Through-Space Charge Transfer in Rod-Like Molecules: Lessons from

Article pubs.acs.org/JPCC

Through-Space Charge Transfer in Rod-Like Molecules: Lessons from Theory Ilaria Ciofini,† Tangui Le Bahers,‡,§ Carlo Adamo,†,∥ Fabrice Odobel,⊥ and Denis Jacquemin*,⊥ †

Laboratoire LECIME, CNRS UMR-7575, Chimie-ParisTech, 11 rue P. et M. Curie, F-75231 Paris Cedex 05, France Laboratoire de Chimie de la Matière Condensée (LCMCP), UMR7574 CNRS/UPMC/Chimie Paristech, Chimie Paristech, 75231 Paris 05, France § Rhodia, Centre de Recherches et Technologies d’Aubervilliers, 52 rue Haie Coq F-93308 Aubervilliers Cedex, France ∥ Institut Universitaire de France, 103, bd Saint-Michel, F-75005 Paris Cedex 05, France ⊥ Laboratoire CEISAM - UMR CNRS 6230, Université de Nantes, 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France ‡

S Supporting Information *

ABSTRACT: Time-dependent density functional theory calculations are performed within a range-separated hybrid framework to quantify the efficiency of through-space charge transfer (CT) in organic rod-like push−pull compounds. Our model allows us to quantify the CT distance, the amount of transferred electron, as well as the spread of the charges. The impact of several kinds of variations has been investigated: (1) the nature and length of the π-conjugated bridge; (2) the strength of the terminal groups; (3) the presence of a central groups; and (4) the use of a polar environment. In α,ω-nitro-dimethylamino chains, we found that the charge transfer is maximized when four to six conjugated rings are separating the donor and the acceptor. The maximum CT distance is ca. 5 Å for these chains but can be improved by 1−2 Å in polar environments. Adding a stronger electron-donating group does not systematically induce an enhancement of the CT if a strong electron-accepting moiety is used, the latter tending to extract the electron from the conjugated chains rather from the donor moiety. There is indeed a fine equilibrium to respect to improve CT. This investigation is a further step toward the rational optimization of charge transfer properties.

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INTRODUCTION Intramolecular charge transfer transitions are formed when light absorption induces a partial electronic shift from one moiety of a compound to another one, and they are actively investigated for many applications.1−7 For instance, these states play a ubiquitous role in organic light-emitting diodes, photosynthesis, and solar cells. Specifically, in dye-sensitized solar cells (DSSCs), the absorption of light by a dye grafted on a semiconducting surface induces a hole−electron separation, one charge being injected into the bulk material and the other residing on the sensitizer, which represents a key step in the light-to-electricity conversion process.8 Of course, to be effective, one should limit the probability that the electron and the hole recombine. Toward that goal, a maximum separation between the two charges is highly desirable. This is even more true in p-type DSSCs where a hole rather than an electron is injected into a p-type semiconductor, as these cells are strongly affected by recombination.9 In other words, one often wishes to create a strong through-space charge transfer (for the sake of compactness, we use CT as an acronym for through-space charge transfer in the following) to maximize the efficiency of DSSCs. To promote the formation of CT states, the typical strategy consists of plugging one electron-donating (D) and one electron-accepting (A) group at the extremities of a π-conjugated spacer. This leads to rod-like donor−acceptor © 2012 American Chemical Society

systems, also referred to as push−pull molecules. In these compounds, a photon absorption qualitatively induces a shift from a D−π−A ground state (GS) to a D+−π−A− excited state (ES). However, this simplistic picture should be refined as it is obvious that the actual electron transfer depends on all three components of the molecules. Indeed a stronger acceptor/ donor fragment often improves the macroscopic properties that are CT dependent, e.g., the total efficiency of DSSCs. There are countless investigations aiming at tuning DSSC properties by modifying the D, bridge, and/or A moieties.10−26 In the present contribution, we investigate with ab initio tools the CT of a large series of organic molecules, to provide fair comparisons between different molecular architectures. We have tested a wide panel of D and A groups and selected π-connectors of different natures and lengths. To assess the efficiency of rod-like molecules, we have recently proposed a simple approach to quantify CT.27 This model is completely general and requires only GS and ES total electronic densities. Indeed, the central idea is to compute the barycenters of the regions of gain/depletion of electronic densities (see next section for details).27 Often, these regions Received: March 30, 2012 Revised: May 6, 2012 Published: May 9, 2012 11946

dx.doi.org/10.1021/jp3030667 | J. Phys. Chem. C 2012, 116, 11946−11955

The Journal of Physical Chemistry C

Article

⎧ if Δρ(r) > 0 ⎪ Δρ(r) ρ+ (r) = ⎨ ⎪ 0 if Δρ(r) < 0 ⎩

are significantly entangled,27,28 so that the above-mentioned D+−π−A− picture should, at best, be mitigated. For instance, apart from the shortest (and therefore least interesting) push− pull compounds, the effective CT distance, that is, the Cartesian norm of the vector linking the two barycenters, is significantly smaller than the separation between the two electro-active groups.27 Very recently, we have demonstrated that using partial atomic charges to perform the same task is less satisfying than relying on the total electronic densities, although potential-derived models (e.g., Merz−Kollman) could restore most qualitative features.28 Despite its generality, our CT model has a limit: the qualities of the obtained parameters are dependent on the accuracy of the selected densities. Here, as we treat a very large number of molecules (more than 100), these densities should be obtained at a theoretical level that is both computationally affordable and chemically sound. We have therefore chosen Time-Dependent Density Functional Theory (TD-DFT) which stands as the most popular ab initio approach to determine the optical properties of both organic and inorganic compounds. 29−34 TD-DFT is an exact theory,29,30 but, as all DFT methods, its practical applications require the selection of an exchange-correlation functional which concentrates the physical approximations of TD-DFT. Fortunately, CT excited states have attracted a lot of attention in the TD-DFT community during the last 10 years, so that there are no doubts on how to select meaningful functionals. Indeed, it is well-known that CT states cannot be adequately modeled by most traditional hybrids (nor, for sure, pure functionals) that tend to severely underestimate the transition energies of these states.35−37 This is due to the shortsightedness of global hybrids: the electron and the hole do not “see” each other, leading to a biased description. To solve this difficulty, range-separated hybrids (RSHs), originally proposed by Savin 15 years ago,38 are methods of choice. In RSH, the Hartree−Fock like exchange (HFE) ratio increases with the distance between two electrons, so that more HFE is injected in large charge-separation situations. As, on the one hand, the HF exchange is by definition exact (in the limits of the selected basis set and of a single-determinant wave function) and as, on the other hand, the (dynamic) correlation between two very distant electrons is tending to zero, RSHs provide a very consistent description of CT phenomena.36,39 In particular, during previous TD-DFT benchmarks, it has been found that CAM-B3LYP36,40−42 and ωB97X-D43−45 are probably the best available compromises: they provide an accurate evolution of the excited-state properties for increasingly long chains while not significantly deteriorating the absolute accuracy of TD-DFT wavelengths.

and similarly for ρ (r). Subsequently, the amount of charge transferred simply becomes qCT =

∫ ρ+(r)dr

(3)

a value that could of course be defined from ρ−(r). One next computes the barycenters corresponding to the ρ+(r) and ρ−(r) functions r + = (x + , y+ , z+) = r − = (x− , y− , z −) =

1 qCT

∫ rρ+(r)dr

1 qCT

∫ rρ−(r)dr

(4)

(5)

The distance separating these two points is the charge transfer distance d CT = |r + − r −|

(6)

whereas the norm of variation of dipole moment between the ground and excited states is || μCT || = d CTqCT

(7)

a value that is equal to the difference of dipoles computed from the total GS and ES densities. To quantify the spread of the charge on the D and A groups, one can calculate the rootmean-square deviation (rms), e.g., for the positive component along the x axis σ +x =

1 qCT

∫ ρ+(r)(x − x+)2 dr

(8)

and similarly for other terms. For the rod-like systems treated here, the CT predominantly occurs along the longitudinal (x) axis, and one can define an H index H=

σ +x + σ −x 2

(9) CT

H can be compared to d to determine if there is a significant overlap between the electron-donating and electron-accepting regions.27 The interested reader will find a comparison between this CT index and the related Tozer’s Λ36 in our seminal methodological contribution.27 Codes for computing the CT parameters are available on our Web sites.27,28

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COMPUTATIONAL DETAILS All DFT and TD-DFT calculations have been performed with Gaussian09.46 To determine the optimal GS structural parameters, we have used the PBE0 functional and the 6311G(d,p) atomic basis set, a combination known to provide suitable geometries for most organic compounds.47,48 The optimized structures correspond to a residual mean square force below the 1 × 10−5 au threshold (tight criterion). As we (predominantly) investigate CT states, we have used a RSH and a diffuse atomic basis set to compute the electronic densities of the GS and ES states. More precisely, all values reported in this manuscript have been computed with the CAM-B3LYP/6-311++G(d,p) method.40 The CAM-B3LYP functional generally provides accurate estimates for the transition energies of CT states.34,36,42,49,50 Therefore, we will

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METHODS CT Parameters. The procedure allowing us to define from the GS and ES densities the CT distance (dCT), transferred charge (qCT), and dipole (μCT) is described in refs 27 and 28. Let us briefly summarize the methodology herein. First one computes the difference of densities between the excited and ground states Δρ(r) = ρ ES (r) − ρGS (r)

(2)

−

(1)

Subsequently, one splits this function into two parts according to the increase/decrease of the density resulting from the electronic transition. In the first case, one defines 11947



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Scheme 1. Representation of the Oligomeric Systems

wavelength of maximal absorption (λmax) first increases rapidly with chain length and then saturates, as expected. Unsurprisingly, the smoother selenophene bridge (O5), that is expected to have the smallest gap, yields the largest λmax (ca. 520 nm for long chains). Irrespective of the nature of the linker, both the CT distance and CT charge increase for small chains, reach a maximum at intermediate chain length, and start to decrease for elongated compounds. This behavior is easily understandable: when the spacer becomes longer, one first improves the delocalizability of the central chain by adding π-electrons which allows more efficient CT. However, in long oligomers, the terminal groups are “dissolved” in the total system, and the excitation becomes a local process typical of the nonsubstituted (and symmetric) chain. This phenomenom is well illustrated in Figure 2 for the stilbene systems: in the trimer, the CT character is marked with clear zones of loss and gain on the dimethylamino and nitro moieties, respectively. In the hexamer, the majority of the density variations is located on the central unit, but the nitro group still plays a small role. Eventually, in the nonamer the variations are almost completely symmetric and exclusively located at the center of the molecule: the push− pull groups have a trifling impact on the first optical transition. Interestingly, the same kind of dromedary-back curves were predicted for the evolution of the first hyperpolarizability per unit cell of push−pull chains,62−64 a property that also depends on the balance between asymmetry and delocalization. Of course, the optimal oligomer length depends on the nature of the central connector (see below and Figure 1), but it could also be tuned by using different terminal groups. Among all tested α,ω-NMe2,NO2-chains, the maximum CT is obtained for the tetramer of O1 that allows us to transfer 0.8 e− over 6.0 Å. These parameters are significantly higher than their stilbene (O2) or thiophene (O4) counterparts, underscoring that increasing the π-conjugation does not systematically imply enlarging the electron−hole separation. Of course, the phenylene chains require a 322 nm (3.85 eV) wavelength to produce a 6.0 Å CT, whereas in O4 a 4.7 Å CT is reached with a ca. 460 nm (2.70 eV) input light, such that in terms of energetic yield (Å-per-eV) the thiophene remains more efficient. In addition, O4 absorbs light in a region that is much more suitable for most practical applications. Stilbene segments provide a valuable CT distance, but the position of the optimum qCT does not match to the maximal dCT, a clear drawback. With that respect, phenylacetylene chains, O3, are significantly superior and are additionnally characterized by slowly decreasing dCT and qCT when chain length increases, a

not perform individual comparisons between experimental and theoretical absorption wavelength in the following. We redirect the reader to previous TD-DFT benchmarks for an assessment of the accuracy of CAM-B3LYP and other functionals.34,36,41,42,51−53 In the vast majority of cases, the first excited state is strongly dipole-allowed and was considered for our calculations. Except for the smallest chains, this state encompasses a complex orbital contribution, well beyond the crude HOMO−LUMO picture, so that just considering these two frontier orbitals would not provide a balanced account of the electronic phenomena. To obtain a better description, one should investigate the total densities (as here) or use natural transition orbitals (NTOs).54−57 Except when noted, all simulations have been performed in the gas phase. When specified, the solvent effects have been considered within the polarizable continuum model (PCM)58 in its linear-response (LR) nonequilibrium approximation.59 Note that the LR model is only a first approximation of solvent effects, and more refined (but costly) approaches exist, such as Improta’s state-specific (SS) model,60,61 which provides a more accurate description of the polarization of the cavity at the excited state. For the monomer, dimer, and trimer of O1, we have tested the SSPCM model, and it turned out that the LR-PCM scheme overestimates the transition energies of the dimer and the trimer (the values being essentially equal for the monomer). The same is true for dCT; the SS-PCM values are 2.34, 4.26, and 6.32 Å, whereas the LR-PCM distances are 2.72, 4.76, and 6.54 Å. In fact, the SS dCT are systematically in between the LR and gas-phase values for the three considered oligomers: the LRPCM CT distances should be viewed as higher limits. In the following, the iso-contour used to represent the Δρ(r) plots is 0.0004 au.

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RESULTS AND DISCUSSSION

To allow straightforward comparisons between the different molecules, we have performed separate variations of the donor and accepting groups as well as of the central spacer. The reference moieties are NMe2, NO2, and (oligo)thiophene, for the donor, acceptor, and spacer, respectively. Push−Pull Oligomers. A series of α,ω-NMe2,NO2-systems differing only by the spacer have been modeled and are sketched in Scheme 1. Tables collecting all key numerical data for these ten oligomeric series may be found in the Supporting Information, whereas graphical representations of the evolution with oligomer length of the different properties are given in Figure 1. Except for the p-phenylene chains, the longest 11948



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Figure 1. Evolution of the main parameters for increasingly long chains. Top: the vertical transition wavelength (nm). Center: amount of transferred charge (e−). Bottom: charge transfer distance (Å).

Figure 2. Representation of the difference between excited- and ground-state densities (red, density increase upon transition; blue, density decrease) as well as the CT distance (in green) for the trimer, hexamer, and nonamer of α,ω-NMe2,NO2-stilbene (O2). 11949



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Figure 3. Representation of the impact of solvent for increasingly long O1 and O4 chains. Left: CT distance in Å. Right: CT charge in e−.

Scheme 2. Representation of the Push−Pull Pentathiophene Chains

clear-cut advantage if one is interested in designing long systems. Indeed, for the decamer of O3, our procedure foresees

a CT of 5.0 Å, whereas the corresponding thiophene decamer value is 2.9 Å; however, this is related to a more energetic 11950



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in Supporting Information), the λmax is in the 340−350 nm domain independently of the oligomeric size, and the maximal CT is reached for the dimers (24 π electrons in the central bridge) with dCT of 5.5 and 5.2 Å and qCT of 0.7 and 0.7 e−, for O9 and O10, respectively. For two series, namely, O1 and O4, we have also investigated the impact of solvent effects (acetonitrile). The numerical data can be found in the Supporting Information, whereas a graphical comparison between gas and condensed phase results is given in Figure 3. Obviously, the presence of a polar environment improves the CT: the maximal dCT increases by ca. 1.6 Å, whereas qCT is enhanced by about 10%. In the same time, the related transition energies decrease. These trends were expected: the ES is relatively more stabilized by the dielectric environment than the less polar GS, and the medium allows the stabilization of stronger electron−hole separations. However, it is worth noting that both the general shape of the curves and the optimal oligomeric lengths remain almost unaffected by the solvent. As the relative performances of both phenylene and thiophene linkers are also conserved, calculations in the gas phase may be used to compare all the compounds. Donor and Acceptor Groups. To investigate the impact of the terminal groups, we have used several electron-donating and electron-withdrawing groups using a constant central πconjugated bridge, namely, a pentathiophene segment (see Scheme 2). This connector has been selected because of its widespread use in organic chemistry65,66 and its length that maximizes the CT distance (see above). The optical features and the CT data of all derivatives are listed in Table 1. All seven donors yield virtually the same absorption wavelength (440− 460 nm), but it is noticeable that di- and triphenyl amino groups significantly boost the transition probability. The transferred efficiency remains close to half an electron, irrespective of the donor. The dimethylamino group is indeed efficient: it provides a stronger (qCT), longer (dCT), and tighter (H) transfer than the corresponding di-/triphenyl amino systems. This conclusion fits previous joint experimental/ theory assessments performed on smaller push−pull chains.2 These latter groups do not outperform significantly the simple methoxy donor within the selected architecture. Interestingly, the fact that OMe and N(Ph)2 are poorer donors than NH2 and NMe2 fits Hammett’s σp ordering.67 Indeed, the two former present σp values of −0.27 and −0.22, respectively, whereas the two latter have σp of −0.66 and −0.83, respectively. However, the correlation remains very qualitative; e.g., NHMe’s σp (−0.70) seems to indicate a dCT closer to the amino than from the dimethylamino donor, a prediction negated by ab initio estimates. The result might also be understood from the densities: for all these molecules the density variations are closer to the nitro group (see Figure 4), and consequently the nature of the donor group is not essential. Indeed, the electron goes from the bridge to the electron-withdrawing group. One should be careful as this conclusion could differ with shorter spacers. Indeed, for the monomer and trimer of D7, we foresee qCT of 0.74 e− and 0.62 e− and dCT of 3.82 and 4.57 Å, respectively. This implies stronger CT than in the corresponding dimethylamino chains that are characterized by qCT of 0.49 e− and 0.61 e− and dCT of 1.70 and 3.70 Å, respectively (see Supporting Information). In the same vein, if one removes the NO2 acceptor from D3 and D5, one localizes the CT on the donor group. Subsequently, dCT is much more dependent on the nature of this group as theory, respectively, yields 1.08 and

Table 1. Computed Transition Wavelengths (nm) and Oscillator Strength for the Compounds of Scheme 2a structure

λ

f

qCT

dCT

H

D1 D2 D3 D4 D5 D6 D7 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 A16 A17 A18 A19 A20 A21

447 457 458 447 441 450 453 436 458 439 429 474 450 447 443 481 464 454 467 505 495 527 488 461 712 445 532 505

1.69 1.71 1.75 1.96 1.68 2.32 2.35 1.82 1.75 1.80 1.69 2.10 2.18 2.21 2.16 2.10 2.11 2.19 2.16 2.41 2.05 2.18 2.40 1.93 0.74 2.19 1.44 1.28

0.55 0.58 0.58 0.55 0.55 0.54 0.55 0.50 0.58 0.52 0.50 0.50 0.53 0.50 0.63 0.59 0.56 0.52 0.56 0.62 0.62 0.68 0.58 0.54 0.56 0.48 0.74 0.59

4.29 4.63 4.71 4.08 4.05 4.03 4.33 3.32 4.71 3.58 3.05 3.21 3.95 3.55 5.54 4.88 4.43 3.60 4.25 4.93 5.23 5.54 4.67 3.92 3.80 2.48 6.13 3.12

5.50 5.73 5.88 6.29 5.47 6.75 7.02 5.41 5.88 5.36 5.10 5.96 6.44 6.29 6.76 6.25 6.22 6.27 6.38 6.63 6.24 6.60 6.56 6.55 5.50 6.04 6.52 5.62

q is in e−, dCT and H are in Å. All values have been obtained at the CAM-B3LYP/6-311++G(d,p)//PBE0/6-311G(d,p) level.

a CT

Figure 4. Density variation plot for D7 and CT distance (in green).

Figure 5. Density variation plot for A20 and CT distance (in green).

transition in O3 than in O4. The behavior of all five member rings is similar to the one of thiophene, but for two exceptions: namely, the maxima is reached for a smaller number of unit cells in bithiophene chains, and push−pull pyrrole oligomers behave like phenylacetylene with a strong qCT and an almost constant dCT from n = 5 to 10. However, this success is again at the cost of a larger energy required to induce the CT. For the 9,9′-dimethyl-fluorene and the 9-methyl-carbazole push−pull series (O9 and O10, not represented in Figure 1 but available 11951



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Scheme 3. Representation Systems with a Varying Central Spacer

Twenty-one different acceptors have been tested, including classical groups (A3−A8), typical pulling moieties used in DSSC dyes (A9−A13) or in cyanines (A14 and A15), as well as more “modern” structures based on benzodithiazole or related compounds (A17 to A20). The results are listed in Table 1. As for the donor, the dCT ranking qualitatively follows Hammett’s parameters for classical groups; e.g., σp equals 0.78 and 0.45 for the acceptors of A2 and A167 that, respectively, present a dCT of 4.71 and 3.32 Å. However, using Hammett’s scale remains ineffective as no quantitatively valuable correlation could be obtained due to several mismatchs between the dCT and the σp scales. Interestingly, one also notices no obvious relationship between the transition wavelengths/probabilities and the CT character; e.g., for A14 theory predicts a 712 nm absorption and a quite poor CT, whereas similar CT parameters have been computed for A4 that absorbs at 429 nm. Likewise, A7 and A8 present almost identical optical features but CT distances differing by 2.0 Å. Therefore, there is room for separately optimizing the transition energy (e.g., to locate it close to 550 nm, which corresponds to the maximal intensity of the solar spectra) and the CT efficiency. It turns out that the nitro group is significantly more effective than its cyano counterpart, whereas the carboxylic acid and perfluoromethyl attractors have comparable effects. To improve above the simple nitro group,

Table 2. Computed Transition Wavelengths (nm) and Oscillator Strength for the Compounds of Scheme 3a structure

λ

f

qCT

dCT

H

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12

458 412 410 481 448 586 706 695 466 418 430 448

1.75 1.99 1.91 2.18 2.31 1.63 1.93 1.77 1.79 1.67 1.61 1.55

0.58 0.58 0.59 0.61 0.56 0.44 0.46 0.49 0.63 0.59 0.60 0.61

4.71 4.79 4.82 4.86 5.00 3.48 2.91 3.30 5.09 4.86 4.07 3.81

5.88 7.11 6.93 6.47 7.17 5.50 5.10 5.08 5.87 5.88 5.43 4.98

q is in e−, dCT and H are in Å. All values have been obtained at the CAM-B3LYP/6-311++G(d,p)//PBE0/6-311G(d,p) level.

a CT

2.13 Å. Nevertheless, results in Table 1 illustrate that increasing the size and potential strength of the donor does not systematically allow taking the inner track to maximal CT, a well-optimized balance between the three parts of the molecules has to be found. 11952



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Figure 6. Density variation plot for C7 (left) and C9 (right) and CT distancse (in green).

rings and the same dimethylamino/nitro end groups) . For N = 1, 3, and 5, we obtain transition wavelengths of 389 nm (f = 0.74), 454 nm (f = 2.36), and 460 nm ( f = 4.44), respectively. The corresponding qCT are 0.76, 0.55, and 0.53 e−, whereas the dCT reach 0.74, 5.09, and 4.35 Å. Therefore, such a copolymer strategy does not represent a significant improvement over C9.

one should go for multicyano structures (A8, A14, and A15 all show a dCT larger than 5 Å), whereas the pyridinium is not such an impressive attractor once its counterion has been accounted for. The classical DSSC attractor-anchoring group is unsurprisingly efficient with a qCT of 0.6 e− and a dCT of nearly 5 Å. The other anchoring groups that have been recently proposed17 induce shorter CT. The benzodithiazole unit (A17) does not outclass a single cyano group. Overall, the dithiazole−cyano combination (A20) seems the most effective: it induces a CT of 0.7 e− over 6.13 Å. The difference density plot for this compound might be found in Figure 5, and it is obvious that the regions of density increase/decrease are better separated than in previous examples. Nevertheless, we emphasize that, even in that case, dCT remains much smaller than the distance separating the two terminal groups (ca. 19 Å). Of course, A20 could not be used as a DSSC anchoring group, and we have therefore tested an extra acceptor group in which the CN group of A20 has been replaced by the A9 acceptor. In this way, we obtain a λmax of 576 nm ( f = 1.51), a qCT of 0.7 e−, and a dCT of 6.19 Å. Therefore, such types of molecules may be worth the synthetic effort, as the structure presents both a very large CT character and absorbs light in the most intense region of the solar spectra. Additional Connector. We have also tested the impact of replacing the central thiophene rings by another π-conjugated group, a popular procedure, notably to include secondary acceptors or to improve the delocalizability of the chain; see ref 18. The molecules that have been modeled are represented in Scheme 3, and the main results can be found in Table 2. Three units, namely, the diketopyrrolopyrrole (C6), the benzodifuranone (C7), and benzodipyrrolidone (C8) groups, strongly modify the λmax. All other connectors, including fluorene and carbazole, yield variations limited to ±40 nm, though C4 and C5 allow us to improve the transition probability significantly, which is comparable to the bithiophene effect (see Supporting Information). The only two connectors that allow dCT to go beyond the 5.0 Å threshold are C5 and C9, though the improvements remain limited compared to the standard pentathiophene (dCT of 4.7 Å for C1). If C6−C8 decreases the transition energy, this is at the prize of degraded CT features: qCT decreases by 0.1 e−, and dCT shortens by ca. 1.5 Å. C7 and C9 are compared in Figure 6. It is obvious that benzodifuranone snatches the excited state and acts as the electron-withdrawing group, which consequently deteriorates the CT. This behavior is consistent with the very stable LUMO of these dyes.26 On the contrary, C9 allows a better charge separation with electron depletion/gain zones mainly located at the left/right of the connector (close to the donor/acceptor). As the C9 bridge was found to be the most efficient in terms of improving the CT distance, we have investigated oligomers of the alternating copolymer based on thiophene and benzotriazole, considering structures ranging from the monomer to the pentamer (that is five thiophene and benzotriazole

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CONCLUSIONS AND OUTLOOK Using range-separated hybrids, we have simulated the electronic densities of both the ground and excited states of a large panel of rod-like compounds constituted of one electrondonating and one electron-withdrawing group, separated by a π-conjugated linker. On that basis, we have determined charge transfer parameters, notably the amount of CT charge and the corresponding effective CT distance, in a consistent way. It turned out that there is not a systematic relationship between the transition energy and the CT data. In α,ω-NMe2,NO2 oligomers, the maximal CT is obtained for typical oligomeric length of 3−5 connecting rings, shorter systems being limited by the lack of delocalization and longer rods being ineffective as the push−pull groups cannot significantly influence the absorption typical of the unsubstituted oligomers. Among all acceptors, the strongest are the NO2, the multicyano groups, or the dithiazole-cyano pattern. In that case, one can induce a CT exceeding 5 Å in a push−pull pentathiophene. However, the electron is extracted from the bridge to the electron withdrawer, so that the strength of the donor is not essential. This fact further underlines the crucial role played by the spacer which is often and erroneously considered as an inactive fragment in push−pull dyes. In this context, we have tested a series of central connecting units, and it appeared that one should very carefully select them, so that they do not limit the CT by trapping the electron. In short, there is a systematic fine balance between the three elements of the rod-like compounds, and simply increasing the strength of the terminal electro-active groups or improving the delocalizability by adding more π-electrons in the bridge does not necessarily implies improvements of the CT properties. As the effective CT distance is much shorter than the separation between the two capping moieties, the use of adequate theoretical models is helpful, if not necessary, to design more efficient dyes. It is our hope that the present work will stimulate more investigations in that line of research.

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ASSOCIATED CONTENT

S Supporting Information *

Computed optical transitions and CT parameters for oligomeric systems. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 11953



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Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS 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, respectively. This research used resources of the (1) GENCI-CINES/IDRIS (Grants c2011085117 and c2012085117), (2) the CCIPL (Centre de Calcul Intensif des Pays de Loire), and (3) a local Troy cluster acquired thanks to the help of the Région des Pays de la Loire. The authors are indebted to the COST program CODECS and its members for support and many helpful discussions, respectively.

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