Spectral Signatures of Perylene Diimide Derivatives: Insights From

Article pubs.acs.org/JPCC

Spectral Signatures of Perylene Diimide Derivatives: Insights From Theory Ymène Houari,† Adèle D. Laurent,† and Denis Jacquemin*,†,‡ †

Laboratoire CEISAM - UMR CNR 6230, Université de Nantes, 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France Institut Universitaire de France, 103, bd Saint-Michel, F-75005 Paris Cedex 05, France

‡

S Supporting Information *

ABSTRACT: Perylene diimides and related compounds (naphthalene diimides, anthracene diimides, etc.) are one of the most important classes of organic dyes. Therefore, the prediction and the rationalization of both their transition energies and the particular shape of their absorption and emission spectra is essential to improve their design. Here, we report the simulations of both adiabatic and vibronic signatures of a series of perylene diimide derivatives with a state-of-the-art timedependent density functional theory (TD-DFT) approach. First, the 0− 0 energies have been computed and compared to experimental data. In a second stage, the determination of vibronic shapes has been performed to shed light on the vibrational modes implied in the experimental band topologies. Both anharmonicity and functionnal effects are also discussed. It turns out that theory consistently reproduced 0−0 energies but does not always yield band shapes in perfect match with experiment. In a last stage, new structures are designed, and it is shown that a full push effect is more effective than a push−pull strategy for the present class of molecules.

■

INTRODUCTION Perylene diimides (PDIs) have attracted an increasing interest during the past decades, and this can be traced back to their valuable properties, e.g., high electron affinities, large electron mobility, excellent thermal and oxidative stabilities, high molar absorptivities, and quantum yields of fluorescence. 1−12 Consequently, several exciting applications have emerged including photovoltaic cells,13−27 photochromic materials,28,29 optoelectronic devices,30−33 chemosensors,34,35 fluorescence probes in biological media,36 as well as other original applications in a wide range of fields.37−47 To optimize their performances and to develop new diimide structures, several synthetic efforts have been made, e.g., extending the πconjugated segments, using nucleophilic substitutions, designing asymmetric cores, and so on. PDIs can be synthesized in several manners.1−6,48,49 Typically, core-unsubstituted naphthalene diimides (NDIs) only absorb in the UV region,50,51 whereas core unsubstituted PDIs possessing a more extended π conjugated path are red dyes with maximum absorption around 530 nm and emission bands at slightly larger wavelength.1,52 Simulation of the excited state (ES) properties of diimide derivatives are certainly useful to complement experimental measurements, to analyze the principal vibrational modes involved in the specific band shapes of PDI, and subsequently to design derivatives with tailored properties. Due to the size of these compounds, a theoretical model presenting a valuable compromise between accuracy and computational burden is required. Therefore, density functional theory (DFT) and more precisely its time-dependent form,53,54 TD-DFT, are methods of choice. Though a majority of TD-DFT applications are still © XXXX American Chemical Society

performed within the vertical approximation, several works computing the 0−0 energies have appeared,55−57 as this offers more adequate theory−experiment comparisons, even though such calculations are much more time-consuming. The vibronic structure in the UV−visible spectra is due to simultaneous excitation of electronic transition and one or more vibrational modes. The coupling between both types of transitions can be estimated by computing the Franck−Condon (FC) factors. For instance, vibronic spectra with a complete interpretation of the different vibrational modes involved was recently performed for gas phase acrylonitrile.58,59 For larger compounds, the challenge is more significant as the coupling is more complex, therefore, less works have been performed for obtaining the complete interpretation of the fine structure of dyes. In fact, to the best of our knowledge, no previous TD-DFT investigation has been devoted to the simulation of the 0−0 energies and the analysis of band shapes of a large set of diimides, although specific examples appeared (see below). As stated above, calculating the 0−0 energies is crucial to reach meaningful comparisons between experimental and theoretical values, and more precisely, we use here the meeting point between absorption and fluorescence curves (AFCP: absorption/fluorescence crossing point) as experimental reference, following a procedure recently proposed and extensively tested.57 Benchmarks performed for 0−0 energies for a set of molecules including one substituted PDI have been Received: July 17, 2013 Revised: September 23, 2013

A

dx.doi.org/10.1021/jp407104m | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

Scheme 1. Diimides Investigated in This Work

proposed by both Goerigk and Grimme60 and our group.57 Besides these methodological works, only a few theoretical studies have been performed with TD-DFT for PDI derivatives,61−66 several of which are limited to the vertical approximation, which yields transition energies but provides no information on vibrational effects.61,63,65 Vibronic works slowly appeared in the TD-DFT community but they remain focused on the parent (non-substituted) PDI and consequently did not consider a statistically significant set of dyes. Indeed, Clark et al.62 simulated the vibronic spectrum of PDI monomers and dimers in gas phase and showed the existence of two strong vibronic bands, but they did not fully assigned them. More recently, a combined experimental and theoretical study of the vibronic spectra of perylenecarboximides embedded in a thin polymer film was realized by Diehl and co-workers.64 For low frequency vibrational modes, discrepancies in the intensities were observed due to linear electron−phonon coupling, which is not properly modeled in the harmonic approximation.64 The band shapes of the absorption and the emission spectra of 20 representative molecules, including one PDI, were investigated in the framework of a vibronic benchmark.67 It was concluded that the functional that provides the optimal compromise between absolute energies and accurate topologies while avoiding dramatic qualitative failures is M06-2X.68 However, no complete interpretation of the band shape have been performed. M06-2X is also known to be successful for usual calculation of the vertical transition energies.69,70 Following these conclusions, in the present work, spectral properties of

compounds based on diimides (see Scheme 1) have been calculated with TD-DFT combined with the M06-2X hybrid functional. The paper is organized as follows. First, we detail the computational process employing to obtain absorption/ fluorescence spectra. Second, AFCP results are analyzed and compared to experiment. Third, vibrational mode assignments are discussed. Further discussions about anharmonicity and functional effects are provided. Eventually, new structures are designed.

■

METHODOLOGY All calculations were executed with the Gaussian09 program71 using the M06-2X hybrid exchange-correlation functional.68 Default procedures and algorithms have been applied except for tighten self-consistent field (10−10 a.u.) and geometry optimization (10−5 a.u.) convergence thresholds. As stated in the Introduction, several recent studies indicated that the M062X hybrid functional is suitable for evaluating ES properties (both vertical and 0−0 transition energies).57,67,69,70,72 Here, we apply a recently proposed strategy,57 which is to determine the geometrical and vibrational parameters with the 6-31G(d) atomic basis set, whereas the transition energies are corrected with a much more extended atomic basis set, namely 6311+G(2d,p). Both vertical TD estimates and 0−0 energies (corresponding to AFCP)57,60 are obtained following the above-mentioned protocols.57 In this methodology, solvent effects are accounted for through the use of a polarizable B



Article

continuum model (PCM).73 Three different solvents are used here consistently with experimental data:74−80 dichloromethane (DCM), n,n-dimethylformamide (DMF), and chloroform (CHL); see Table 1. The PCM approaches73 combined with

integrals to be computed for each class was set to 106. In the cases where convergence of the FC factors was not reached (≤0.9) with this number of integrals, a larger number of integrals (1010) has been used. In the SI, we list the FC factors for all vibronic spectra. The Franck−Condon approximation has been employed as we consider strongly dipole-allowed ES. Note that in the following, the experimental fluorescence spectra measured in the wavelength scale have been transformed in line shape by applying an intensity correction proportional to ω2,90 as this correction, which allows consistent theory experiment comparison, significantly affects the band shapes.91 The impact of the temperature on the band topologies are also taken into account (T = 298 K). However, the absorption and fluorescence spectra of PDI are not significantly affected by the temperature except for I and III, where a rather small effect is observed (see the SI for details).

Table 1. Experimental AFCP Energies of the Perylene Diimides Treated Herea molecule

solvent

AFCP

ref.

molecule

solvent

AFCP

ref.

I II III IV V VI VII VIII

DCM DCM DCM DMF DMF DMF DMF DCM

2.42 2.56 2.63 2.31 2.34 2.35 2.34 2.26

74 74 74 77 77 77 77 78

IX X XI XII XIII XIV XV XVI

DCM DCM CHL DCM DCM DCM DCM DCM

1.89 2.37 2.34 1.68 1.84 1.48 1.82 1.46

76 80 79 75 75 75 75 75

a

■

RESULTS AND DISCUSSIONS Adiabatic Energies. To allow quantitative comparisons between theoretical and experimental results, the adiabatic energies have been calculated following the methodology described previously.57,92 Our protocol gives access to the three approximations for solvent effect on the 0−0 energies: (1) LR,eq; (2) SS,eq, and (3) SS,neq; the latter being the AFCP. These models correspond to eq 5, 6, and 7 in ref 92, respectively. Our results are listed in Table 2 for the PDI

All values are in eV.

both linear response (LR)81 and state specific (SS)82 models have been employed to model the environmental effects. In the latter model, the polarization of the PCM cavity at the ES is self-consistently determined by considering the real ES electronic density, whereas in the more crude LR scheme the ES density is not considered in the calculation. Again, we redirect the interest readers to ref 57 for a complete description of the methodology. In the ES, we distinguish the equilibrium (eq) and nonequilibrium (neq) PCM limits. In the former, the solvent has the time to fully adapt to the excitation of the compound (e.g., rotational changes of the solvent molecule are allowed) while in the latter, only the electrons of the solvent react to the ES of the dye (the nuclei being frozen). The latter approach is optimal for fast phenomena, that is, electronic transition (absorption and fluorescence), and considers as effective dielectric constant the optical limit, ε∞, for the nonequilibrium part of the calculation. On the contrary, in the equilibrium regime, the static dielectric constant of the solvent is used throughout. In the following the (SS,eq) notation stands for state specific PCM-TD-DFT calculations performed in the equilibrium limit. The ES geometries and vibrational signatures have been determined with analytical PCM-TD-DFT gradients and numerical derivatives (in the equilibrium limit), respectively.83−86 Nonequilibrium effects are subsequently accounted for, at the SS level, to determine theoretical AFCP energies57 that therefore account for both SS and vibrational (ΔEZPVE) effects here. To lighten the computational burden, point group symmetry has been employed when possible. No imaginary frequency are observed for all optimized structures in both GS and ES, and zero point energies are therefore meaningful. Vibrationally resolved spectra have been obtained using the FCclasses program.87−89 Here the Franck−Condon simulations have been performed considering Duschinsky rotation and accounting for changes of both frequencies and structures between the two electronic states. Examples of simplified approximation can be found in the Supporting Information (SI), and it can be seen that Duschinsky’s rotation has a rather negligible impact on the band shapes. The reported spectra have been simulated using a convoluting Gaussian functions presenting a half width at half-maximum (HWHM) that has been adjusted to allow accurate comparisons with experiments (typical value: 0.04 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

Table 2. Theoretical Estimates of the Experimental 0−0 Energies for the Panel of Dyes (Scheme 1) with the M06-2X Functionala dyes

0−0 (LR,eq)

0−0 (SS,eq)

AFCP (SS,neq)

I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI MSE MAE SD R2

2.685 2.805 2.854 2.174 2.179 2.179 2.176 2.681 1.909 2.478 2.274 1.963 2.197 1.708 2.064 1.739 −0.124 0.211 0.366 0.713

2.655 2.846 2.945 2.443 2.448 2.469 2.455 2.582 2.056 2.619 2.472 2.041 2.233 1.867 2.272 1.926 −0.265 0.265 0.365 0.903

2.684 2.860 2.942 2.445 2.450 2.471 2.457 2.621 2.064 2.622 2.472 2.057 2.266 1.878 2.279 1.940 −0.277 0.277 0.367 0.889

a

All values are in eV. In the bottom of the table, a statistical analysis is given: mean signed errors (MSE), mean absolute errors (MAE), standard deviation (SD), and linear determination coefficient (R2).

derivatives of Scheme 1, together with the mean signed and mean absolute errors (MSE and MAE), standard deviation (SD), as well as the linear determination coefficient (R2) obtained by comparing experimental and theoretical values. When the SS-PCM model is employed, the linear determination coefficient strongly increases indicating that this approach restores a chemically meaningful ranking of the C



Article

Figure 1. Comparison between M06-2X/experimental AFCP energies (left) and calculated vertical absorption/AFCP energies (right). All values are in eV.

of the chemical information. Nevertheless, there is, of course, a ca. 0.2 eV discrepancy between vertical and adiabatic estimates, a value in the line of previous works.56,60 Vibrationally Resolved Band Shapes. Perylene diimides possess not less than 108 normal vibrational degrees of freedom (for X) and several are strongly coupled with the main electronic transition leading to vibronic effects. We have identified the key vibrational modes involved for I, X, and XI that correspond to naphthalene diimides, anthracene diimides, and perylene dimiides, respectively (see Scheme 1). Vibronic spectra for other molecules of our set can be found in the SI. As can be seen in Figure 3, Figure 4 and Figure 5, the agreement between experiment and theory is overall rather satisfying despite noticeable discrepancies for several relative intensities. Indeed, the first observation is that the TD-DFT simulations often overrate the intensities of the second and third peaks compared to the experimental spectra. The relative positions of the two main peaks are well reproduced of both absorption and emission for I and XI. In all compounds, we can distinguish a few vibrational modes significantly contributing to the band topologies (see stick spectra with numbering of the most significant contributions). In Table 3 and Table 4, we list the two or three principal vibrational modes strongly contributing to the absorption and emission band shapes, respectively. Movies of these modes are available in the SI. We observe that the contributions of flanking groups correspond to low frequency modes whereas the contributions of the central core mostly imply coupling with high frequency modes. For instance, the second experimental maximum of I can be mainly ascribed to one vibrational mode (see stick spectra) at 1471 cm−1 and 1516 cm −1 for absorption and emission, respectively. They correspond to CC stretching in the central core of I (see movies in the SI). We can compare the results for XI with the PDI core vibronic spectra published previously.62 Even if this former theoretical work is in gas phase and only absorption is discussed, we observe that the values reported in ref 62 are close to our study. For example, the vibrational mode at 1308 cm−1 identified in ref 62 corresponds to a stretching of CC and a bending of CH in the central core and, for XI, this mode appears at 1327 cm−1 here. Further Discussions. Anharmonicity. The harmonic approximation used to determine vibrational modes and, consequently, the vibronic couplings, might be considered as a significant source of errors. Indeed, in some cases, computing anharmonic spectra allows mimicking experimental results more accurately.67,91 The determination of anharmonic ES vibrations is practically impossible (but for very small molecules): however, anharmonic GS frequencies can be

PDI. Experimental and theoretical AFCP energies are compared in the left panel of Figure 1 and the correlation is obvious. However, this SS success is at the price of a slightly larger MAE compared to LR-PCM, but overall, this benchmark shows that the LR approach is not sufficient to reproduce experimental trends for PDI. Note that differences of ca. 0.2− 0.4 eV between LR-PCM and SS-PCM results are not uncommon,92,93 and much larger variations have been reported for twisted chromophores,94 and indicate that the variations of the polarization of the cavity between the ES and the GS is far from negligible. In addition, the equilibrium and the nonequilibrium limits of SS-PCM yield almost equal MAE and R2 (≈ 0.01), as can be deduced from the two rightmost columns of Table 2: the neq corrections are indeed negligible here. The good theory/experiment match can also be confirmed by considering individual cases. For instance, if we focus on the first three dyes; a bathochromic shift (III to I) is observed both experimentally and theoretically. Indeed, going from III to II and next to I induces successive EAFCP shifts of −0.14 eV and −0.07 eV experimentally, to be compared to −0.18 eV and −0.08 eV with TD-DFT using SS,neq data. Theory only slightly overestimates the auxochromic shifts. These results confirm that AFCP energies are influenced by the side groups. We can understand this phenomena as the side rings of II and III participate in the ground state π-conjugated path, but the central core acts as an electron-accepting center (see Figure 2). There is therefore a partial charge transfer from the side groups to the PDI, and the stronger this effect, the smaller the transition energies, as expected.

Figure 2. Electron density ES-GS difference plots (EDD) for (from left to right) I, II and III. The red (blue) zones indicate increase (decrease) of density upon electronic transition.

We also compared the calculated AFCP and vertical energies in the right panel of Figure 1. As can be seen, in this homologous series of molecules, they are connected by a nearly perfect linear relationship (R2 = 0.982). This shows that the 0− 0 energies can be replaced by vertical energies for designing new molecules (see below), as the vertical values capture most D



Article

Figure 3. Computed absorption (left) and fluorescence (right) spectra with principal vibrational modes (stick) for I. The experimental values in dashed lines are taken from ref 74. The first maximum was set to 0 cm−1 for both theory and experiment to allow straightforward comparisons.

Figure 4. Computed optical spectra of X. The experimental values are taken from ref 80. See caption of Figure 3 for more details.

Figure 5. Computed optical spectra of XI. The experimental values are taken from ref 79. See caption of Figure 3 for more details.

Table 3. Vibrational Modes Significantly Contributing to the Absorption Band Shapesa

Table 4. Vibrational Modes Explaining the Topologies of the Fluorescence Bandsa

Absorption

emission

I X XI

−1

n

character

I

ω (cm )

9 114 2 78 13 131 176

thiophene t CC s anthracene t anthracene CC s + CH3 w cyclohexane t CH b + CC s CC s

0.193 0.268 0.914 0.252 0.337 0.240 0.362

93 1471 37 1449 144 1327 1691

I X

XI

n

character

I

ω (cm−1)

9 118 2 69 90 13 131

thiophene t CC s anthracene t CH b + CC s CC s cyclohexane t CH b + CC s

0.189 0.129 0.450 0.188 0.276 0.324 0.198

91 1516 40 1305 1653 143 1366

a

a

obtained through numerical differentiation of the analytic harmonic GS frequencies for a significant, but tractable, computational cost.71,95 This procedure has been applied for X, one molecule for which theory/experiment difference are

large, and allowed to obtain a corrected emission spectra. As can be seen in Figure 6, the anharmonic vibration corrections have a small impact on the band topology with M06-2X. The impact of anharmonic corrections is larger at the PBE0 level96 but the incorrect ordering of the relative intensities of the two first peaks pertain. Consequently, theory-experiment discrep-

All results at the TD-DFT/M06-2X level of theory. First three columns are as follows: number (n), nature of the vibrational mode and the intensity (I). s, w, t and b correspond to stretching, wagging, twisting and bending, respectively.

E

See caption of Table 3 for more details.



Article

Figure 6. Comparison of the fluorescence spectra of X computed with both anharmonic and harmonic ground state vibrational modes with the experimental data adapted from ref 80. The left (right) panel correspond to the M06-2X (PBE0) functional.

Figure 7. Computed optical spectra of X. The experimental values are taken from ref 80. See caption of Figure 3 for more details.

ancies cannot be completely ascribed to the harmonic approximation for the present set of molecules. Functional Effect. We have evaluated the influence of the exchange-correlation functional in the obtained vibronic spectra. The absorption and the emission spectra of X are illustrated in Figure 7. We have tested the four functionals of the M06 family68 that present an increasingly large exact exchange ratio: M06-L (0%), M06 (27%), M06-2X (54%), and M06-HF (100%). B3LYP,97 PBE0,96 ωB97X,98 and LC-PBE99 spectra can be found in the SI, but the trends are rather similar to the one obtained with the M06 series. We can observe that the selected functional significantly affects the band shapes. For the first peak, the relative intensity tends to decrease when the exchange ratio becomes larger. To reproduce the topology of the two main peaks, M06 (and B3LYP and PBE0) and M06HF (and LC-PBEPBE) are the closest to experiment for absorption and emission, respectively. However, no functional provides a reasonable agreement in all cases, e.g., M06-HF overshoots the intensity at large energies for the emission, whereas M06 underrates the intensity of absorption at large energies. The same holds for range-separated hybrids that are not able to provide an accurate fit to experiment in all cases (see the SI). Therefore, as we do not aim to perform a throughout functional benchmark here, we have kept the M062X functional in the following. Design of New PDI Dyes. In this last section, we design new molecules (see Scheme 2) that are based on the central core of the molecule III but with new side groups, both electron acceptors (CN) and donors (NMe2, NH2 and OH). Following adiabatic energy results and, in particular, the nearly perfect correlation between vertical and adiabatic figures (see Figure 1), the vertical energies are first used in this case. Table 5 lists the vertical computed absorption energies. As expected, we can observe that the side groups play a crucial role on the

Scheme 2. List of New Molecules Tested

auxochromic shifts: a range of ca. 0.9 eV can be attained despite the fact that the core of III is conserved. A decreasing order of energy III′ > III > V′ > I′ > VII′ > VI′ > II′ > VIII′ ≃ IX′ > IV′ is found. Depending on the nature of the flanking groups (electrodonating or electro-attracting), the shift can be dramatically high and not systematically bathochromic. Indeed, a dicyano subtitution (III′) yields hypsochromic displacement (+0.213 eV). This can be further analyzed from the electronic density differences of molecules II′, III′ and IX′ represented in Figure 8. For III′ the charge transfer from the side groups to the core is almost zero: the cyano accepting groups do not play a significant role in the π-skeleton and have only an inductive effect. On the contrary, for II′, one notices a strong implication of the lone pairs of the nitrogen atoms in the excited-state, for which they act as donors, explaining the strong associated bathochromic shift. When the symmetry of the molecule is broken (IX′), the charge transfer is localized from the NMe2 group to the PDI core, and once again, the cyano group is a rather passive element as it does not play a major role in the density reorganization. Therefore to induce strong chargetransfer effects (and large bathochromic shift), a symmetric pushing substitution is more effective than an asymmetric push−pull strategy. F



Article

Table 5. Theoretical Absorption Vertical Energies for the Panel of Dyes Shown in Scheme 2a

a

dyes

III

I′

II′

III′

IV′

V′

VI′

VII′

VIII′

IX′

V-abs

3.296

3.037

2.724

3.509

2.525

3.168

2.810

2.850

2.592

2.594

All values are obtained with the M06-2X functional in the state-specific non-equilibrium PCM limit, and are given in eV.

several substituents for a typical molecule, and it was found that, on the one hand, the auxochromes affect mostly the position of the band, rather than their shape (that can only be significantly modified by changing the core), and, on the other hand, that adding two symmetric electron-donor groups induces a stronger bathochromic displacement than the usual asymmetric push−pull strategy. This investigation of PDI dyes clearly suggests come general recommendation for dye study: (i) it is worth testing solvation models going beyond the LR approximation in the TD-DFT framework, as these models might improve the consistency of the evaluation; (ii) computations of the ES Hessian is, despite the associated computational effort, worth it because it allows meaningful theory−experiment comparisons of both band shapes and absorption/emission crossing points (going beyond verticality is certainly helpful in TD-DFT); (iii) beyond transition energies, charge-transfer signatures can be rapidly obtained by theoretical calculations, and this is useful to perform such simulations before synthesis, irrespective of the selected class of dyes.

Figure 8. Electron density ES-GS difference plots (EDD) for (from left to right) II′, III′ and IX′. The red (blue) zones indicate increase (decrease) of density upon electronic transition.

We have simulated vibrationally resolved spectra of VIII′, one of the molecules for which the bathochromic shift is particularly strong. Results are displayed in Figure 9. The band shapes for both absorption and emission are qualitatively similar to the one computed both for I and III. We can therefore reasonably assume that changing the side moieties has no strong direct impact on the vibronic band shapes (that are mostly related to the nature of the central core) but mainly shifts the transition energy.

■

■

ASSOCIATED CONTENT

* Supporting Information S

CONCLUSIONS The simulations of both adiabatic and vibronic signatures of a large panel of diimide derivatives have been performed following a recently established procedure,57,67 that accounts for state-specific solvation and vibrational effects. Adiabatic calculations demonstrated that the LR approach is not sufficient to consistently describe the experimental results for these dyes. Applying the SS approach clearly improves the theory/ experiment match in terms of trends, whereas a comparison between the nonequilibrium and equilibrium PCM limits indicated rather small nonequilibrium corrections in the present case. Vibronic spectra of PDI have been compared to experiment and an overall satisfying agreement was reached, though for some individual cases, e.g., the emission of X, theory could not reasonably reproduce the measurements. This failure cannot be satisfactorily cured by changing the functional nor including anharmonic effects. Globally we observed that the fine structure and the presence of a second (and/or third) peak(s) are due to vibrations centered in the core of the PDI which occurred at around 1400−1600 cm−1. We have tested

Additional vibronic simulations, movies of several key vibrational modes, temperature effects, list of FC factors, list of ZPVE energies, effect of various FC approximations, additional functional tests for X. This material is available free of charge via the Internet at http://pubs.acs.org/.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +33 (0) 2 51125564. Fax: +33 (0) 2 51125712. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Y.H. acknowledges the ERC (Marches -278845) and the Région des Pays de la Loire for her Ph.D. grant. D.J. acknowledges the European Research Council (ERC) and the Région des Pays de la Loire for financial support in the framework of a Starting Grant (Marches -278845) and a recrutement sur poste stratégique,

Figure 9. Computed optical spectra of VII′, left: absorption, right: emission. G



Article

nisms in Organic p/n-Junction Solar Cells. Sol. Energy Mater. Sol. Cells 2000, 63, 37−47. (21) Tian, H.; Liu, P.-H.; Zhu, W.; Gao, E.; Wu, D.-J.; Cai, S. Synthesis of Novel Multi-Chromophoric Soluble Perylene Derivatives and their Photosensitizing Properties with Wide Spectral Response for SnO Nanoporous Electrode. J. Mater. Chem. 2000, 10, 2708−2715. (22) Huang, C.; Barlow, S.; Marder, S. R. Perylene-3,4,9,10tetracarboxylic Acid Diimides: Synthesis, Physical Properties, and Use in Organic Electronics. J. Org. Chem. 2011, 76, 2386−2407. (23) Zhan, X.; Facchetti, A.; Barlow, S.; Marks, T. J.; Ratner, M. A.; Wasielewski, M. R.; Marder, S. R. Rylene and Related Diimides for Organic Electronics. Adv. Mater. 2011, 23, 268−284. (24) Alam, M. M.; Jenekhe, S. A. Efficient Solar Cells from Layered Nanostructures of Donor and Acceptor Conjugated Polymers. Chem. Mater. 2004, 16, 4647−4656. (25) Ahmed, E.; Ren, G.; Kim, F. S.; Hollenbeck, E. C.; Jenekhe, S. A. Design of New Electron Acceptor Materials for Organic Photovoltaics: Synthesis, Electron Transport, Photophysics, and Photovoltaic Properties of Oligothiophene-Functionalized Naphthalene Diimides. Chem. Mater. 2011, 23, 4563−4577. (26) Fabiano, S.; Chen, Z.; Vahedi, S.; Facchetti, A.; Pignataro, B.; Loi, M. A. Role of Photoactive Layer Morphology in High Fill Factor All-Polymer Bulk Heterojunction Solar Cells. J. Mater. Chem. 2011, 21, 5891−5896. (27) Schubert, M.; Dolfen, D.; Frisch, J.; Roland, S.; Steyrleuthner, R.; Stiller, B.; Chen, Z.; Scherf, U.; Koch, N.; Facchetti, A.; et al. Influence of Aggregation on the Performance of All-Polymer Solar Cells Containing Low-Bandgap Naphthalenediimide Copolymers. Adv. Energy Mater. 2012, 2, 369−380. (28) Berberich, M.; Krause, A.-M.; Orlandi, M.; Scandola, F.; Würthner, F. Toward Fluorescent Memories with Nondestructive Readout: Photoswitching of Fluorescence by Intramolecular Electron Transfer in a Diaryl Ethene-Perylene Bisimide Photochromic System. Angew. Chem., Int. Ed. 2008, 47, 6616−6619. (29) Tan, W.; Li, X.; Zhang, J.; Tian, H. A Photochromic Diarylethene Dyad Based on Perylene Diimide. Dyes Pigm. 2011, 89, 260−265. (30) Zang, L.; Che, Y.; Moore, J. S. One-Dimensional Self-Assembly of Planar π-Conjugated Molecules: Adaptable Building Blocks for Organic Nanodevices. Acc. Chem. Res. 2008, 41, 1596−1608. (31) Bhosale, S. V.; Bhosale, S. V.; Bhargava, S. K. Recent Progress of Core-Substituted Naphthalenediimides: Highlights from 2010. Org. Biomol. Chem. 2012, 10, 6455−6468. (32) Sakai, N.; Mareda, J.; Vauthey, E.; Matile, S. Core-Substituted Naphthalenediimides. Chem. Commun. 2010, 46, 4225−4237. (33) Würthner, F.; Stolte, M. Naphthalene and Perylene Diimides for Organic Transistors. Chem. Commun. 2011, 47, 5109−5115. (34) Che, Y.; Yang, X.; Loser, S.; Zang, L. Expedient Vapor Probing of Organic Amines Using Fluorescent Nanofibers Fabricated from an n-Type Organic Semiconductor. Nano Lett. 2008, 8, 2219−2223. (35) Cao, H.; Diaz, D. I.; DiCesare, N.; Lakowicz, J. R.; Heagy, M. D. Monoboronic Acid Sensor That Displays Anomalous Fluorescence Sensitivity to Glucose. Org. Lett. 2002, 4, 1503−1505. (36) Zhu, L.; Wu, W.; Zhu, M.-Q.; Han, J. J.; Hurst, J. K.; Li, A. D. Q. Reversibly Photoswitchable Dual-Color Fluorescent Nanoparticles as New Tools for Live-Cell Imaging. J. Am. Chem. Soc. 2007, 129, 3524− 3526. (37) Jones, B. A.; Ahrens, M. J.; Yoon, M.-H.; Facchetti, A.; Marks, T. J.; Wasielewski, M. R. High-Mobility Air-Stable n-Type Semiconductors with Processing Versatility: Dicyanoperylene-3,4:9,10bis(dicarboximides). Angew. Chem., Int. Ed. 2004, 43, 6363−6366. (38) Guo, X.; Zhang, D.; Zhu, D. Logic Control of the Fluorescence of a New Dyad, Spiropyran-Perylene Diimide-Spiropyran, with Light, Ferric Ion, and Proton: Construction of a New Three-Input and Logic Gate. Adv. Mater. 2004, 16, 125−130. (39) Ranke, P.; Bleyl, I.; Simmerer, J.; Haarer, D.; Bacher, A.; Schmidt, H. W. Electroluminescence and Electron Transport in a Perylene Dye. Appl. Phys. Lett. 1997, 71, 1332−1334.

respectively. A.D.L. thanks the CEISAM laboratory for the warm welcome and the Institut de Chimie of the C.N.R.S. for financial support.

■

REFERENCES

(1) Langhals, H. Cyclic Carboxylic Imide Structures as Structure Elements of High Stability. Novel Developments in Perylene Dye Chemistry. Heterocycles 1995, 40, 477−500. (2) Demmig, S.; Langhals, H. Leichtlösliche, Lichtechte PerylenFluoreszenzfarbstoffe. Chem. Ber. 1988, 121, 225−230. (3) Icli, S.; Icil, H. A Thermal and Photostable Reference Probe for Qf Measurements: Chloroform Soluble Perylene 3,4,9,10-Tetracarboxylic Acid-bis-N,N-dodecyl Diimide. Spectrosc. Lett. 1996, 29, 1253− 1257. (4) Icil, H.; Icli, S. The Synthesis and Spectral Characteristics of a Supramolecular Model: Perylene 3,4,9,10-Tetracarboxylic Acid-bisN,N′-p-aminophenyl Diimide. Spectrosc. Lett. 1995, 28, 595−601. (5) Icil, H.; Arslan, E. Synthesis and Spectroscopic Properties of Highly Pure Perylene Fluorescent Dyes. Spectrosc. Lett. 2001, 34, 355− 363. (6) Icil, H.; Uzun, D.; Arslan, E. Synthesis and Spectroscopic Characterization of Water Soluble Perylene Tetracarboxylic Diimide Derivatives. Spectrosc. Lett. 2001, 34, 605−614. (7) Cazacu, M.; Vlad, A.; Airinei, A.; Nicolescu, A.; Stoica, I. New Imides Based on Perylene and Siloxane Derivatives. Dyes Pigm. 2011, 90, 106−113. (8) Langhals, H.; Kirner, S. Novel Fluorescent Dyes by the Extension of the Core of Perylenetetracarboxylic Bisimides. Eur. J. Org. Chem. 2000, 2000, 365−380. (9) Kaur, B.; Quazi, N.; Ivanov, I.; Bhattacharya, S. Near-Infrared Reflective Properties of Perylene Derivatives. Dyes Pigm. 2012, 92, 1108−1113. (10) Boobalan, G.; Imran, P. M.; Nagarajan, S. Synthesis of Highly Fluorescent and Water Soluble Perylene Bisimide. Chin. Chem. Lett. 2012, 23, 149−153. (11) Asir, S.; Demir, A. S.; Icil, H. The Synthesis of Novel, Unsymmetrically Substituted, Chiral Naphthalene and Perylene Diimides: Photophysical, Electrochemical, Chiroptical and Intramolecular Charge Transfer Properties. Dyes Pigm. 2010, 84, 1−13. (12) Georgiev, N. I.; Sakr, A. R.; Bojinov, V. B. Design and Synthesis of Novel Fluorescence Sensing Perylene Diimides Based on Photoinduced Electron Transfer. Dyes Pigm. 2011, 91, 332−339. (13) Meissner, D.; Rostalski, J. Photovoltaics of Interconnected Networks. Synth. Met. 2001, 121, 1551−1552. (14) Tang, C. W. Two-Layer Organic Photovoltaic Cell. Appl. Phys. Lett. 1986, 48, 183−185. (15) Li, J.; Dierschke, F.; Wu, J.; Grimsdale, A. C.; Mullen, K. Poly(2,7-carbazole) and Perylene Tetracarboxydiimide: A Promising Donor/Acceptor Pair for Polymer Solar Cells. J. Mater. Chem. 2006, 16, 96−100. (16) Dentani, T.; Funabiki, K.; Jin, J.-Y.; Yoshida, T.; Minoura, H.; Matsui, M. Application of 9-Substituted 3,4-Perylenedicarboxylic Anhydrides as Sensitizers for Zinc Oxide Solar Cell. Dyes Pigm. 2007, 72, 303−307. (17) Shibano, Y.; Umeyama, T.; Matano, Y.; Imahori, H. ElectronDonating Perylene Tetracarboxylic Acids for Dye-Sensitized Solar Cells. Org. Lett. 2007, 9, 1971−1974. (18) Wang, H.; Peng, B.; Wei, W. Solar Cells Based on Perylene Bisimide Derivatives. Prog. Chem. 2008, 20, 1751−1760. (19) Ramanan, C.; Smeigh, A. L.; Anthony, J. E.; Marks, T. J.; Wasielewski, M. R. Competition between Singlet Fission and Charge Separation in Solution-Processed Blend Films of 6,13-Bis(triisopropylsilylethynyl)pentacene with Sterically-Encumbered Perylene-3,4:9,10-bis(dicarboximide)s. J. Am. Chem. Soc. 2012, 134, 386− 397. (20) Rostalski, J.; Meissner, D. Photocurrent Spectroscopy for the Investigation of Charge Carrier Generation and Transport MechaH



Article

(40) Schmidt-Mende, L.; Fechtenkötter, A.; Müllen, K.; Moons, E.; Friend, R. H.; MacKenzie, J. D. Self-Organized Discotic Liquid Crystals for High-Efficiency Organic Photovoltaics. Science 2001, 293, 1119−1122. (41) O’Neil, M.; Niemczyk, M.; Svec, W.; Gosztola, D.; Gaines, G., III; Wasielewski, M. Picosecond Optical Switching Based on Biphotonic Excitation of an Electron Donor−Acceptor−Donor Molecule. Science 1992, 257, 63−65. (42) Baffreau, J.; Leroy-Lhez, S.; VanAnh, N.; Williams, R. M.; Hudhomme, P. Fullerene C60-perylene-3,4:9,10-bis(dicarboximide) Light-Harvesting Dyads: Spacer-Length and Bay-Substituent Effects on Intramolecular Singlet and Triplet Energy Transfer. Chem.Eur. J. 2008, 14, 4974−4992. (43) He, X.; Liu, H.; Li, Y.; Wang, S.; Li, Y.; Wang, N.; Xiao, J.; Xu, X.; Zhu, D. Gold Nanoparticle-Based Fluorometric and Colorimetric Sensing of Copper(II) Ions. Adv. Mater. 2005, 17, 2811−2815. (44) Zhao, Y.; Zhang, X.; Li, D.; Liu, D.; Jiang, W.; Han, C.; Shi, Z. Water-Soluble 3,4:9,10-Perylene Tetracarboxylic Ammonium as a High-Performance Fluorochrome for Living Cells Staining. Luminescence 2009, 24, 140−143. (45) Würthner, F. Perylene Bisimide Dyes as Versatile Building Blocks for Functional Supramolecular Architectures. Chem. Commun. 2004, 0, 1564−1579. (46) Li, C.; Wonneberger, H. Perylene Imides for Organic Photovoltaics: Yesterday, Today, and Tomorrow. Adv. Mater. 2012, 24, 613−636. (47) Lu, X.; Guo, Z.; Sun, C.; Tian, H.; Zhu, W. Helical Assembly Induced by Hydrogen Bonding from Chiral Carboxylic Acids Based on Perylene Bisimides. J. Phys. Chem. B 2011, 115, 10871−10876. (48) Tröster, H. Untersuchungen zur Protonierung von Perylen3,4,9,10-tetracarbonsäurealkalisalzen. Dyes Pigm. 1983, 4, 171−177. (49) Nagao, Y.; Misono, T. Synthesis and Properties of N-Alkyl-NAryl-3,4:9,10-Perylenebis(dicarboximide). Dyes Pigm. 1984, 5, 171− 188. (50) Alp, S.; Erten, S.; Karapire, C.; Köz, B.; Doroshenko, A. O.; Icli, S. Photoinduced Energy-Electron Transfer Studies with Naphthalene Diimides. J. Photochem. Photobiol., A 2000, 135, 103−110. (51) Licchelli, M.; Orbelli Biroli, A.; Poggi, A. A Prototype for the Chemosensing of Ba2+ Based on Self-Assembling Fluorescence Enhancement. Org. Lett. 2006, 8, 915−918. (52) Würthner, F.; Chen, Z.; Dehm, V.; Stepanenko, V. OneDimensional Luminescent Nanoaggregates of Perylene Bisimides. Chem. Commun. 2006, 0, 1188−1190. (53) Mohajeri, A.; Alipour, M. Time-Dependent Density Functional Theory Benchmarking for the Calculations of Atomic Spectra: Efficiency of Exc-ETDZ Basis Set. Theor. Chem. Acc. 2012, 131, 1−10. (54) Leang, S. S.; Zahariev, F.; Gordon, M. S. Benchmarking the Performance of Time-Dependent Density Functional Methods. J. Chem. Phys. 2012, 136, 104101. (55) Dierksen, M.; Grimme, S. The Vibronic Structure of Electronic Absorption Spectra of Large Molecules: A Time-Dependent Density Functional Study on the Influence of “Exact” Hartree Fock Exchange. J. Phys. Chem. A 2004, 108, 10225−10237. (56) Send, R.; Kühn, M.; Furche, F. Assessing Excited State Methods by Adiabatic Excitation Energies. J. Chem. Theory Comput. 2011, 7, 2376−2386. (57) Jacquemin, D.; Planchat, A.; Adamo, C.; Mennucci, B. TD-DFT Assessment of Functionals for Optical 0−0 Transitions in Solvated Dyes. J. Chem. Theory Comput. 2012, 8, 2359−2372. (58) Ilakovac, V.; Houari, Y.; Carniato, S.; Gallet, J.-J.; Kukk, E.; Horvatić, D. Vibrationally Resolved N 1s Absorption Spectra of the Acrylonitrile Molecule. Phys. Rev. A 2012, 85, 062521. (59) Ilakovac, V.; Carniato, S.; Gallet, J.-J.; Kukk, E.; Horvatić, D.; Ilakovac, A. Vibrations of Acrylonitrile in N 1s Excited States. Phys. Rev. A 2008, 77, 012516. (60) Goerigk, L.; Grimme, S. Assessment of TD-DFT Methods and of Various Spin Scaled CIS(D) and CC2 Versions for the Treatment of Low-Lying Valence Excitations of Large Organic Dyes. J. Chem. Phys. 2010, 132, 184103.

(61) Engel, E.; Schmidt, K.; Beljonne, D.; Brédas, J.-L.; Assa, J.; Fröb, H.; Leo, K.; Hoffmann, M. Transient Absorption Spectroscopy and Quantum-Chemical Studies of Matrix-Isolated Perylene Derivatives. Phys. Rev. B 2006, 73, 245216. (62) Clark, A. E.; Qin, C.; Li, A. D. Q. Beyond Exciton Theory A Time-Dependent DFT and Franck Condon Study of Perylene Diimide and Its Chromophoric Dimer. J. Am. Chem. Soc. 2007, 129, 7586− 7595. (63) Liang, B.; Zhang, Y.; Wang, Y.; Xu, W.; Li, X. Structures and Properties of 1,7-Disubstituted Perylene Tetracarboxylic Diimides: The Substitutional Effect Study Based on Density Functional Theory Calculations. J. Mol. Struct. 2009, 917, 133−141. (64) Diehl, F. P.; Roos, C.; Jankowiak, H.-C.; Berger, R.; Khön, A.; Diezemann, G.; Basché, T. Combined Experimental and Theoretical Study of the Vibronic Spectra of Perylenecarboximides. J. Phys. Chem. B 2010, 114, 1638−1647. (65) Pugliesi, I.; Megerle, U.; Suraru, S.-L.; Würthner, F.; Riedle, E.; Lochbrunner, S. Influence of Core-Substitution on the Ultrafast Charge Separation and Recombination in Arylamino Core-Substituted Naphthalene Diimides. Chem. Phys. Lett. 2011, 504, 24−28. (66) Oltean, M.; Calborean, A.; Mile, G.; Vidrighin, M.; Iosin, M.; Leopold, L.; Maniu, D.; Leopold, N.; Chis, V. Absorption Spectra of PTCDI: A Combined UV-Vis and TD-DFT Study. Spectrochim. Acta Part A 2012, 97, 703−710. (67) Charaf-Eddin, A.; Planchat, A.; Mennucci, B.; Adamo, C.; Jacquemin, D. Choosing a Functional for Computing Absorption and Fluorescence Band Shapes with TD-DFT. J. Chem. Theory Comput. 2013, 9, 2749−2760. (68) Zhao, Y.; Truhlar, D. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215−241. (69) Jacquemin, D.; Perpète, E. A.; Ciofini, I.; Adamo, C.; Valero, R.; Zhao, Y.; Truhlar, D. G. On the Performances of the M06 Family of Density Functionals for Electronic Excitation Energies. J. Chem. Theory Comput. 2010, 6, 2071−2085. (70) Isegawa, M.; Peverati, R.; Truhlar, D. G. Performance of Recent and High-Performance Approximate Density Functionals for TimeDependent Density Functional Theory Calculations of Valence and Rydberg Electronic Transition Energies. J. Chem. Phys. 2012, 137, 244104. (71) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, revision C.01; Gaussian, Inc.: Wallingford, CT, 2009. (72) Laurent, A. D.; Jacquemin, D. TD-DFT Benchmarks: A Review. Int. J. Quantum Chem. 2013, 113, 2019−2039. (73) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 2999−3094. (74) Li, Y.; Zhang, G.; Yang, G.; Guo, Y.; Di, C.; Chen, X.; Liu, Z.; Liu, H.; Xu, Z.; Xu, W.; et al. Extended π-Conjugated Molecules Derived from Naphthalene Diimides toward Organic Emissive and Semiconducting Materials. J. Org. Chem. 2013, 78, 2926−2934. (75) Li, C.; Xiao, C.; Li, Y.; Wang, Z. Synthesis and Properties of Heterocyclic Acene Diimides. Org. Lett. 2013, 15, 682−685. (76) Tsai, H.-Y.; Chen, K.-Y. 1,7-Diaminoperylene Bisimides: Synthesis, Optical and Electrochemical Properties. Dyes Pigm. 2013, 96, 319−327. (77) Pasaogullari, N.; Icil, H.; Demuth, M. Symmetrical and Unsymmetrical Perylene Diimides: Their Synthesis, Photophysical and Electrochemical Properties. Dyes Pigm. 2006, 69, 118−127. (78) Thalacker, C.; Röger, C.; Würthner, F. Synthesis and Optical and Redox Properties of Core-Substituted Naphthalene Diimide Dyes. J. Org. Chem. 2006, 71, 8098−8105. (79) Kong, X.; Gao, J.; Ma, T.; Wang, M.; Zhang, A.; Shi, Z.; Wei, Y. Facile Synthesis and Replacement Reactions of Mono-Substituted Perylene Bisimide Dyes. Dyes Pigm. 2012, 95, 450−454. I



Article

(80) Mohebbi, A. R.; Munoz, C.; Wudl, F. Synthesis and Characterization of 2,8-Diazaperylene-1,3,7,9-tetraone, a New Anthracene Diimide Containing Six-Membered Imide Rings. Org. Lett. 2011, 13, 2560−2563. (81) Cammi, R.; Mennucci, B. The Linear Response Theory for the Polarizable Continuum Model. J. Chem. Phys. 1999, 110, 9877−9886. (82) Improta, R.; Scalmani, G.; Frisch, M. J.; Barone, V. Toward Effective and Reliable Fluorescence Energies in Solution by a New State Specific Polarizable Continuum Model Time Dependent Density Functional Theory Approach. J. Chem. Phys. 2007, 127, 074504. (83) Caillie, C. V.; Amos, R. D. Geometric Derivatives of Excitation Energies Using SCF and DFT. Chem. Phys. Lett. 1999, 308, 249−255. (84) Caillie, C. V.; Amos, R. D. Geometric Derivatives of Density Functional Theory Excitation Energies Using Gradient-Corrected Functionals. Chem. Phys. Lett. 2000, 317, 159−164. (85) Furche, F.; Ahlrichs, R. Adiabatic Time-Dependent Density Functional Methods for Excited State Properties. J. Chem. Phys. 2002, 117, 7433−7447. (86) Scalmani, G.; Frisch, M. J.; Mennucci, B.; Tomasi, J.; Cammi, R.; Barone, V. Geometries and Properties of Excited States in the Gas Phase and in Solution: Theory and Application of a Time-Dependent Density Functional Theory Polarizable Continuum Model. J. Chem. Phys. 2006, 124, 094107. (87) Santoro, F.; Improta, R.; Lami, A.; Bloino, J.; Barone, V. Effective Method to Compute Franck−Condon Integrals for Optical Spectra of Large Molecules in Solution. J. Chem. Phys. 2007, 126, 084509. (88) Santoro, F.; Lami, A.; Improta, R.; Barone, V. Effective Method to Compute Vibrationally Resolved Optical Spectra of Large Molecules at Finite Temperature in the Gas Phase and in Solution. J. Chem. Phys. 2007, 126, 184102. (89) Santoro, F.; Lami, A.; Improta, R.; Bloino, J.; Barone, V. Effective Method for the Computation of Optical Spectra of Large Molecules at Finite temperature Including the Duschinsky and Herzberg−Teller Effect: The Qx Band of Porphyrin as a Case Study. J. Chem. Phys. 2008, 128, 224311. (90) Valeur, B. Molecular Fluorescence: Principles and Applications; Wiley-VCH: Weinheim, Germany, 2002. (91) Avila Ferrer, F. J.; Cerezo, J.; Stendardo, E.; Improta, R.; Santoro, F. Insights for an Accurate Comparison of Computational Data to Experimental Absorption and Emission Spectra: Beyond the Vertical Transition Approximation. J. Chem. Theory Comput. 2013, 9, 2072−2082. (92) Chibani, S.; Charaf-Eddin, A.; Le Guennic, B.; Jacquemin, D. Boranil and Related NBO Dyes: Insights From Theory. J. Chem. Theory Comput. 2013, 9, 3127−3135. (93) Chibani, S.; Le Guennic, B.; Charaf-Eddin, A.; Maury, O.; Andraud, C.; Jacquemin, D. On the Computation of Adiabatic Energies in Aza-Boron-Dipyrromethene Dyes. J. Chem. Theory Comput. 2012, 8, 3303−3313. (94) Pedone, A. Role of Solvent on Charge Transfer in 7Aminocoumarin Dyes: New Hints from TD-CAM-B3LYP and State Specific PCM Calculations. J. Chem. Theory Comput. 2013, 9, 4087− 4096. (95) Barone, V. Anharmonic Vibrational Properties by a Fully Automated Second-Order Perturbative Approach. J. Chem. Phys. 2005, 122, 014108. (96) Adamo, C.; Barone, V. Toward Reliable Density Functional Methods Without Adjustable Parameters: The PBE0Model. J. Chem. Phys. 1999, 110, 6158−6170. (97) Becke, A. D. A New Mixing of Hartree-Fock and Local DensityFunctional Theories. J. Chem. Phys. 1993, 98, 1372−1377. (98) Chai, J. D.; Head-Gordon, M. Systematic Optimization of LongRange Corrected Hybrid Density Functionals. J. Chem. Phys. 2008, 128, 084106. (99) Song, J. W.; Hirosawa, T.; Tsuneda, T.; Hirao, K. Long-Range Corrected Density Functional Calculations of Chemical Reactions: Redetermination of Parameter. J. Chem. Phys. 2007, 126, 154105.

J


Spectral Signatures of Perylene Diimide Derivatives: Insights From

Recommend Documents