max ratio is 1.0 : 1.8 : 3.1 for 2 : 3 : 4 whereas the corresponding TD-DFT values extracted from our vibronic calculations are 1.0 : 1.9 : 3.4. This is a much better agreement than the one provided by bluntly selecting the oscillator strengths from standard vertical calculations that would lead to a 1.0 : 1.5 : 2.2 ratio.

Fig. 3 Comparison between the experimental (insets) and theoretical band shapes for the absorption (top) and fluorescence (bottom) spectra of 2 (black), 3 (blue) and 4 (red), in dichloromethane. No offset or normalization was applied to the theoretical data. Experimental spectra adapted with permission from Wetzel et al. Org. Lett. 2014, 16, 362–365, Copyright 2014 American Chemical Society.

The topologies of the absorption bands are also nicely reproduced with a very clear vibronic progression for the absorption of 2 (the only one not quantitatively reproduced), a very intense shoulder for 3 and a shoulder with a ca. half intensity compared to the main peak for 4. For the emission, not only are the theoretical shapes correct, but also their evolution with respect to absorption is accurate. Indeed, the emission band presents a less marked vibronic progression for 2 and less intense shoulders compared to absorption for the two substituted dyes; these changes are restored by the theoretical data. In Fig. 4 we report the density difference plots for the three compounds that allow us to investigate the nature of the excited states on a more qualitative basis. As can be seen the states are delocalized and the cyano/aldehyde groups are mostly in red indicating that, as expected, these moieties act as electron acceptors. Therefore in 3 and 4 there is a partial charge transfer from the core to the extremities, but this effect is far from being exclusive or vastly dominating. This conclusion of moderate charge transfer therefore mitigates the qualitative conclusion obtained on the sole basis of the topology of the frontier orbitals.⁴² The integration of the density differences gives access to the amount of transferred charge,^61,62 that was found to be smaller in 2 (0.39e) than in 3 (0.46e) and 4 (0.45e).

Fig. 4 Density difference plots for (from top to bottom) 2, 3 and 4. The blue (or red) regions indicate the decrease (or increase) of the electronic density upon the absorption of light.

3.3 Molecules 5 and 6

We have also modeled the spectra of dithiophene-fused tetracyanonaphthoquinodimethanes, 5 and 6, two regioisomers (α and β, respectively) proposed by Yanai and coworkers.⁴³ We have replaced the large TIPS groups with hydrogen atoms to lighten the computational burden, but experimentally, the nature of the substituents (R in Fig. 1) has only a small impact on the absorption spectra.⁴³ The theoretical and experimental graphs are compared in Fig. 5 and it is again obvious that our TD-DFT protocol is successful, as it provides accurate relative wavelengths and intensities as well as correct band shapes for both dyes. Nevertheless, the absolute ε is overestimated by the calculations, and the difference in the intensity between the most intense bands of 5 and 6 is slightly underrated. The stick spectra for the two dyes are available in the ESI† as are the movies of the key vibrational mode (no 79) that is centered on the naphto core and is therefore similar for the two dyes. We note that the vertical calculations that provide the correct bathochromic displacements between the α (5) and β (6) derivatives incorrectly predict the ordering of the intensities: the associated oscillators strengths are 1.10 and 1.26, respectively (see the central panel in Fig. 5).

Fig. 5 Comparison between the theoretical (left: vibronic; center: vertical) and experimental (right) absorption spectra of 5 (blue) and 6 (red) in dichloromethane. No offset or normalization was applied to the theoretical data. Experimental spectra adapted with permission from Yanai et al. Org. Lett. 2014, 16, 240–243, Copyright 2014 American Chemical Society.

3.4 Molecules 7–9

These three small chromophores, that have been fully characterized experimentally in 2010,⁴⁴ constitute an interesting series due to the presence of several transitions that are close on the energetic scale, leading to the overlapping of bands, each possessing its own shape. In Fig. 6, the vibronic band shapes of the first four electronically excited states of 7 are shown, together with their total that can be compared to the experimental spectrum. Our calculations indicate that the second excited state yields a completely negligible contribution, and that the first excited state provides a relatively weak but broad and structured absorption in the 320–360 nm domain, whereas the shape of the most intense experimental band could be due to the combination of the third and fourth electronically excited states. It is the latter state that “transforms” the marked second vibronic peak of the third state to a shoulder (see the top panel of Fig. 6). We note nevertheless that the theoretical data misses some absorption at ca. 300 nm and overestimates the intensity of the absorption at longer wavelengths.

Fig. 6 Top: vibrationally resolved spectra computed for the first four states of 7. Bottom: comparison between the computed and measured absorption spectra; no offset was applied but the intensities were normalized to allow straightforward comparisons of the relative heights. The solvent is dichloromethane. Experimental spectra adapted with permission from Shinamura et al. J. Org. Chem. 2010, 75, 1228–1234, Copyright 2010 American Chemical Society.

For molecule 8 (Fig. 7), the situation is similar but there are only two excited states significantly contributing to the final band shapes, the first and the third states, respectively leading to absorption in the 320–370 and 260–310 nm domains. For 8, TD-DFT foresees no significant overlap between these individual contributions. In contrast to its sulfur counterpart, both absolute and relative intensities of the long-wavelength absorption are overshot by TD-DFT for the seleno 8. A comparison of 7 and 8 indicates that the replacement of sulfur atoms by selenium atoms induces, despite apparently similar band topologies, a variation in the nature of the individual components.

Fig. 7 Top: comparison between the experimental and theoretical data (no offset or normalization) for molecule 8. Bottom: comparison between the experimental and theoretical data (no offset or normalization) for molecule 9. All results are obtained in dichloromethane. Experimental spectra adapted with permission from Shinamura et al. J. Org. Chem. 2010, 75, 1228–1234, Copyright 2010 American Chemical Society.

9 is an example in which TD-DFT becomes less efficient. Indeed, one clearly notices in the bottom panel of Fig. 7 the presence of two bands above 280 nm, which are correctly restored by theory but the details of the spectra (both absolute and relative intensities of the two peaks, shapes of both bands, etc.) are not satisfying. Such an outcome can be related either to the selected exchange–correlation functional (M06), to the application of the harmonic vibrational approximation, or to specific effects (e.g. aggregation) not accounted for in the calculation.

3.5 Molecules 10 and 11

Finally, we have tackled two large butterfly-like π-conjugated systems proposed in 2014,⁴⁵ to confirm that the accuracy obtained for the rather compact dyes is maintained for more extended architectures. The results are displayed in Fig. 8 and once again, TD-DFT provides good insights, reproducing the 10 → 11 bathochromic shift of the first band, as well as the overlapping position of the second (or third) band of 11 and the first (or second) band of 10. The overall vibronic progression is also reasonably reproduced in both cases. Additional examples for three fused-thiophene derivatives can be found in the ESI.†

Fig. 8 Comparison between the experimental (inset) and theoretical band shapes for the absorption spectra of 10 (blue) and 11 (red) in tetrahydrofuran. Experimental spectra adapted with permission from Nakanishi et al. J. Org. Chem. 2014, 79, 2625–2631, Copyright 2014 American Chemical Society.

4 Conclusions

In this contribution, we have applied state-of-the-art TD-DFT approaches to mimic the spectral features (both absorption and emission spectra) of a series of conjugated structures recently proposed for applications in the field of organic electronics. Despite the approximations inherent to the use of TD-DFT, the agreement with experimental data is generally excellent; only one out of 11 cases leads to a poor match. This performance holds not only for spectroscopic properties (position of absorption and emission bands, molar extinction coefficient and band shape) but also for their evolution with chemical modifications (regioisomers, substitutions, etc.). Our vibrationally-resolved electronic spectra allowed a refined analysis of the experimental data (e.g. understanding overlapping bands, identifying key vibrational modes, etc.), which subsequently paves the way towards a more rational and efficient design of new molecules with specific spectral signatures.

This work also illustrates the limits of the usually-applied vertical TD-DFT approximation. For instance, we have found several examples in which the relative experimental ε cannot be understood by investigating the relative (vertical) oscillator strengths even in structurally similar chromophores. It is therefore our hope that this work will participate in the stimulation of the use of a more “modern” TD-DFT protocol outside the theoretical community.

Acknowledgements

A.C.E. thanks the European Research Council (ERC, Marches no 278845) and the Région des Pays de la Loire for his post-doctoral grant. D.J. also acknowledges both the ERC for the starting grant (Marches no 278845) and the Région des Pays de la Loire for the recrutement sur poste stratégique. Allocations of computation time from the GENCI-CINES/IDRIS (c2014085117), the C CIPL (Centre de Calcul Intensif des Pays de Loire), and the CEISAM’s Troy cluster are gratefully acknowledged.

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Footnotes

† Electronic supplementary information (ESI) available: Additional spectra and molecules, cartesian coordinates, movies of the vibrational modes. See DOI: 10.1039/c4ra10731d

‡ Present address: Centre Interdisciplinaire de Nanoscience de Marseille (CINam), UMR CNRS no 7325, Aix Marseille Université, Campus de Luminy, Case 913, 13288 Marseille Cedex 9, France.

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